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RGNTtëEPORT

We regret that some of the pages in the microfiche copy of this report may not be up to the proper legibility standards, even though the best possible copy was used for preparing the master fiche.

RCN- 203

NUCLEAR PHYSICS WITH THERMAL AND RESONANCE ENERGY NEUTRONS

Proceedings of a symposium

held at Petten, May 22-25, 1973.

RCN does not assume any liability with

respect to the use of, or for damages

resulting from the use of any information,

apparatus, method or process disclosed

in this document.

Petten, December 1973.

-3-

Nuclear physics with thermal and resonance energy neutrons, proceedings

of a symposium held at Petten, May 22-25, 1973.

Reactor Centrum Nederland. 1973, December. 370 pp, 93 fig., 42 tab.

These proceedings contain the contributions of the fourth symposium that

was organized in the frame of the tripartite agreement between the USSR

State Committee for the Utilization of Atomic Energy> the Belgian

Commissariat for Nuclear Energy and Reactor Centrum Nederland. Papers

were contributed in four sessions: neutron capture y-ray spectroscopy,

neutron induced fission, neutron resonance reactions, and experiments

with oriented nuclei. Contributions have been made by groups from the

following institutes: ITEP (Moscow), Kurchatov (Moscow), Dubna, CBNM

(Geel), SCK/CEN (Mol), the universities of Gent and Leuven, the F0M-*RCN

group (Petten), RCN (Petten), and the state universities of Utrecht and

Groningen.

In an introductory lecture a discussion is presented of the set of

propositions on which strong arguments for spin and parity assignments

are based as formulated by the Nuclear Data Group.

In the present proceedings five contributions are in Russian language

(preceded by an abstract in English) and 23 contributions in English are

presented.

Keywords:

|p. 14| A = 21 - 44 NUCLEI |p-

BRANCHING RATIO

DATA

ENERGY-LEVEL TRANSITIONS

ENERGY LEVELS

FT VALUE

PARITY

SPIN 'P'

STRENGTH FUNCTIONS

20| ENERGY-LEVEL TRANSITIONS

NEUTRON BEAMS

P INVARIANCE

POLARIZED BEAMS

T INVARIANCE

WEAK INTERACTIONS

57 j DATA

ENERGY-LEVEL TRANSITIONS

-4-

GAMMA SPECTRA

NUCLEAR STRUCTURE

ROTATIONAL STATES

lp-TANTALUM 182 '

CAPTURE

GAMMA RADIATION

INTERFERENCE

NEUTRON BEAMS

SPIN

SPIN ORIENTATION

THERMAL NEUTRONS 'P'

CORRELATIONS

ENERGY-LEVEL TRANSITIONS

GAMMA RADIATION

IRON 57

IRON 58

NEUTRON BEAMS

NUCLEAR REACTIONS

Q-VALUE

SPIN ORIENTATION

THERMAL NEUTRONS

ALPHA PARTICLES |p.

CERIUM 140

ENERGY-LEVEL TRANSITIONS

GAMMA RADIATION

NEODYMIUM 143

NEUTRON BEAMS

NEUTRON SEPARATION ENERGY

NUCLEAR REACTIONS

R MATRIX

IP-FISSION

FISSION FRAGMENTS

GAMMA RADIATION

MASS

NEUTRONS

PLUTONIUM 239

RESONANCE

100| FISSION

FISSION NEUTRONS

MULTIPLICATION FACTORS

PLUTONIUM 239

RESONANCE

STRUTINSKY THEORY

URANIUM 235

1 131 CAPTURE

DATA

ELASTIC SCATTERING

GAMMA RADIATION

LEVEL WIDTH.

NEUTRON BEAMS

NEUTRONS

NUCLEAR REACTIONS

PARTICLE WIDTH

PLUTONIUM 242

PLUTONIUM 243

TOTAL CROSS SECTIONS

135| COMPARATIVE EVALUATIONS

FISSION FRAGMENTS

KINETIC ENERGY

PLUTONIUM 239

PLUTONIUM 240

SPONTANEOUS FISSION

THERMAL FISSION

THERMAL NEUTRONS

147| EV RANGE

FISSION YIELD

NEUTRON BEAMS

PLUTONIUM 239

TERNARY FISSION

TIME-OF-FLIGHT METHOD

-5-

169 j CAPTURE

FISSION ISOMERS

NEUTRON BEAMS

NUCLEAR REACTIONS

URANIUM 235

172| COUPLING

ENERGY LEVELS

FISSION

LEVEL WIDTH

NEPTUNIUM 238

NUCLEAR MODELS

PORTER-THOMAS DISTRIBUTION

PLUTONIUM 243

STRUTINSKY THEORY

194| CROSS SECTIONS

ENERGY LEVELS

LEVEL WIDTHS

NEUTRONS

P WAVES

RESONANCE

S WAVES

SHELL MODELS

219| DATA

LEVEL WIDTHS

NEODYMIUM 143

NEUTRONS

RESONANCE

STRENGTH FUNCTIONS

TRANSMISSION

226| CROSS SECTIONS

DATA

ENERGY LEVELS

FAST NEUTRONS

FISSION PRODUCTS

HAUSER-FESHBACH THEORY

MEV RANGE 01-10

PALLADIUM 107

PARITY

SPIN

| p. 2421 CADMIUM HI

CADMIUM 113

DYSPROSIUM 16!

DYSPROSIUM 163

ENERGY LEVELS

GADOLINIUM 157

LEVEL WIDTHS

SPIN

STRENGTH FUNCTIONS

|p. 254J ENERGY LEVELS

LEVEL WIDTHS

SAMARIUM 147

SAMARIUM 149

SPIN

STRENGTH FUNCTIONS

|p. 269| CAPTURE

CROSS SECTIONS

IRIDIUM 191

IRIDIUM 193

LEVEL WIDTHS

NEUTRON BEAMS

RESONANCE

TIME-OF-FLIGHT METHOD

|p. 279| CAPTURE

CROSS SECTIONS

ENERGY LEVELS

LEVEL WIDTHS

S WAVES

SLOW NEUTRONS

STRENGTH FUNCTIONS

URANIUM 236

-6-

[p. 2891 CAPTURE

COMPARATIVE EVALUATIONS

ENERGY LEVELS

GAMMA RADIATION

NUCLEAR REACTIONS

POLARIZED BEAMS

SILICON 29

SILICON 30

STRIPPING

THERMAL NEUTRONS

|P- 298| ANGULAR CORRELATION

CAPTURE

ENERGY LEVELS

GAMMA RADIATION

NUCLEAR REACTIONS

POLARIZED BEAMS

POTASSIUM 39

POTASSIUM 40

THERMAL NEUTRONS

|p. 314| BEAM OPTICS

COLLIMATORS

FOCUSING

HFR REACTOR

MODERATORS

POLARIZED BEAMS

REFLECTION

THERMAL COLUMNS

THERMAL NEUTRONS

jp. 319j ANGULAR CORRELATION

CAPTURE

CRYOGENICS

ENERGY LEVELS

GAMMA RADIATION

ORIENTED NUCLEI

POLARIZED BEAMS

SLOW NEUTRONS

SPIN

I p. 3331 CAPTURE

LITHIUM 8

NUCLEAR MAGNETIC RESONANCE

POLARIZED BEAMS

POLARIZED TARGETS

THERMAL NEUTRONS

[p. 358| ORIENTED NUCLEI

POLARIZED BEAMS

RESONANCE

SPIN

THERMAL NEUTRONS

TRANSMISSION

URANIUM 235

|p. 365) CAPTURE

ERBIUM 168

EXCITED STATES

NEUTRONS

NUCLEAR MAGNETIC MOMENTS

ORIENTED NUCLEI

TIME-OF-FLIGHT METHOD

TRANSMISSION

- 7 -

L I S T O F C O N T E N T S

Page

PREFACE by J . A , Goedkoop И

LIST OF PARTICIPANTS 12

P.M. E n d t :

PROPERTIES OF NUCLEI IN THE A = 21-44 REGION. 14

Session on neutron capture y-ray spectroscopy (to be continued on page 289)

P.A. Krupchitsky: SEARCH FOR SPATIAL PARITY NON-CONSERVATION AND TIME INVERSION VIOLATION IN NUCLEAR INTERACTIONS WITH POLARIZED NEUTRONS. 20

J.M. Van den Cruyce, et al.: ROTATIONAL STRUCTURE OF THE DOUBLY ODD DEFORMED 182Ta NUCLEUS. 57

K. Abrahams, J. Kopecky and F. Stecher-Rasmussen: CHANNEL SPIN INTERFERENCE AND POTENTIAL CAPTURE OF NEUTRONS. 69

J. Kopecky, K. Abrahams and F. Stecher-Rasmussen: THE 57Fe(n,Y)58Fe REACTION. 75

W.I. Furmati, et al. : AN ESTIMATE OF THE HINDRANCE FACTORS FOR Y~TRANSITIONS NEAR THE NEUTRON BINDING ENERGY FROM THE FRACTION 1 4 3 N d ( n , Y c O l t t 0 C e . 89

Session_gn neutron induced fission

P.H.M. Van Assche, et al.r THE MASS DISTRIBUTION OF NEUTRON-INDUCED FISSION FOR 239Pu AT THE 0.297 eV RESONANCE. 95

-8-

Page

J.P. Theobald, et al.: NEUTRON MULTIPLICITY MEASUREMENTS ON RESOLVED FISSION RESONANCES OF 2 3 5U AND 233Pu. 100

F. Poortmans, et al.: NEUTRON CROSS SECTIONS FOR 2lt2Pu BELOW I keV. 113

G, Wegener-Penning and A.J. Deruytter: COMPARISON OF THE THERMAL NEUTRON INDUCED FISSION OF 2 39p u AND THE SPONTANEOUS FISSION OF 240Pu. '35

С Wagemans and A.J. Deruytter: TERNARY TO BINARY FISSION RATIO FOR NEUTRON INDUCED FISSION IN 239Pu IN THE ENERGY REGION 0.02 eV - SO eV. 147

G.A. Otroschenko and P.E. Vorotnikov: ON THE FISSION ISOMER YIELD IN THE REACTION 2 3 5U + n. 169

R, Werz, et al.: ESTIMATION OF RESONANCE PARAMETERS OF CLASS II LEVELS USING THE MAXIMUM LIKELIHOOD METHOD. 172

Session^ on neutron jresgnmee reactions

H. Weigraann and G. Rohr: SYSTEMATICS OF TOTAL RADIATIVE WIDTHS OF NEUTRON RESONANCES. 194

H. Ceulemans: ANALYSIS OF NEUTRON RESONANCES IN 143Nd. 219

H. Gruppelaar: NEED OF NUCLEAR LEVEL SCHEMES FOR CALCULATED CROSS SECTIONS OF FISSION PRODUCT NUCLEI. 226

E.N. Karzhavina, Kira Sek Su and A.B. Popov: SPINS OF n i' 1 1 3Cd, 157Gd, 161*163Dy NEUTRON RESONANCES. 242

- 9 -

Page

E.N. Karzhavina, Kim Sek Su and A.B. Popov*.

SPINS OF 11+7Sm AND l l t9Sm NEUTRON RESONANCES. 254

L. Lason, e t a l . :

NEUTRON RESONANCES OF IRIDIUM ISOTOPES. 269

L. Mewissen, et al.: CROSS SECTION MEASUREMENTS OF 2 3 6U BELOW 2 keV. 279

F. Corvi and M. Stefanon: ESTIMATE OF THE RATIO R - ff(3)/F (4) FOR 235U(n,f). 286

Session on neutron capture у-гац spectroscopy

(continned) and experiments with oriented nuclei

A.M.J. Spits: THE REACTION 29Si(n,Y)30Si. 289

A.M.F. Op den Kamp: CIRCULAR POLARIZATION AND Y~Y ANGULAR CORRELATION MEASUREMENTS IN THE 39K(n,y)lt0K REACTION 298

F. Stecher-Rasmussen: ON A SYSTEM OF MODERATING NEUTRON MIRRORS TO PRODUCE AN INTENSE BEAM OF POLARIZED THERMAL NEUTRONS. 314

H. Postma: A REVIEW OF NUCLEAR ORIENTATION TECHNIQUES APPLIED IN EXPERIMENTS

WITH LOW-ENERGY NEUTRONS. 319

Session on experiments with oriented nuclei

A.D. Gulko, e t a l . :

NUCLEAR MAGNETIC RESONANCE OF SHORT-LIVING ^-ACTIVE NUCLEI FORMED BY CAPTURE OF POLARIZED NEUTRONS. 333

-10-

Fage

E.R. Reddingius, et al.: SPINS OF LOW ENERGY NEUTRON RESONANCES ОГ 2 3 5U. 358

V.P. Alfimsnkov, et al.: MAGNETIC MOMENTS OF 168Er STATES EXCITED BY NEUTRON CAPTURE. 365

-II-

PREFACE

In March 1965 an agreement was signed in Moscow by representatives of the

USSR State Committee for the Utilization of Atomic Energy, the Belgian

Commissariat for Nuclear Energy and Reactor Centrum Nederland about co­

operation on peaceful applications of nuclear energy. The agreement com­

prises the exchange of group visits of specialists, the exchange of

individual research scientists for longer periods and the organization of

joint tripartite symposia.

The first of such symposia was held at Petten, the Netherlands, in

December 1967, on "Statistical methods in experimental reactor kinetics

and related techniques". The second symposium was organized at Melekess,

USSR, in February 1970 on "Fast reactor physics". The third symposium was

held in Brussels, Belgium, on "Safety measures in nuclear research". The

proceedings of each of these symposia have been published by the organizing

institution.

The present volume contains the contributions of the fourth symposium

that was organized in the frame of the tripartite agreement. The

symposium took place again at Petten, the Netherlands, in May 1973. This

time the subject was "Nuclear physics with thermal and resonance energy

neutrons". Of the participants 5 were from the Soviet Union, 15 from

Belgium and 15 from the Netherlands.

The symposium languages were Russian and English with consecutive trans­

lation. In the present proceedings each contribution is reproduced from

the best available copy. Those papers that are written in Russian are

preceded by an abstract in English.

J.A. Goedkoop Managing Director for Research

Reactor Centrum Nederland

- 1 2 -

L I S T O F P A R T I C I P A N T S

UNION OF SOVIET SOCIALIST REPUBLICS

A.D. Gulko

V . I . Pe l echov

G.A. Otroschenko

E.I. Sharapov

A,B. Popov

Institute of Theoretical and Experimental Physics, Moscow.

Institute of Atomic Energy of I.V. Kurtchatov, Moscow.

Institute of Atomic Energy of I.V. Kurtchatov, Moscow.

Joint Institute of Nuclear Studies, Dubna.

Joint Institute of Nuclear Studies, Dubna.

BELGIUM

G. Carraro

H. Ceulemans

C. Coceva

F. Corvi

A.J. Deruytter

W.L. Mewissen,

M. Nève de Mëvergnies

F. Poortmans

J.P. Theobald

P. Van Assche

J.M. Van den Cruyce

C. Wagemans

Central Bureau for Nuclear Measurements, Geel,

Nuclear Research Centre, SCK/CEN, Mol.

Central Bureau for Nuclear Measurements, Geel.

Central Bureau for Nuclear Measurements, Geel.

Central Bureau for Nuclear Measurements, Geel.

Nuclear Research Centre, SCK/CEN, Mol.

Nuclear Research Centre, SCK/CEN, Mol.

Nuclear Research Centre, SCK/CEN, Mol.

Central Bureau for Nuclear Measurements, Geel.

Nuclear Research Centre, SCK/CEN, Mol,

University of Leuven.

University of Gent and Nuclear Research Centre, SCK/CEN, Mol.

Mrs. G. Wegener-Penning University of Gent and Nuclear Research Centre, SCK/CEN, Mol.

-13-

H. Weigmann

R. Verz

Central Bureau for Nuclear Measurements, Heel.

Central Bureau for Nuclear Measurements, Geel.

THE_METHEEMNDS

K. Abrahams

G. Aupers

J. de Boer

J.J. Bosman

M. Bustraan

P.M. Endt

J.A. Goedkoop

H. Gruppelaar

W. Kraak

J. Kopecky

A.M.F. Op den Kamp

H. Postraa

E.R. Reddingius

A.M.J. Spits

F. Stecher-Rasmussen

FOM-RCN Nuclear Structure Group, Petten (N-H).

FOM-RCN Nuclear Structure Group, Petten (N-H).

FOM-RCN Nuclear Structure Group, Petten (N-H),

FOM-RCN Nuclear Structure Group, Petten (N-H),

Reactor Centrum Nederland, Petten (N-H).

State University of Utrecht.

Reactor Centrum Nederland, Petten (N-H).

Reactor Centrum Nederland, Petten (N-H).

Reactor Centrum Nederland, Petten (N-H).

FOM-RCN Nuclear Structure Group, Petten (N-H),

FOM-RCN Nuclear Structure Group, Petten (N-H),

State University of Groningen.

FOM-RCN Nuclear Structure Group, Petten (N-H),

FOM-RCN Nuclear Structure Group, Petten (N-H)

FOM-RCN Nuclear Structure Group, Petten (N-H)

At RCN nuclear physics research is carried out in a coordinated programme with the Foundation of Fundamental Research on Matter (FOM). The collabor­ators in the FOM-RCN Nuclear Structure Group are employed by either FOM, RCN or one of the universities in the country.

ЪпЬетртеЬет

Т. de Graaf.

AcbrtLnistFattve seovetapy

Miss M. Struijf.

- 1 4 -

PROPER.TIES OF №CLEI IN THE A = 21-44 REGION

P.M. Endt

Fysisch Laboratorium der Rijksuniversiteitл Utrecht^ Netherlands

Abstrac t

A recent review on. the A = 21-44 nucle i has provided copious mate r i a l for the s t a t i s t i c a l eva lua t ion of e . g . y- and B - t r a n s i t i o n p r o b a b i l i t i e s . This ( a . o . ) leads to a d iscuss ion of the s e t of p ropos i t ions on which s t rong arguments for sp in and p a r i t y assignments are based as formulated by the Nuclear Data Group. In p a r t i c u l a r the inf luence of i s o b a r i c spin is e labora ted .

1. Introduction

Recently, the manuscript has been completed of a new review paper | l | on the A =• 21-44 n u c l e i . I t i s about of the same s i z e and scope as a preceding review (2J (which covered the Z = 11-21 r e g i o n ) , and supersedes the l a t t e r . Some innovations a re t h a t the signs of mixing r a t i o s were a l l reduced to the same sign convention, tha t of Rose and Brink | 3 J , and tha t a l l log f t values have been computed in two decimals (and have obtained an experimental e r r o r ) with the aid of recent t ab les of f -funct ions J 4 | .

2. Gamma-ray strengths

The review provides easy access to the input data (lifetimes, y-ray branchings and mixing ratios) for the calculation of у-хау strengths (in Weisskopf units). The calculations were limited to transitions between bound states, because one of the main purposes of collecting y^ay strengths was to investigate the influence of isobaric spin, and because evidently isospin purity will be high­er for bound states at low excitation energy and low density than for unbound states at high level density. Only transitions were taken for which the spin, parity and isospin of initial and final state were known unambiguously, and for which the strength had an experimental error of at most 50%.

The se t of "propos i t ions on which s t rong arguments are based", formulated by the Nuclear Data Proup (and published regu la r ly in Nuclear Data B), nas been accepted as a bas is for unambiguous J assignments. A general fea ture of the strong arguments i s tha t they are p r a c t i c a l l y model i n ­dependent. Particle-gamma and gamma-gamma angular c o r r e l a t i o n measurements ( i f analysed on the b a s i s of a 99.9% confidence l i m i t ) are good examples. Also i n e l a s t i c e l ec t ron s c a t t e r i n g and, in genera l , a l l measurements based on the well understood :veak i n t e r a c t i o n . All arguments based on e i t h e r the s h e l l model, the r o t a t i o n a l or the s t a t i s t i c a l model are considered as weak (and thus are not admi t t ed ) . Although c e r t a i n l y bandl ike s t r u c t u r e s occur in the A = 21-&Д reg ion , bands are too much mixed to accept them as a b a s i s for J'' ass ignments .

About 600 t r a n s i t i o n s conform to the c r i t e r i a mentioned above. I t i s shown in t ab le I how these are d i s t r i b u t e d according to charac ter (E or M), m u l t i p o l a r i t y and T-forbiddenness . The T-forbidden El and T-retarded Ml t r a n s i t i o n s occur i n se l f -con juga te nuc le i and obey the s e l e c t i o n ru le AT = 0.

About i sosp in r e t a r d a t i o n for E2 t r a n s i t i o n s (with ДТ = 1 in se l f -con juga te nuc le i ) l i t t l e i s known. In such t r a n s i t i o n s , the i s o s c a l e r con t r ibu t ion to the matr ix element, p ropor t iona l to e +e (where e and e are the e f f ec t ive

p n p n charges of the proton and the neut ron , r e spec t ive ly ) would be equal to ze ro . In a T-allowed E2 t r a n s i t i o n , t h i s c o n t r i b u t i o n would be expected to be la rge compared to the i sovec to r c o n t r i b u t i o n , p ropor t iona l to e - e . No such ДТ = 1 E2 t r a n s i t i o n in T = 0 n u c l e i are known, but one can get an

z estimate of the isovector contribution by comparing the strengths of mirror transitions in T = { doublets or T = 1 triplets. For 16 mirror pairs the retarded E2 strengths thus extracted are equal to zero within two times the experimental error (the actual values are all below 1 W.u); for one pair only (the lowest 1/2 ->5/2 transitions in 25Mg and 2 5A1), the extracted re­tarded E2 strength, 0.25 +_ 0.01 W.u., has a relatively small error. The same procedure has been applied to 14 pairs of Ml mirror transitions. The strengths in any particular group were used to derive strength upper limits which are necessary tools in nuclear spectroscopy. I want to em­phasize that the average strength in a particular group is not a useful quantity. With the increase in size of Ge(Li) detectors ever more weak transitions will be found, such that the average will decrease with time.

i

- 1 6 -

I t should a lso be remarked t h a t except iona l ly s t rong t r a n s i t i o n s i n a

given group should be regarded with susp ic ion . A good example i s the

9.83^0 MeV, }+-0+ , T = 0 0 Ml t r a n s i t i o n in 2t*Mg of 0.055 +_ 0.016 W.u. +

The upper l eve l i s s i t u a t e d a t a d i s t ance of only 140 keV from the 1 ,

T = 1, 9.97 MeV l e v e l , and i s thus in a l l p r o b a b i l i t y of low i sosp in

pu r i t y . The s t ronges t El t r a n s i t i o n s (both T-allowed and forbidden)

were found from (dubious) y-ray resonance f luorescence work. Checks

on t h e i r s t r eng ths e . g . by means of h i g h - r e s o l u t i o n i n e l a s t i c e l ec t ron

s c a t t e r i n g would be very d e s i r a b l e .

There i s no unambiguous way to der ive upper l im i t s from the s t r eng th

his tograms. I f s t a t i s t i c s are good enough, l ike for the allowed E l ' s

E2's and M i ' s , one can f i t the histogram with some s o r t of s u i t a b l e

function e . g . an asymmetric Gaussian. The upper l im i t then can be de­

fined as the s t r eng th which i s exceeded with 0.1% p r o b a b i l i t y . The a s ­

signment of upper l i m i t s to the groups with poor s t a t i s t i c s i s s t i l l

more a r b i t r a r y . Proposed upper l im i t s a re l i s t e d in t ab le 1.

I t i s evident tha t a coordinated search for r a r e t r a n s i t i o n s l i k e M2's

or T-re tarded E2 's would be highly rewarding. Needed are more accurate

l i f e t imes and branching r a t i o s , but e spec ia l ly more (and b e t t e r ) mixing

r a t i o s .

3. Beta-decay log f t values

There are about 200 be ta t r a n s i t i o n s in the A = 21-44 region for which

the f t value has an e r r o r of a t most 50%. Most of these have allowed

charac te r for which we w r i t e : f t ( s ) - 6080/(<F>2+1.39<GT>2), where

<F> and <GT> are the matr ix elements for the Fermi and the Gamow-Teller

c o n t r i b u t i o n s , r e s p e c t i v e l y .

Except ional ly f a s t a re the superallowed t r a n s i t i o n s between members of

i sosp in doublets (<F>2 = 1, log f t <3.78; 12 c a s e s ) , i sosp in t r i p l e t s

(<F>2 = 2, log f t <3.48j 14 c a s e s ) , and i sosp in quadruplets (<F>2 = 3 ,

log f t <3.31; 1 c a s e ) . The l a t t e r t r a n s i t i o n i s the 3 3Ar(S-) decay to

the 5.55 MeV T = 3/2 l e v e l i n 33C1 (ac tua l ly the 33Ar mass has not been

measured but i t can be ca lcu la ted with a high degree of confidence from

the quadra t i c i soba r i c mass equation based on the energies of the 3 3P

ground s t a t e and of the lowest T = 3/2 s t a t e s in 33S and 33C1) i t has log

f t = 3.35 + 0 .05 .

-17-

A special subgroup of the transitions between T = ] analogues is formed by those which proceed between 0 states- The additional condition <GT>2 = 0 leads to log ft = 3.48 (9 cases).

The log ft values of all 27 known superallowed transitions agree within the experimental error with the conditions given.

There are some other allowed (but not superallowed) transitions which + + are remarkably fast, Especially mentioned should be the 0 (T=l)->-l (T=0)

transitions; the record is held by the **2Ti(g ) decay to the 0.61 MeV level in 1+2Sc, with log ft = 3.17 +_ 0,12. The main configurations involved in the decay are (f7/2)0? in the initial and (f7/2^2in i n t h e f i n a l state; the two indices stand for J and T, respectively.

The unique first-forbidden ( Ы = 2) transitions form another interesting group (14 cases). The (considerable) spread in log ft values can be much reduced by calculating log f.t instead of log ft; see ref. [4|. The lowest log f.t value in this group is 9.14 +_ 0.07 and thus the values agree with the Nuclear Data rule that they should exceed 8.5. The application of this rule, which is too little known, has led to un­ambiguous J = 2 assignments to the ^°С1 and ^ K ground states.

-18-

References

|l| P.M. Endt and C. van der Leun, Nucl. Phys. to be published

|2j P.M. Endt and С- van der Leun, Nucl. Phys. A105 (1967) 1

|3| H.J. Rose and D.M. Brink, Revs. Mod. Phys. 39 (1967) 306

|4| N.B. Gove and M.J. Martin, Nuclear Data A_l£ (1971) 206

Table I Numbers and proposed upper l imits on the strenghts of Y~ray t rans i t ions

between bound s ta tes in the A = 21-44 region.

Type Number Upper limit

(W.u.) Type

Upper limit (W.u.)

E1(T-allowed) 14 0.02 Ml (T-allowed) 173 10

El(T-forbidden 33 0.002 Ml (T-retarded) 20+(14)* 0.02

E2(T-allowed) 268 100 M2 (T-allowed) 5 2

E2(T-retarded) (17)* 2 M3 1

E3 8 100

E4 1

Strengths calculated from pairs of mirror t r ans i t ions (see t ex t ) .

1

- 2 0 -

SEARCH FOR SPATIAL PARITY NON-CONSERVATION AND TIME INVERSION VIOLATION

IN NUCLEAR INTERACTIONS WITH POLARIZED NEUTRONS.

P.A. K r u p c h i t s k y (pape r p r e s e n t e d Ъу A.D. Gu lko) .

I n s t i t u t e of T h e o r e t i c a l and E x p e r i m e n t a l P h y s i c s , Moscow, USSR.

A b s t r a c t

The theory and experiments concerning search for spatial parity non-conservation and time invariance violations in nuclear y-transitions performed with the polarized neutron beams are reviewed. Theoretical estimates of the expected effects and the experiments classification are given. The experiments described are performed in the Institute for Theoretical and Experimental Physics (ITEP, Moscow) resulting in discovery of the weak nucleon-nucleon interaction non-conserving spatial parity. The ITEP experiments which set up the upper limit for the strength of T-non-invariant interaction are also described.

The results obtained in ITEP are compared with those obtained in other institutes.

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псл* КРУПЧЩКЙЯ

ПОКОКЙ НЕСОХРАЕЕШН ПРОСТРЛЕОГВЕШЮй ЧЕЛЮСТИ И КАРУПШШ ВРЕЖЭНОЙ ОБРАТИМОСТИ В ЯДЕРНЫХ В З А Ш 0 -ДЕИСТВШХ С ПОМОЩЬЮ ПОЛЯРИЗОВАННЫХ НЕЙТРОНОВ

I * В В Е Д Е Н И Е

В классической физике давно известна тесная связь кежку свойствами симметрии пространства и времени и законами сохра­нения. Однако вплоть до появления квантовой механики принци­пы симметрии были распространены не очень широко»

Принцип зеркальной симметрии и связанное с ним преобразо« ваиие инверсии пространственных координат приводит з квантовой механике ie закону сохранения пространственной четности (/"« четкости)* Инвариантность относительно инверсии пространствен^ них координат (/ -инвариантность) выражается в существовании у квантово-гглехашяеекой системы сохраняющегося квантового, чк-ела /*"" -четности, которое может • принимать значение +1 или ~ I* Введены также понятия ••временной инвариантности ('/^инвариант** ности) и зарядовой четности С (^««четноети)* Соответствующие законы сохранения вытекают из инвариантноетей относительно об~

n~f . ' '

ращения времени ( У ^инвариантности) и относительно замени частиц-'" на античастицы ( ^«-вгаарианткостд) о Связь мекду сля<-ном частиц и отатистшеой^которой пс?дч1ишотоя частицы9' требует инвариантности гамильтониана ьзаимодействия этих частиц о?-, иооителько произведения всех трех преобразование. Эта .тяорег.-а записываемся в ъто CPÏ---Ï и называется 0РТ~теоре?ло1и OHQ связывает гло ду собой три затеска сохранения GSV и Т~чеа^осте::

Долгое- время ЗФЗЭНЫ- сохранения четное тей считались yys~ зешальнагди для EÜSX элемеитарикх.физических процессов*

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Янг Б сгоей Нобелевской речи так характеризовал роль свойотз С1~.:::з?рпи: "Позвольте 1.ке подчеркнуть, что для физиков являлась шгучкд источником вдохновения идейная простота и внутренняя кра-сотз- сЕл;,1е-тр11Чгоонаругя1БаемоЙ в слояных экспериментах» Появля­лась кадсй-да» что природа таит в себе определенную упорядочен­ность, которую шзшо постигнуть"* Однако в 1956 году Ля и Янг flj пришли к выводу а том,; что в слабых взаимодействиях Р«четность не сохраняется* Там se было обращено внимание на то9 что в про« цессах, обусловленных ядерными сшгами? Р^четностъ может не со-хракяться» Степень несохранения Р~четности в ядерных силах ха«-растеризуется параметром Г.~ отношением потенциала, не сохраня­ющего четность, к потенциалу?- сохракявдему четность*

Вскоре после тогой как несохранение Р^етиосты в слабых взаимодействиях'было обнаруяено fzj ,. была высказана гипотеза об универсальной природе слабого взаимодействия и создана тео«~ рия универсального взаимодействия / з в &J « Эта универсальность проявляется Б ТОМ* ЧТО адронам и лептонаы присуще в одинаковой мере слабое взаимодействие. Благодаря этому и-.возникает меявук-лошшй потенциал, не сохранявдий Р*четностьо

Анализируя создавшееся положение, Ландау /б/обратил внжза*» нке на тоfЧТО несохранение только Р~четнссти приводил: к аенгл*-ушрт пространства относительно пространственной инверсии,; в то ърс:ля как известной что пространство полностью изотропно» Выход из этого Ландау нашел в прздполсаэнги^ что в слабых вза1&50-дейотш-ях наряду о несохракеш-к-гл Р^етнсстм не сохрншетоя и С-чекюстЬр ко TGKg что кх врсшзвгдешШл наззанкоз "комбшти-развитой -чекпеоты)" (СР-четксота),. сохраняется«

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Одпако у;::е в 1964 гв Кронпк и сотр» ƒ67 обнаружили а распадах Кр° - ыезонов несохранение СР ** четности* Б силу GPT-Угеореш. нарушение СР-инвариантностя означает нарушение •и Т--инвариантноети. Теоретический анализ показывает, что вза** шлодейетвие.ответственное за нарушение GP-лпвариапткости, по своей силе монет быть сверхслабым, слабым, электромагнитным и полусильвым (OM./7J )• В двух последних случаях несохра­нение GP-четпости может проявляться и в ядерных силах»

Таким образом; ядерные потенциалы согут быть неинвариак'. ными как относительно инверсии пространственных координат, так и относительно обращения времени» Осуществляются ли эти возможности в природе, мозно определить только в результате экспериментальной проверки»

Данный обзор посвящен экспершентам9 поставленным для выяснения вопроса о нарушении Р и Т^инвариантностей в ядер­ных «У^переходах;, выполненный на пучках поляризованных нейт*-ронов Института теоретической и экспериментальной физики (Москва), В разделе 2 обзора даются теоратяческие оценки ожидаемых эффектов и классификация экспериментов* В разде­ле Записываются эксперЕментк;приведшие к обнаружению слабо­го нуклон йз?1Угозного. взаимодействиЯв не сохраняющего Р^ет~ ностьэВ разделе 4 описываются • экспершенты^установкБИие версий предел вклада Ъ* неинвариантного взаимодействия-»

Ьзлее полный, но более ранний обзор теории и других экспериментов на эту же тему дан в работе / б /

2» TeorrjaTjgjrecKnG оценки эффектов и клаоо^асйдм, эксперн-дентов

Согласно ззикотезэ 'универсального' взаимодействуй гами-.

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// /JO f }~f гУ у".

/^-/{-/.У/, % / ; где./-- константа слабого взаимодействия, ,Т-ток слабого Бзашодсйстг.1;'т.г Вследствие перемнояениа тока

самого на себя возникают Г Ш К Л Ь Т О Ц П С Н Ы вида f где /.-.А •••'.'.. -волновся функция соответствующих

частиц, <Л£- известные чет-фехряддше матрицы* Гамильтониан Ну соответствует коктакткоглу взаимодействию нуклонов» а гамильтониан Но соответствует взаимодействию на конечном расстоянии»

Вашшм предположением рассматриваемой гипотезы является то» что СР-несохрагшющшли эффектами можно пренебречь» Де£ст« витально *• обнаруженные в распадах К°2 » мезонов несожрэлявдие СР^четность эффекты составляют всего лишь 2»10 от эффектов* сохраняющих СР^ четкость^

Гамильтониан H-j- рассматривался Майклом/э/ , Рассчитать соответствующую диаграмму нельзя, тек<* между всеми четырьмя нуклонами возможен обмен /Т^мезонагж. Можно лишь оценить по­рядок величины /'как отношения#v«-«мплитуды рассеяния нук~ лонов,; обусловленного слабым взаимодействием* к > *«зглпли~ туде рассеяния,, обусловленного сильным взаимодействием» Это отношение содеркат хюнотанту етЮ"^^ • , гдеД*. *-2соипто« новскея длина волны нуклона* Обезрашериваться это отноше­ние иокот лишь характеристической длиной снднгого взаиглодей-стиня* T»Ö* ксыптоновской длиной волны у/ -сезона А - ? Б резул* тате- / ' * / > V / V r V w / ^ / ; V V " -/<? •

Оценка /•" f щюязвтшенная Ея>ш-Стойлом /10/ для гакиль** токаагга Нр3 лр&годкт к той ж величине 10 * Неточность обоих оцотюз: герядЕЕ Ï0*

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Д'Ш обнаружения такой малой величины г необходимо вос­пользоваться кехаакзками усиления, которые возникают в ядрах* Рассматривая слабое взаимодействиеР как возглущение, моано по-каратьь что волновые функции определенного состояния /?систе« ш нуклгшов имеют вид:

ръ -fr + J*, (!) где £<f «мера амплитуды,- не сохраняющей четность»

Вшпшнсон / i f f разбил вое эксперименты на 2 больших класса: I) поиски нарушений абсолютных правил отбора £.П) поиски

наблюдаегжх псевдоскалярных величин* Эксперименты I класса имеют дело с эффектами, 1фопорщонэлъныш г , которые по это»-щ трудно обнаруЕШЫ* Эффекты в экспериментах П класса пропори цвональян г в силу того, что в них проявляется интерференция переходов из состояний с "нормальной" и "аномальной" четности-шх» Этот класс экспериментов разбивается на 2 подкласса; Па) измерение циркулярной поляризации >^*изяучения, вознкаодегс-при распаде неполяризованинх ядер и Ив) измерение асимметрии У" • излучения поляризованных ядер вперед-назад» В последнем слу«

=•*»*>•*> __

чае псевдоскалярной величиной является произведение D / - , — ч -—•» . ' t

где СГ поляризация ядра,- а А-.- нашульс ^чквантаь-. Вознгжанщце при использования ядерных *~«* переходов уси­

ления ксжяо согласно И»СЛ11апиро / Ï 2 / разбить на 3 вида: кипе-»' матшеокое; структурное и динашгсеское усиления» Для харак~

О терисяглт величин усияея^я вводится фактор усиления А г которой сяазнас&т величину сх о величиной / :

Княо^гпческое усиление возникает за счет использования в гачоств-з регч'дятяюго .У"«* перехода магнитного перехода //•••- „

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Тогда прпглесвш переходом является электрический переход/".^» Так как атлпдптудн магнитных переходов подавлены по сравнению с е?лилитудааш электрических перзходов на множитель I/I0» то А ^ Г 10.

Структурное усиление возникает; когда исследуемый ре<~ гуяярный переход подавлен из«за причин, связанных со струк­турой уровней, между которыми происходит переход*

Динамическое усиление возникает в СЛОЕНЫХ ядрах при большом возбуждении составного ядра за счет близости уровней с одинакоБыгл полным моментом,* но с противоположной четностью© Оценка динамического усиления;1 произведенная Блин-Стойлом / Ï3J и И*С*Шапиро /"I4J ; приводит к выражению:

Л. , & / ^ £ сз) где ut *• энергетический интервал, в котором особенно хорошо смешиваются состояния разной четности, £) -среднее расстоя­ние мезду уровнями в ядре*

2) Т~ нешшариантхше 'эффекты*

Сразу se.после опыта Кронпна-и сотр [~§J возник вопрос о том» какое взаимодействие ответственно за нарушение СР -~;ш~ вариантности к о возможном нарушении' СР«-январиантности в других процессах* В'нескольких работах/1М7Д была предложена гшо~ теза, о том» что взаимодействие^ ответственным за нарушение СР^швариаистооти, является адрон«-адронное взаимодействие9

/У Г)

сохраняющее странноет»/-> и пространственную четность /"' s

которое воего на несколько порядков слабое обычного сильного взйк?,гадс:]уств1и» Позтоцу это взаимодействие назшэают проио* яуточным сильным взаимодействием или милли-сильки-л взашодей-cjSïite;,-:» По Ж1яоощ}^:"1щя Л*Б50кукя / 7 / оно обозначается

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}{& (адрол^2дрокное, д£~0 t / ° =+I).

Другая гипотеза / l 8 / переносит кесохранение СР~четиости в адрон*фотонное взаимодействие, танке сохраняющее странность п пространственную четность* Это взаимодействие С £0 ) да своей силе монет быть таким »е, как и обычное электромагнитное взаимодействие.

Обе гипотезы предсказывают существование Т«неинваряантных амплитуд порядка 10 +10 от Т^инвариантных амплитуд как в ядерных силах» так и в электромагнитном излучении ядер*

Существуют еще и другие возможности. Среди них отлетим гшотозу сверхслабого взаимодействия адронов с адровамл с из­менением странности на 2 единицы и сохранением пространствен»* ной четности ( Х2' ) [щ9 Константа такого взаимодействия мо-жет иметь величину порядка 10 хч-10 ,• и поэтому ни в одном другом эксперименте, кроме как в экспериментах с Кнйезонамя," где происходит большое усиление эффекта нарушения СР-иквариант ности из-за близости масс Е?у и K?g - мезонов»наблюдаться на-* рушений СР«Ш1вар2аитности ка заметном уровне не будет,.

Велишяну несохракяюцих СР«четность (или Т-инвариаитность) сил принято характеризовать величиной /" -отношением временно-пешшардгнтной части потенциала к потенциалу сильных взаяко-ДСЙСТВИДв

Хопли / 8 J предложил ел едущую классификащш экспериментов по.исследованию Т-шзориантности:

I) Эксперименты, в которюс участвуют слабые взаимодействии; П) Эксперименты, в которых участвуют электромагнитные

взакшдекствия t Ш) Эксперта-нти по исследования поляризации в упругом

рассеянии ;

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IV) Эксперименты по детально^ равновесию в ядерных реакциях £

V) Исследование структуры ядера

Мы рассмотрим в дальнейшем только эксперименты с учес*» ТЕСЫ электромагнитных переходов в ядрах0

Б случае полкой инвариантности аярон*-вдрс1щого и адрсп-* фотонного взаимодействий по отношению к обращению времени фазы приведенных ядерных матричных элементов,- описывающих угловые корреляции последовательныхУ~*~ переходов» могут быть выбраны одинаковыми, а сами матричные элементы ~ дейст­вительными [щ* Сильное нарушение Т^январианткости адрок~ адропных ИЛИ адрокг-фотонных взаимодействий может проявить себя через эффекты высших порядков» как Т^еинвараактная примесь порядка 0,1 Ф 1% в амплитуде матричных элементов. к, следовательно; привести к появлению разности фаз матрич««*

>5#7- „ч „„о них элементов óy , отличной от 0 шпг-на вели-пшул-Ю -Я0 Yj

Возникающего разность фаз тотю обнаружить,- изучая интерес*-ренционине члены в смешанных . Jf~~ переходах» Б этом случае параметр смешивания:* т*е« огпоигэние приведенных глатрлчкхл; элементов r-елду ядерятзяи состояниями со спинами ^ и ,.-?

>~ MJ*? &/i*ijz^ O-^/ó/e {4)

является ко*шлекешм {а7и*{ *-:.?ультшюл5ностя излучения) Назшпю смешанного пврзхода необходимо9 так кшс только

в этом олуше возникает шгк'р^ерепцкодишй член. содср:;й::';;:!1 разность Ф'лз Afy „ Б случае чистого перехода штерф&рй»-щ онлый Ч-У&1 отсутствует^ тгк как интоыспвнесть иелучевп'з:

-29-опредеяяется швздрата-ли модулей матричных элементов,, Зкс« перлменты наиболее чувствительны к штерфэрежц-ш излучений разной иуяьитольностн.» если оба излучения икеют близкие амп­литуды, т.eв когда/èyti.

Хэклп и Якобсон /21/ разбили эксперименты с целью оп­ределения ,4/? на 2 класса: I) угловые корреляции» чувстви­тельные к ШйЬ • и) угловые корреляции;, чувствительные к -PA/j'J? , Опыты I класса мало чувствительны к А р » так как

они измеряют члены второго порядка ho A # „ Опыты П класса наиболее чувствительны к A h ; так как измеряются чле­ны с Si*Aft —At? tпропорциональные параметру /-? .

В экспериментах этого класса начальное состояние ядра должно быть поляризованным или выстроенным» Поляризация начального состояния кокет быть получека различными способа­ми* Практически используются три способа: I) поляризация с помощью / У « распада» 2) поляризация с по­мощью эффекта Heccöayqpa, 3) поляризация путем захвата по** лярнзованкого нейтрона»

3» Зкспйпплеитй по изменение Р^нешваркантннх эффектов' « r t l i O M A _ j * .• i •• i .mj j» n.iM И И Ч 1 il I i i • n . w J i H Hi I •" T" II i f I I I I I I I I I • I I ^ I I H M H • • gn i i • П H l i l i r h il ~ i I I I •

с noMOisx-fi) полягрхтзовапз-п г нейтронов» I ) г:.:бор ядра

Основные резульаты получены в экспериментах, в которых изморялаоь асхЕ.'-аетрия Л*~~ излучения с энергией 9Г04 Мэв после захвата, ядрами <>-±:/ поляризованных нейтронов*

- Б эксперименте этого типа используются два усиления •даленлческое i-r Ksricwa-WKecKOCe Для ядра/> ч*1 Мзв и/--20 .эв м потоку согласно (3) A^v ~* 10" / 1 4 / »

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Обций коэф&чцяепт усилен;:^ таким образом, равен

Зггловое распределение >*~«язлученш из ядра после зах-.-вата поляризованных нейтронов имеет вид;

1//ДУ-• d + / ; / # Ш б?, (5) где- /^ ^степень поляризации нейтронов» @~ угол иезду направлениями спинов нейтронов я импульсов Л~~ квантов»

Я i=2oi А -коэффициент асимметрии, А -спиновый коэффициенте Ядро кадмия является уникальным ядром для наблюдение:

искомого эффекта» Сечение захвата тепловых нейтронов кад~ мнем очень велико и обусловлено почти полностью резонансом при энергии 0» 178 а в изотопа ш ^ 3 со спином I» Переход с возбужденного состояния LCf на основное состояние Or является /'/«* переходом Г ^ О * , в этом случае А равно максимально возможной величине +1» Разность меяду энергиями двух саглых энергичных переходов .равна 0Р56 Мэв и позволяет разделить их вклады друг от друга (рисЛ)*

Для протяженных мишени и детектора >*~»*ваитов око** рость счета (\Г** квантов по направлению и против направлен­ная спинов нейтронов равна

$Т = C№t/ff± &a-&X (6) где Si- &S О _ геометрический коэффициент«,

Эксперимент подобного типа впервые был произведен в 1953 г» ЭдеЯрогл и сотр* /22'J * Их результат клесте с ре-?ультата:лй ноеледуищлх экспериментов пркзеден в таблице I*

В 1934 году в 1-5ТЭЗ (СССР) был закопчен эксперимент^ сблщ^ив^'ш ипетткз неоохрэленне Р*четности в ядерных си-

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S2 /Л° Впсследствие эксперимент на С±г' был повторен в ШШ дважды /24,25/ f так как другие группы не обнаружи­вали в этой не реакции эффектов асишетрни ( ^ излучения па поляризованных нейтронах /26-28 ƒ ,

Мы опишем коротко эксперименты ИТЗЗ, а затем произведем сравнительный анализ ьсех экспериментов*

2) Описание акспершентов ИТЗФ Во всех трех экспериментах пучки поляризованных нейтро­

нов получались на горизонтальном канале реактора ИТЭФ пу<-* тем отражения от намагниченных кобальтовых зеркал (см.книгу /2Sj )• В нервом эксперименте /23J это было одно зеркало

длиной 1,5 ыг а в следящих двух была применена система ЕЗ 10 слегка сходящихся зеркал длиной по 1»05 м каждое, Цучок поляризованных нейтронов,проходя через ряд коллиматоров и шгнптопроводов, падал на мишень из кадмия толщиной 0Р4 ш * Схеиа нейтронного тракта приведена на рио«2« Выходящие из. мишени ƒ " - кванты регистрировались двумя идентичными сндпти.*-ляционныгяи спектрометрами с кристаллами A'u-s (•'(-/ диамет­ром 70 и толщиной 100 Ш: Вся установка отделена от зала реактора толстой бетонной стеной. Рассеянные на мишени ней** троны поглощались либо слоем прессованного углекислого ли-* тая, обогащенного Ы./ , .либо слоем прессованного карбида 6opaft Алюминиевые фильтры толщшой 85 мгл защищали детекторы от кнгких £" -квантов» Фотоэлектронные умножители вместе с кристаллами защшцалксъ от вяпякия магнитных полей кескодыШ-ми экранами из стали и пермалоя и закрывались слое?л свища толщиной 60 к-л» Шпульсн с фотоумнояк-хелой анЕяизкровал::аъ по амплитуде и поступали через коммутатор на пересчетнпе czts'A

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Окка д^Т-фэрепъ^алъншс анализаторов Б каэдогл спектрометре устанавливались^ таге, чтобн регистрировались У~~ кванта в энер­гетическом 1штервале 8,5-9,5 Мэв, соответствующие основное переходу &# • Для этого в течеш::- всего эксперимента ежед­

невно производилась калиброкка спектрометров по пикам в спект« ре >^ « излучения из реакции /"<? / 4 / / ' с ЕЛИ ИЗ реак--НИИ /Г/ / / ?<ƒ / - " ' ,

Большое в/Дшние было уделено устранению наложений кмпулъ~ coBt которые могли привести к появлению в исследуемой облает л энергий вмпульсов от У~«квантов меньших энергий» что привез­ло бы к уменьшению эффекта. Импульсы снимались с последнего дикода фотоумножителя и формировались так» что лх длительность составляла 0Я25 шесек. Использовались пороговые дискрЕишато-рн ка туннельных диодах, управляющие линейными пропусксаощЕМИ схемами*, Кроме того для уменьшения общей загрузки кристаллов пришлось уменьшить обдучаег-лую площадь мишени с помощью диафраг­мирования пучка нейтронов в 3 раза, так что интенсивность пучка не превосходила ГО нейт^сек» Электроника установки от опыт^ к опыту совершенствовалась так,, что, как правило, все элемента ее замедлись ка новые» Еяск^ехема электроники третьего опыта, привод сна «а рис&3.

Глгзиая трудность подобкого эксперимента состоит в кокл»-' ч&нни ксстабильксоти работы аппаратуры и в полной исхжнен'ли

fivTfl* IIT^'T;'•J<'irï'ur.7? 7ПГГГ F i T m V s W ^ '•.••.ТРГШГЧЛ ПО*"МТЧ. .

T! 'iV","iv~."|f" mr T " , f f > T!T)rt''il"'T'"\1ÏT'',,.tnr'T- |<^"г,>7>Т.ЛА р г А 1 м т а и ч р •r.\f"'".ViO»j4jif4Tï

-vi> fi.-\yf{ïv •c> ,ji ,\p'i:jTï ,ï", ' Iff ТГГ->'ПЛ-/СГ|'»*,!'''*Л'!Э*31'ЕТ";,'>*-'' ] ! o { t a w i •;*."- ТГт ГГ t*"ïV"L'T'~i Wfl

*"7:"f«7ï *.".' •""-•-•iTiAtTOTl ï":-'"i"'''^**fï1"-i*ï!'i" pT\t"«t^»'' ,itlï*:"''«W !V"'Tr''ViTC!'v4n-i-j<-Sftv>T-i "я •. v'Tyret

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круга} два протпвополо;:зшх квадранта которого зазгриты желез* кой фольгой* а два оставлены открытыми* Пучок нейтронов 20 раз в сек оказывался перекрытие фольгой, п е . полностью де~ поляризованным. Электронный кошутатор направлял шпульсы с анализаторов в соответствующие пересчетпые схемы. Для исклю­чения приборной асимметрии опыт проводили с двумя противополож­ными направлениями спинов нейтронов.- Изменение направления спинов осуществлялось с помощью поворотного магнита один раз в 20 ш н й Кроме того' проводился эксперимент, в котором весь цикл измерения каадые 40 шн> повторялся при полностью депо«-ляризованном пучке* Для этого на пути пучка нейтронов ставилась на весь цикл вторая с-(постоянная) деполяризующая железная фоль­га.

Во втором и третьем опытах проводилось быстрое сравнение эффектов для двух протдЕОПОлогашх направлений С Ш Ш О Е 0 ДЛЯ ЭТОГО 10 раз в сек. менялось направление тока в поворотном магните* Во всех трех экспериментах синхронно с переключением направленияГв поворотном магните включался или выключался ток в фольге с током или в проволочном экране, стоящем на пути нейтронов /soj * Это устройство для неадиоатпческого переворот та спинов необходимо для того, чтобы менять направление спинов нейтронов, не кеняя направления магнитного поля в районе ми-шенир и тем са-лиял ИСКЛЮЧИТЬ влияние переключения поля на фо« тоуикозЕтели. В качество контрольного эксперимента з этом случае слуэаял эксперимент на деполяризованном пучкеf который пронизодшся через шпщдо 20 цжзут» Вое зтл эксперименты опре­деляли Ескскр> aüias«!i8Tpjf.3, вызваидун шлзкческшяи эффектами и П р Е Й О р Н у Ю aCll'.-s?\lSTpiS)p

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Далее во всех трех опытах было цроделано большое число дсхюлнцтеяьшх контрольных экспериментов* К числу таких зкепе-рл^ептоз прг^адлеялт эксперимент на поляризованных нейронах с /V рдаохрзцаей jp* кюантов и/ в другом интервале" энергий^ где зффгктоз быть не дол;зо кзг-за того» что в J-ГОТ интервал вно­сят вклад т.зого переходов,' дающих асимйзтрз» разных знаков, Б первом опыте этет интервал был 4 Д -3-5j 5 Мэв, во втором опыте •* 6f8*7#8 M S B я оба эксперимента ставились в промежутках меаду основными экспериментами»

Б третьем ?ке опыте этот эксперимент в интервале энергий ^-квантов 6^3 ~8а5 Мзв шел' параллельно с основными экспери­ментами за счет некоторого усложнения амплитудных анализаторов*

Ставились контрольные эксперименты с ядрамиj в которых эффектов бнтв не.ДОЛЕНО t- это эксперименты с мишенями из са~ марш» титака* свинца и графита* Эксперименты с титаном и свин­цом проверяют' отсутствие чувствительности установки к циркуляр»-ной поляризэщгй Х~~ квантов» так как циркулярная поляризация выбранных квантов равна циркулярной поляризации Х~*~ квантов (if'' с F =ф&4Мзвв

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в наием случае указанный член для лдс-глзяои гос™а?р:£н равен кулю* ко отличие реальной геометрии от цяеолънои MOEGT при­вести к его появясшпсь

Контрольный эксперимент проводится в такой георлетрплв что член &~/J£x£r I максимален»

Ежедневно производилась проверка правильной работы кощутаторов и перзечетных охемр Для этого ДцЗ входы обоих коммутаторов подавали сигнал от одного из каналов и требовали

Г"

одинаковости показаний пересчетннх схем с точностью 10 9

Результаты ЕССХ контрольных экспериментов позволяют утверждать г что наблюдаемый в основных экспериментах эффект асимметрия обязан своим происхождение! угловой асимметрий

i7" «квантов и'- с энергией 9г04 гаэв». вылетающих пос« л с захвата поляризованных нейтронов,,

3) Результаты экспетжмеитов и сравнение их В первом опять ШЬЪ бил 'получен результат /237 ;

# =-(3,7+ О ^ У Л С Г 4 (7) В этом-результате учтена приборная, асклглетрия т»к© в него включенл результаты на деподазризовактоа пучко* Во втором опы­те ИГЭФ был- получен коэффициент на полярпзовашкш пучке; „„(3 5-'-0 3 U 0 ~ ^ и^ Дсп<^рйзоваь2кВ"'1^кЁ:\._

^ ^ ( O o T ^ S b ï C T 4

Так как тшборпая еоимкетрпя. была к:г&юрака с той но точностью-, что и эффект*а звакнасшй^трин одазаднев рас:^,;м3 то в окон­чательном результате ш учли лишь G«:.at-'fey иймс-рсиия прдоорпой 4;СНМ1?!ет;о!:;Я5,прсд(Стаяиз ого в виде: £7 ^(З^Д-ё/ДО""*"* /24/..

-36-Есугм se произвести процедуру аналогичную ток,что производится E других опита:-:, т«еФ вычесть приборную асиьэлетрпю щ эффектов на поляризованном пучке, то коэффициент асимметрии окажется равным:

Q =-(4,2 + I^.ICT4. С8)

Наконец, в третьем опыте ИТЗФ ни имеем /"SöJ :

# =~(255 + О^ЛО"4 . (9)

Среднее взвелязнное всех трех опытов ИТЭФ получается равным: ^ = ~ ( з ^ + о.бЭдо"4 . ( 1 0 )

Таким образом, результаты ИТЭФ по исследованию асегшетрии ƒ " г- квантов в реакции ffl/fyfJ й ? / 1 1 4 с несомненностью

указывают ка кесохраненяе пространственной четкости в электро­магнитном переходе 1-*о+ с энергией 9»04 Мэв в ядре (2/~^-\

Однако, как ш указывали ужф,в'годобныкаеперимеЕтах доугих институтов, не оо'нару~>:.<шг эффекта. Сводка всех результатов Б хронологическом порядке представлена в таол* Iv

Таблица. I Результаты экспериментов по измерению асимметрии

ƒ" «получения О/ ^ - с анергией 9t04 Мэв после захвата поляризованных нейтронов*

' f Институт Год интервал знеюгни ! Козйфшшент ,, ч.г

^«i;i;s:rroByf.feB j асаы»йОтряк^е>\л*1лс,>ах.У1? IfevravfecH (CïïïA) ТУ59 I 8,3^9,3 „ \ htr* (СССР) тг;54 ! 8,5^.6 А ' P.i:c-ö .(•;а:е-я) li>3? ; ^.8»->9,5 1Ж;> (ССОР) Ш 8 ! Öft5-9;5 )0.:р~тсруэ ('СИ') Ï---Ö9 : 8:X"0s6 ï . j -v "' (üCUP) .ПГ<'2 П,5~2,Б

l 1,2*7*8 ! 22 ;• и. зтъ-о-э ) 23 | ~ 2г5^;:.У

24 : Я7

X 5 ;>.> г' Л ч i .' : £8 25

x) Л г ' ^^г^сажг^эй работе OSIHO'O':::TO указал интервал энергий

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При взгляде на таблицу I бросается в глаза, что эффект близок к нуль1) в тех работах, в которых начало интервала энзргий Jfa квантов близко к 8,0 Изв» И здесь, очевидно, леяит объяснение отсутствия эффекта в этих работах. Дело в том, что в этот рас­ширенный интервал: попадают >^кванты с энергией 8:48 Мэв, со­ответствующие переходу с верхнего уровня 1+ на первое возбуж­денное состояние 2\ Этот переход такие является Щ~ перехо­дом (возмозша примесь Е2), Следовательно, нерегулярным переходом является такяе EI- переход, как" и в случае- основного перехода с энергией 9,04 Мэв*

Однако спиновый коэффициент для перехода с Е=8,48 Мэв равен А=~0,5 (для чистого ГЯ~перехода), T«es противоположен по знаку спиновому коэффициенту перехода с Е=;9,04 Мэв, который p:v-вен А=+1« Интенс леность более"мягкого пе£>ехода в 2 раза больше о Зти два. перехода дают асимметрию противоположных знаков* Если не прпглть мэр для хорошего энергетического разделения обоих

пйрахо/дов»то измеренная асимметрия, естественно будет занижена* -Это и произошло в работах[ZÜ и./28 J ••

В выбрашшй в работах ЙТЗФ интервал энергий 8е5^9,5 Мэв при разрешении кристаллов /ад^йорядка 1Z% также попадают j r ~ квактн перехода с энергией 8,48 Мзв, что закинает аекзшетриюв Ши оцештБаем вклад от этого перехода равным ~15&» Кроме того фон, обуоиозленный калойенияш импульсов от ^--квантов с энергиями меншкли 8Р5 Шъ,, ш фон яоелгорешиа .^квантов тагс.~о уменьшат)!? acm^orpim* Вклад обоих источников фона оценивается ~Ъ%*

Поправка па занийоипе асимметрии кожст быть в портом приол»-й:еюк5 Hai&sna,спетая, что 20$ в общей интекелкюсти рег;:-с трпрус •&££/-* квантов является- фоном, не вносящим вклада в

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ео:г.Сметр:гзСучст Eas;:r:::rio;i пр::.:оси ES в переходе с Е=8,48 Mo в cn:i::r.eT асii-'i^Tp:^)»Тогда пс тяглая аии.х-ютрйя найдется по фор-тлулс <Й„- - Ct/ft-fi).

/

Полагая /? =0*2Г получим г. качество ИСТИННОГО среднего з;;г.-:ик;и ког'Тфпшепта ас:ззметр"И дуй ошпюв ИТсо;

^ г = " С4Д + 0Г8) •1<Г4 (12) Зто значение следует сравнить со значением циркулярной поля­ризации /г ^-квантов с энергией больше 8 Мэв в той Ее ре­акция О/ fft{<fj &Р/ , на неполяризовапвых нейтронах, недавно измеренной в работе / з Д *

Зто опит класса Па по поиску псездоскшшрнше величин типа Of Д,- f рде 6^. -полпризацля ƒ" нквакта,

Величина циркулярной поляризации для ЧИСТЫХ переходов определяется формулой

/? *2PF (13) л отличается от величины коэй&ищиента асшдиетрии (7-2 кг'/? отсутствием мнояителя /и

Как видно знак циркуляркой поляризации не зависит от спинового шопителя Л и для обоих переходов с Е=3»^8 ^§ Б я у' Е-:Э?04 Мев одинаков* Следовательно, Энергетическое разделение sTii'f переводов ив обязательно*

Шфлузяриая полярл5£тщ:я в работе/31/ оказалась рав:юй

fO^ „(6 + 1,5)* ICT4 (14) X) s:\jjj-~;i-~<. <-*- v-ч* !- i-^viv v1..'.'. *-.'•—• V J . J : « -*'..*.'.•.**•,'..>. X A J ^ / P f-'-it'-iv. V ^ . A : - ' - A U \ . : „ - / i-ч AVA

/ ~ —7

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•1* 3::снт;

I ) ктбог> метода поляр;:-пнии к ятъ^_

В IG62 году в га;лзй работе? /Вз7 било предложено для ис­следования временной инвариантности ядерных сил использовать полярлзовашшз нейтроны, а кглсшю, исследовать /~ нонвлзариаптщгю коррэ.тацшо :епда _ л

($£jf^*ï*&Js (15) возникающую Б сглелиаштом <^^-персходе8а поляризацию начального состояния О получата» путем облучения ядер поляризованны-ш нейтронакн (Кг и К> •* единичные векторы в направлении дм~ пульсов первого и второго ^^^квантов каскада)*

Работа [ 33 J возникла еще до обнаружения несохранения СР-четиооти в распадах 1С5 - мезонов и рассматривалась9 как пред­ложение экс11ср;а№кта, не имеющего шансов на обнаружение эф­фекта* После экспериментов Пронина и сотр«/б/ работа приоб­рела новое значение, как один кз способов исследования: проб-яетлн СР -нечетного взаимодействия ƒ 54J*

В работе /2 I J приведена в самом общем виде корреляцион­ная фушоцпя для двух каскадных Л^иквантоз,, испускаемых возбуя-ДОКГ-З-ЙЛ поляризовавши -ядром, В работе 7 33 J приведена формула уг^егой корр'жщ™!! для двух каскадных A'"- KBaiiTCBj когда пер­вый переход с^ошаппш:,, В работе Г .А* Лобова /357эта' формула p.iciTpooïpariViïa па боле© общий случайf когда оба ƒ""« перехода 5АШУ:;:)ТСЛ ci;.c-i:isniïuaïiv& Угловая / - пеш^артгантная корреляция отсутствуй:;-, ОСЛЕ 'ncpauit У" -переход каскада является ЧГ.СТЗЙЯ

С Of --0). Углевая корреляция J'""-квитов -даскадса вообще оисут-сткуот, гол;: ошш /л промежуточного ссотошшя ядра равен 0 яшт л/.-'-п

- 4 0 -

Bn::3::;j вопрос о воогххллазти шлиташш нарушения T~misa-рг~:;7ност;т рлз-слч-"7-:;! гф^о::ч •:•:*:! облепа в!1ртуалкп1М] |~ квакха'.п: ::::зу i:s4S?iivr=r.ïs npo:.;c:::yio":i:~j к конечным СОСТОЯНИЯМИ бил рас­с о р е н з работе / 3 5 / о Результаты расчета показывают, что для 6;Х''1КЛИ[СТЕЗ 1.;Х и Ш га;.-: ла-пор сходов в реальных ядрах вклад, соуслоБдеыг-'й oCiiGEOi.! Ефтуйльныгли У'—квантами составляет

7 —Л Iö -J-I0 j. т«е» очень мая»

Предложенный эксперимент наталкивается на ту трудность^ что число и^тучепянх ядер со смешанным излучением после захвата нейтрона очень невелико о При этом параметр шекивания о дол-X'GÏI быть блгтзок к 1о До смешглкого перехода ДОЛЕНО происходить м.*"-:::л:ялькое (и известное) количество переходов с верхнего воз« бубонного уровня с темгчтобы поляризэуия начального состояния не была бл^ат-игн пулю0 Кроме того исследуемый каскад должок Ул'ътъ заветную ЕЯТСИСИБНОСТЬ И хорошо выделяться ^энергетически1*,

- 4 1 -

Залтгдха СУ n-:i '& эквивалентна изменена направления поллризс"-т::и. п^чг'пяюго состояния ядра на Г1ротиЕополо;~поз • Осуществляется ота операция измененном направления поляризации нейтронов ка противоположное.

Trivia, измеряя ка опыте асимметрию вылета двух гаьзла-квак--тов каскада * I / )

ГД<Э /" *?.В&. £*&<&& &*$ (то) можно определить величину и знак <р^ л?,

В paöoTCj/зз/ в качестве подходящего ядра было предложено ядро v' о Специально поставленные измерения /В?7 показали, что параметр смешивания первого перехода мал и равен ДГ=~0,1 и козффщиент 33=0 (016 мая* Поэтому измерения /~неинваршштной угловой корреляции двух гаша-квантов каскадае сопровождающего

гт* 48 захват кбдлетшьк поляризованных нейтронов ядром У/ ' , выпол-нглгныо КаЯфоиеа и сотр„ /ЗЗ/р дали недостаточно точний резуль­т а т : ^ , ^ = (!//+ 2,5) Л0~2Сем» таблицу И ) ,

Более подхо. лдш оказалось ядроCt ° <> Упрощенная схема уровнен и переходов в ядре CL * взятая из работы Гокзатко и сотр. /üö'j' s показана ка рис.4. Для этого ядра Е=09162»Экспе-гр' р:;глепт но исмерскна / -нешв&риантпой угловой корреляция

.Y".'-ïtEaïiïo:F. каскада 7*79 Мэв - 0*79 Мэв в ядре#' был выполнен '" ' . . . • . о

ЗДхлсро ; /40 [ г Шло получено значение РМ = (0,4£1,2) ДО""* Т:.:"с как точность прошденшх зкепоригх-нтов недостаточна

д-1Д nj4o;;opiU7 г:.:ттотсз о гаругопшт / '-^швар^нтности в адрон~ад~ роинш; л (гиги) о/фон-чЗотошзых взаимодействиях, в Ш'£3 били не» дазшо Гмиояислн ак^лок;чг;ш измерения issue l'* tf но на более, с^зтоеш^ной установке /41 f «

- 4 2 -

C*') ПУТrv-->fl-i •• ••• т ' л г - ' Т ' . " - • •• .-И-.-Ч-. T'fT"^.^ f~~AT ~" • ' — " • « u i i i i Г * i и Г i U

G:cc:.:a зкс::?.р;~.:гнта IITG-j показала на рис*5

Сколп.'ировашшй в горизонтальном канале тюкелоЕоднсго реак-тора пучок теплого-; нейтронов падал на полутораметровое на:лах'~ ипченное кобальтовое зеркалое Отраженный пучок поляризованных нейтронов проходил мезду полюсами электромагнита, определяющего направление поляризации, к далее падал па мишень. Для того ,что~ бы исключить деполяризации пучка, по пути от электромагнита до зеркала~анализатора вдоль тракторяи пучка создавалось ведущее спин постоянное магнитное поле,Поперечное сечение пучка на мд-шени составляло 10 х ЮОма* с интенсивностью 2*10 нейтр/ сек. Степень полпризацилй измеренная методом двойного отражения с использованием зеркала~анялязатора ь составила 0S83+ 0s0Xe Б качество шатки использовался порошок Cg&i в контейнера из топкой алюминиевой фольги с размерами 10x20x100 мм3» ДЛЯ умень­шения шопа от рассеянных нейтронов мишень со всех сторон, кроме

<-Р. 6 /°л одкой, сгружалась экраном я з ^ ( 1 ^ • Гйглт 'а-кваиты радиационного захвата нейтронов в $?ЩЛ№~ L-

гкстрзгровзлись четырьмя детекторагли/^^Й/^ 70x100 ш» распо­л о в и н и л в плоскости., перпендикулярной направлению поляризации пучкаг тзкнм оорзэоМб что средний угол между парой .детекторов составлю 45° ют:: X 35°/Поскольку фотоумнолтятели находились в о&г>з.стп раессшгаого шгпитпого поля, то они тщательно защи­щалась ?.;хр?.й'а1лП по мягкой стали и порлзлоя.

Клз;. о^тетяяооь гад;ю; измерение асимметрии вылета двух re;:-* ria-KmïïïöB интересующего э:г.с каскада означало измерение.-числа созя1Г1ДО?1.\-а- n^nyvLooB от дтух детекторов при дтзух значениях . углов- -Я и -'•-•' « чтоби IÏ'- усложнять установку^ детекторы

- 4 3 -

были смонтпрова-ш пеподвклшо, а замена угла é) на ~Q осущес--влялась реверсированием направления поляризации пучка нейтронов Реверсирование направления поляризация пучка нейтронов произво­дилось когда, секунду, поскольку зта операция одновременно поз­воляла усреднять вэзмо;:шне нестабильности аппаратуры d

Ка^дцй из детекторов гамма-квантов регистрировал как "мят-кую", так и "жесткую" компоненты каскада 7,79 Мэв - 0,79 Мэв, так что четыре детектора обеспечивали 8 комбинаций совпадений, т»е», с учетом реверсирования направления поляризации пучка нейтронов, 8 значений асимметрии, измеряемых одновременно.

Для регистрации восьми -комбинаций совпадений применялась многоканальная электронная аппаратура, блок-схема которой при­ведена па рис,6»

Разрешающее время схемы быстрые: совпадений равнялось

Участие каддого из детекторов в-двух парах комбинаций совпадений, дающих вклад в асимметрию с противоположным знаком, существенно смягчало требования к стабильности аппаратуры» что очень вэзно в условиях довольно большой загрузки фотоумножи­телей /2Л0 ямп/сек/. С целью' исключить возмогшую приборную асимметрию каддие сутки производилось переключение, полярности кошлутзтора ТЕКК*Я ооразегд* что. приборная асимметрия /обуслов­ленная неодппатюгои ч эффактивностъ-о регистрации событии кана­лами . электрогзпе-й аппаратуры, связанкиш с соответствующим напраяяекнем поляризации пучка нейтронов / оставалась неизмен­ной в тогда как физшесяоя асйЬй,«отр".*я долп:а сыла менять знак* Несколько раз в теченЕЗ окспер:-мс;]; а провожались спсцладыше пзмяронпя приборной аеггжзтрии. Для этого порог интегрального

-44-

д::о1ф:::.:илатора устанавливался таким образом, чтобн имели кэото совпадения гаыгла-квантов многих каскадов, а "окна" одиоканаяьнах анализаторов расширялись с тем,чтобы выделять из спектра совпадений пики от гамма-квантов с энергией от 0,5 Мэв до 1,3 ь'эво При это?л в основном регистрировались случайные совпадения к загрузка пересчетных схем была при­мерно на два порядка выше рабочей загрузки» Средневзвешен­ное значение коэффициента асимметрии оказалось равным ï <<? =5-(0е8+1,0)#Ю , в то .время как коэффициент приборной асимметрии Qh^r - (ОД+0,4) Д О • Формальный учет этой асимметрия приводит к значению для асим­метрии вылета двух гамма-квантов каскада в ядре (Ж :

О =(~0,9± 1 Д ) ЛО""4* (19)

Спецкапьно проведенное измерения показали, что пик совпадений от каскада 8,58 Мзв - 0,79 Мэв - 0 Мэв в среднем для ЕСer ВОСЬМИ кшбинацмй на 38^ обусловлен гамма-квантами с энергией 0,79 Мзз* ка 2Ъ% - вкладом от ближайшего каскада 845S Мэв -= 0 Мэв8 и на 34% - фоном случайных совпадений*

Срадне^взвапоиное значение коэффициента Б для этих трех компонент оказалось равным 35- 0,051. Тогда разность фаз пр;-:в-г:дешшх ым^ргииыл' элементов в смешанное электреглаг-питие;,; походе i^pa CC -°° с энергией 7,79 Мэв оказывает-

."•. : •> „ Г г о , <? о\ тл—3 С9-Л^ " f .

3 ) 0"0'?.I.'v"C7-"ivT: С .^УтТ^ ' - '* R ТСС USt) .'"'.*." HTati! И

Результату, яосх экспериментов i.i'o измерен;;*) 'Т*-немт-шзриаи-

«пш.х £^TV-:--:TO3 o ЙС'ГДОЩКО пелирлзоха^щх нейтронов привздени в

- 45 -

Таблща II Результаты экспериментов по нхх'реизз Т-пеивваштаптшх

S^JJOKTOB В ЛД0'0:ИIX У' '-ЛОЯехОДОХ'' С ПОМОЩЬЮ ПОЛЯрИЗОван— ЙЫХ ПСЦТрСЯОВ

Институт Год • Ялро •' Переход"** 1 \ Разность фаз1 Литер,

I 17+25

В£.р;:оруэ (ФРГ; 1068 ; (g 35 Москва,МТЗЗ ; !

(СССР) ÏS73 : ~'V-

[2

: -1,8+2,2

40

41

* S-napsi-летр смешивания Е2 Д11 . Из результатов» приведенных в таб* П, можно сделать

вывод что верхний предел для разности фаз приведенных матрич­ных элементов в смешанных "-переходах равен «(2+ 2) «10 *

Этот результат следует сравнить с результатами наиболее точшх измерений этой же разности фаз в других классах экс­периментов, использующих смешанное,^'- излучение* Наиболее точное измерение J^"~ корреляции из ядра /г '-1 (переход З ^ 24

с энергией 604 кэв и д -~2 su) s поляризованного шгзкотемлера-турким методом, дало S/h Л ft =(5+6)й10 /щ£

Измерения Т-нелшварлантной корреляции с использованием эффекта Мессбауэра дали; в ядре Ю{ (переход 3/2*->* 5/2+

с энергией 90 кэв и 5"=~1,64). . ^ ^ sCl.O+jr^.ICT® /Ц/ л 72 ядре J2 j 3 3 (переход 1/2"*-"' В/2+ с энергией 73 ко в и ö'-0f5G3 ) ЛЛ/} =(I ,I+ Э.ОЭ.КГ3 /44Z

Однако к резульягл^л раозт, использушщх мягкие J^KBaii" ты. следует подходив с осторожностью*, принимая во внимание posyjfbïa'm .работа /£5/* s кот-орэи показало, что разности пзз порядка Ю* ' 1ЛО!ут а-ои::пгать в результате в1гртуольшх'процесс•:•:•

- 4 6 -

Е-:1утр:.п::оЛ ;:о:л:;-рс-:и i::ir;:::x ( / -хтнтов на электронах атом-нюс оболочек*

5» З А К Л Ю Ч Е II И E

Пользуясь значение:.: коэффициента усиленшд^Ю для /С*/ ТТЛ • v „

LC{ и истинным среднлм значением коэффициента асимметрии

из опытов ИТЭй (12) получаем экспериментальную оценку тарамет-

ра />,;-" 2.10 • Этот результат находится в хорошем состоянии

с теоретическими оценками г- ff^-r 10 )•

Существование слабого нуклоЕ-нуклонного взаимодействия,

не сохраняющего пространственную четность, и оценка величины

р подтверждаются и другими экспериментами.

Большой йффэкт был наблюден в эксперименте / 4 б / по и з ­

мерению асимметрии Jf~ излучения ядер //f ,VJ , поляризованных

низкотемпературным методом (класо экспериментов Ив), Большое

количество экспериментов по измерению цлр^лярной. поляризацшх

ƒ""-излучения, возникающего при распаде неполяривоваиных ядер

(класс экспериментов Па), начиная с экспериментов Лобашова и

сотре /477 » также дают вполне достоверные- эффекты (см»

обзор/'8*/) • В последнее воемя найдена цшжулярная поляриза-

ция У"'-кваптоз в реакшш //•syb-?&rs^;'/4BJ о И» наконец, в клас­

се окспйр^детг^ов I таг:;::е найдено проявление слабого нуклон*-

путш^люго взг1-..:::одо!;стк;я / 4 9 / ч

Тазам- офа:;омЕ в шетоящео время существование слабого V U L V '.' • ï! V •5>"i--'-- '• ••-•.-•- '- ' JLJi.-i.i;;-. .4',! i. - . . i l b .L J..V :.'.L f / j . J / w ^ j . U . t u U ^ U i l J . ' . 4/ X.f.-.'.'.«.' J. L" <j\JJtX

об ул.г~з.'.срог :-'-.ой харргг^рй слабого взаимодействия й можно

VÏ-O као^'-^я >гарг7:-:'й1>тя-Т'»::ч'Пг>р11а51Т1Юощив то опиты по ....... ............. .»:- ... ,......,,.,......._. Л Г, >__.. ] Г.„ Т.., .v_.,.^r^,.Tï.T...-i ._ ƒ_ " _ r _ T n r T : r j . v , . . . , v

... __ v -v

я; -:о /.-'...х*: i"-i.v-;---.i----i Jïpt"j£^ д л я Т - 1"0^}1Бцр:-|Л.;^лГой чао:;:;: потзл'цг.тд,:

-47-

- ..'. 2.10' тл-З.

H;.ï одия из постагсюшшх эксперн&ентоз других классов,за поклтгчепясм распадов У? ««езоновэ такяе но о б в а р и т Т-аеия-* Dsp^TiiTiipx эффектов» причем какболее точные опыты определяют тот ;"0 иерхппл продел г й 2ЛСГ° (с:д»обзор /Sjf )«,. Вместо с отсутствием дхшолыюго момента у зхейтрона па уровне 5* 10 б;-

»см* [böj это ставит под сомнение справедливость гшготез о нарушении СР^инвариантности в адрон«*одрошюм или адрок^фотсн^ НОЙ взахллодействпяхо Гипотеза о карунюшш СР-инвариантности в сверхслабом взаимодействии / l 9 / имеет вое больше шансов на успех,,

ê р ^Ч"// >' о. - ; - j •<

SiTWX**»^

- 4 8 -

,/; ! • 'Г С V Cl У У р С,

/у .- •

I, ' "ГЛ^..\ '••г:;^ А :.( ./::.-v Ш,2'Л (I95S)* ?.- /••:: i . S.ry =-•••• - -' <•••., •'•';;/' •'•••' ''- • > /•' / / '•'ƒ• < > - ; ^ /*K»»A', / т /

' ,"*'.•: Г' :, 105Е 1413 (1957 ), 3, \ : : ^^v/ :> : ^ ^ % : ; . . ^ /5:.^>- Ю99 193 (1958 ),. 4, ^ ' . . ^ л й ^ М ^ . / ^ Z ^ ^ f Л&-Ш, I860 (1950), 5л few Л«До ЯЭТФ. 32, 405 (1957) 6, /^J^J>#tó

^ Л & . ^ # Ь , 138 (1964)* 7» Окунь ЛгБо УЗН» 89, 603 (I96S). 8с Мч4 £^ ^Л-^й-êf' 19,367 (1969),

9, -'А:?ЫЫ'/?С &6sJ%:< j I33PB329 (1964) Юс /?d-a$;^Aftf/ïff.tfv: П8Д605 (I960) XL. ffic&tic.ir'Xiï ^f.&s, 109 Д603 (1953)* 12* Шапиро ï-Ь.Оо У2К, 95f 647 (1963) I3c l\'i-J^-X ^;/ч /#.U?w 1201. 181 (I960) PU föanispo ИгС» Материалы семгаара по елоктромакихтншд

ввак^одо^отБЛям в ядерных р^шодих*Дубнар 1967Е стрв 76

- 4 9 -

?i5e Лбов 1?аГе, Данилов IJ«•.*•» Ермаков 0*H«f Карпахiui ^JL> ]"•:•:.. хтн E »lï, .Скорняков Л„М», Ядерная шдзЕяа» _16». 1218 (1972У

/•;•'.-. :у;/./ 25ВЭ 200 (1967 ) .

27, '/S ••••:.; •-• ^ ' * - • - • ' > ' 29В,564 (1969).

23, , ..."'.;•'<;r-'-/:'-Jt/?^y,U-y '£Я* 352 (1969) 29 „ Аоов Ю»Гс?Гулько А,Д0, Крущяцкий П*А» Поляризованные

глодленкыо нейтроны,Атоыиздат» 1966*

0г. Л[ Гм4у 33,524 (IS62)« ar. ЖгШ ^ %&Ы>Ж /4?. &>.Щ

„29,518 (1972)

32* Wt-UOk /£? Частное сообщение,

34* КрунчшкиЙ П,Ав Ядерная физика J3, 974 {1966 ).; 35 s Лобов Г,А* Письма ШСФ^» 7 (1935 ) •

&*A*£&*:;~'-JrA/-i# /$.j(LX4C -?.!/706 fJS66)

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/ 'j - ƒ-' / - A y /•'/ A ... *

f^S.^--. '-'//• ; J6,I579 (1971)

ЛоС: .;-;.:-:л JCJ-U» Назарешю BJW Саешсо ДеФ»вСштряцк1;и Д.й#, Xr^v^irq Гв51*»П::сьнаКЗТЗ» J , 263 (1366), 5,73 (1967), JIcc;;.vjB BJ.U- Как-лисор Доьь* Харкезнч ГаКе? Князев БоА»9 JïosoEoii Н»АегНазареико В*А«»Саенко !•$», Олотршцшй Лей*» Егоров АЛ. ty/^/X^S., _AI97, 241 (1972). / S : v J ; / / ^ / ^ ^ ^ ^ # K . ^ ^ 5 s 9 4 I (I970)

/2$.г. /Й/< 179, 1285 (1969 ).-

- 5 1 -

Подппся под тасуикаш.

,. „ ~ / 2 ^ 114 Рис Л . Схема уровней в ядре и f . Рис.2. Схема нейтронного тракта в опыте с Fuc.3. Блок-схегга электроники в опыте с с г? се с {-.'4

У-^У? ОС

Рис.4. Схема уровней в ядре <^ ° ° ; Рис.5. Схема нейтронного траста в опыте с &С .

I-защита реактора, 2-пучок нейтронов, 3-кобаяътовое зер-каю-поляризатор, 4-пучок поляризованных нейтронов, 5-поворотный магнит, 6-проводочный экран, 7-магнит ведущего поля, 8-коллима-тор, 9-свинцовая защита, 10-детектор У~ - квантов, II-шшень в защитном экране, 12-зеркало-анализатор, 13-нейтроиный счетчик. Р Е С . 6 . Блок-схема электроники з опыте с и? ,

1-детекторы ƒ""- квантов, 2-катодные повторители, 3-усили-тели мягкой компоненты, 4-усилители жесткой компоненты, 5-схеш быстрых совпадений, 6-схеш линейного пропускания, 7-усилители мягкой кошоненты, 8-однокакальные амплитудные ана-лизаторн, 9-усилители жесткой кошоненты, 10-дискриминаторы, П~схемы отбора комбинаций, 12-коммутатор, 13-пере счетные схемы,' 14~§письтваюг4ее устройство, 15-цкфропечатащая машина, 16-перфо-ратор, 17-схема питания поворотного магнита, 18-схема питания проволочного экрана.

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-57-

ROTATIOHAL STRUCTURE OF THE DOUBLY-ODD DEFORMED 182Ta NUCLEUS

J.M. Van den Cruyce, G. Vandenput, L. Jacobs, P.H.M. Van Assche (KUL, Leuven and SCK/CEN, Mol, Belnium), H.A. Baader, D. Breitig, H.R. Koch (TU, Munich. Germany and AEi', Ris0, Denmark), 1J. Delang, P. Settel, С. Hrastnik, H. Seyfarth (KFA, Ju'Hch, Germany), J.К. Alksnis, J. Tanbergs, M.K. Balodis. P.T. Prokofjev (Phys.Inst., Riga, U.S.S.R.)

INTRODUCTION

In 1971, R.G. Helmer et al.d) published the results of a series of experiments, performed in order to gain some Knowledge about the low-energy level'scheme of 182Ta. Although this odd-odd deformed nucleus had already been the sunject of several experiments, most of them using the (n,y) reaction, the work of Helmer et al. was the first successful trial to obtain an understandable scheme of the lowest excited states of this nucleus.

Sy studying the decay of 182(-(f and l82lJlTa, as well as the capture of thermal and 2 keV neutrons, they succeeded in establishing about 12 rotational bands, containing a total of some 30 levels. The predominant use of the primary capture gamma-rays however, limited strongly the spin-values Df the levels which could be observed. On the other hand, there remained an almost complete lack of information on the transitions connecting the observed levels.

In 1969 we started a study of the low-energy part of the gamma-spectrum following thermal neutron capture. The joint study of high-resolution data at

Risd and Ло1, (n.yy) coincidence data at Jülich and the conversion .electron spectrum at Riga yielded a more complete level scheme and much more reliable

information about the decay of the different levels.

EXPERIMENTAL TIETHODS AND RESULTS

High-resolution y-ray spectrum

This spectrum was studied by means of the bent-crystal diffraction spectrometer

[2) of the Technical University Munich at the DR3-reactor in Risó [Denmark).

-58-

Irraüiation af a natural Ta-sample yielded a spectrum containing soms 800

transitions in the energy region from 40 Ke\/ to 1300 keV. About BOO of these

trans 133,, transitions л'еге assigned to Та, the others belonging to Ta. "W and

"'.•:. The high precision for the determination of the energy, obtained with this spectrometer (e.g. 2 eV at an energy of 10D KeV), made the application of the Ritz-combination principle still possible;at least for the lower part

лот of the level scheme. The Та level scheme is the most complicated ever studied bv means of the Risri-spectrometer. Coincidence neasurenent

/\t higher excitation energies, the larger errors involved, together with the high density of the spectrum, makes the use of the Ritz-principle alone much less reliable. Therefore а Сп,уу) coincidence experiment was performed at the KFA-Jülïch {Germany). Coincident events of two Ge С Li) detectors were recorded on magnetic tape. A first, rather crude, analysis proved this meas-urenent to be very valuable when combined with the high-resolution data. Not only the major part of the already obtained level scheme could be confirmed, but several intense transitions, which could not be placed by energy combinations alone, could be given a reasonable assignment in the level scheme.

Conversion-electron spectrum

Some knowledge about the multipolarity of the transitions can be very helpful in determining spin and parity of the different levels. In order to obtain Rome indication about the multipolarities of at least the stronger transitions, the conversion electron-spectrum was recorded at the Physics Institute of Riga С USSR). Although the complexity of the spectrum was quite prohibitive for very precise measurements, interesting information, even on the multipole mixing in the strongest transitions could be gained.

The level scheme

The level scheme, resulting from these experiments, is shown in Fig.1, a-b. Most of the spin- and parity-assignments are taken or deduced from the results of Helnier et al., which are also given in Fig.1, together with some levels found in a (d,p) experiment by Erskine and Buechner (3). Most of the assigned configurations are not based on experimental facts, bit rather result from a comparison of the experimental level scheme with the predictions of the Nilsson-model. The expected Nilsson-states near the Fermi-surface for the odd proton and odd neutron are shown in Fig.2.

-59-

DISCUSSION OF THE LEVEL SCHEME

Suates of negative parity

The four bands of negative parity are interpreted as the coupling of the 7/2 [404] state for the proton, which is the ground state of the odd-A Ta-isotopes, and the 1/2 [510] and 3/2 [512] states for the neutron, being the ground - and first excited states of the isotopes with 109 neutrons. Та the levels Cwith 1^5) already observed by Heimer et al. could be added four I =6 levels. The level indicated as 7 at 5Б1.1 keV should be considered as highly tentative, and does not agree at all with calculatione made so far. An interesting point is the decay of the 173.2 keV level. Although the energy of one of the strongest transitions in the spectrum could coincide with the level energy, this transition could not deexcite the level, while it had 141 multi-polarity, unless the spin assignment were wrong. The coincidence experiment revealed this transition to feed the 270.4 KeV level, while calculations predict the transition probability from the 173.2 ReV level to the ground state to be very small.

The K=0 band at 558.3 KeV, whichwas already seen in the (d,p) reaction (3b could be extendend up to the spin 5 member. The partial [d,p) cross-sections indicate the configuration 7/2+[404] , 7/2~[50з] . The wave function of

u J p *- J n a K=0 band in an odd-odd nucleus can be written C4) :

^-/fS-°- , 1 ± t- ' I»°

The symmetric wave function permits only even spin values, the anti-symmetric only add ones. Treating these levels as belonging to two different bands, one can calculate the parameters of the rotational formula :

E = E0 + AKI+1J + BI2(I+1)2

as

for the "even" band : A = 13.73 KeV В = -D.012 keV

- b O -

f o r t h e " o d d " band : A = 14.37 keV

В = -O.O0D3 keV

The rsoments of inertia seen to be somewhat different for the two bands, while the odd band is lowered in energy with respect to the even band by about 53 keV.

For the K=1 band at 443,6 KeV, the Nilsson-model provides two possible configu­rations : .-/г" [514] , 11/2+[В15] and 5/2+[402] , 3/2~[б12] . The decay of the 1 level, with the strong 173.2 keV to the 270.4 keV level, clearly indicates the latter configuration. This, together with the fact, that we ars not yet sure about ths transitions, feeding and deexciting the 547.1 KeV level, makes the interpretation of the K=3 band at 547.1 keV as the 5/2+ [402] , 1/2~[510] con­figuration, which one expects to occur at a lower energy than the K=1 state, quite uncertain.

States of positive parity + It was found that the 331.3 KeV level could not be considered as the 5 member

of the K=4 band, as proposed by Heimer et al.(1). Instead, a level at 269.8 keV was found, which was hidden by the 270.4 keV level in Helrtier's measurement.

+ + Furthermore, 6 and 7 levels were found at 412.0 keV and 5BD.2 keV. The inter­pretation of the 331.3 keV level remains an open question. At 592.0 keV a 1=1 level was found, which is connected with a strong transition to the 1=2 level at 402.8 keV. A band with four levels could be build on this lsvel. A possible interpretation of this band is the 7/2+[404] , 9/2 [624] configuration.

С0№1ИЯАТМЯ I'tXING KY ЧРС

The small distances between the different configurations indicate that config­uration mixing by rotation-particle coupling will he important. The RPC-term in the Hamiltonian :

H = - — { RPC 2J l

mixes in general configurations with ДК=1, if &Q =1 and Ati = 0 or ДО ';0 and Aft =1 p n p n

-61-

In order to investigate the influence of this effect, calculations were performed for the four lowest states of negative parity and the three lowest bands of positive paritv- The two-particle energies E0 , the parameters A = — and the different RPC matrix-elements were fitted to the experimental level energies. From these values, the perturbed wave functions were deter­mined. The results of these calculations are presented in Tables 1 and 2.

For the positive parity states, the admixed components are all less than 10%. For the negative parity states however, vje see in Table 2 that several states consist primarily of two almost equaly large components, e.g. the 4 states at 97.8 keV and 114.3 keV. In this case, we can hardly speak of rotational bands. A good test for this calculation is a comparison between the observed relative intensities and the transition probabilities, calculated with the RPC-perturbed wave-functions. As an example, such a comparison is presented in Table 3 for

тт — — the К - S and 2 bands. The decay scheme for these bands is shown in Fig. 3. Although the configurations with the 5/2 [402] proton orbital were not included in the calculation, there is at least a qualitative agreement between the exper­imental and calculated values.

CONCLUSIONS

The study of the low-energy (n,y) spectrum resulted in a level scheme containing 50 levels below 1 MeV, which can be grouped into 12 rotational bands. Where the situation for the lowest bands, based on the 7/2 [404] and 9/2 [514] proton orbitals, is quite clear and can be satisfactorily described by the unified model, when the RPC-effect is taken into account, the interpretation of the higher lying states, especially the states based on the 5/2 [402J proton orbital remains questionable.

Other experimental techniques, for instance (d,p) measurements with good resolu­tion, will be needed to obtain a complete comprehensive description Df the level scheme of this odd-odd nucleus,

REFERENCES

(Я R.G. Helmer, R.C. Greenwood and C.W. Reich, Nuclear Physics Al68 (1971) 449 (2] H.R. Koch, H.A. Baader, D. Breitig, K. Mühlbauer, U. Gruber, B.P.K. Maier and

O.W.B. Schuit, in Neutron Capture Gamma-ray Spectroscopy (IAEA, Vienna, 1969) Б5 (3) J.R. Erskine and W.W. Buechner, Phys. Rev. 133 (1964) В 370 and private

communication to R.G. Helmer. (4) 0. Nathan and S.G. Nilsson, in Alpha-, Beta- and Gamma-ray Spectroscopy,

ed. K. Siegbahn, (North-Holland, Amsterdam, 1965) 601.

-62-

к=з К=4 К=5 163.21 -179.4а -2G4.41 СKeV) 14,07 14.3G 14.01 [KeV)

Table 1,a : RPC-mixing in the negative parity states

Parameter VSIUPP :

K=2

T w o - p a r t i c l e energy EQ : 1BB.3Ö

<\ = f i 2 / 2 J 14.04

<К=2(Нррс)к. = 3> = 17.96 [ ( I - 2 ) ( ] > 3 ) ] 1 / 2 KeV <K=3|HRpc!K.=4> = -2.95 [С1-3)С1*4)]1 / 2 KeV <K=4|HRp(:JK=5> = 17.74 [ ( I - 4 J [ I + 5 ) ] 1 / 2 keV

Calculated and experimental energy values (in KeV)

К = 2 К = 3 К = 4 I Exp. Theor. Exp. Theor. Exp. Theor. 2 270.40 270.64 - Q.13 - -3 360.52 360.36 0.0 97.8S - -4 480.03 479.74 97.83 23Б.94 114.32 114.28 5 628.42 62B.63 237.29 396.55 292.94 292.95 S. (BD5.D7) 806.87 396.33 5B3.04 (4BÖ.26) 489.31 7 - 1014.29 (561.11) - - 710.60

К = 5

Exp. Theor .

173.24 173.25

(316 .40 ) 316.04

490.66

K=3 K=4 K=5 89.34 -91.42 -350.95 13.48 12.42 12.27

Table 1ЛЬ : RPC-mixing in the positive parity states

Parameter values :

Two-particle energy Eg : A = R2/2J

<K = 3|HRpcJK=4> = 12.2B [(I-3KI+4)]1/2 KeV <K=4|HRpc|K=5> » 2.69 [(I-4)(I+5)]1/2 KeV

Calculated and experimental energy values (in KeV) 4 К = 5

Theor. Exp. Theor. К = ' 3 К

I Exp. Theor. Ёхр. 3 250.72 251.10 -4 365.10 364.77 150.89 5 506.34 505.87 269.78 6 673.75 674.14 412.04 7 - 8S9.36 (580.17)

151.15 - -269.34 17.01 16.95 412.22 163.78 163.89 5B0.00 335.36 335.31

(Energies between bracKets were not used in the calculation)

-63-

Table 2,а : RPC-perturhed wave-functions for the negative parity states

(Coefficients a,, in the expansion if = I a„ ф„) Гч v Гч 1ч

I EtkeV) а . 2 а 3

3 360 0.932 0 .123

3 0 0.123 - 0 . 9 9 2

4 480 0,983 0.1ВЗ

4 97 0.130 - 0 . 7 1 4

4 •114 0.129 - 0 . 6 7 6

5 628 0.972 0 .232

5 237 0.227 - 0 . 9 5 7

5 293 0.О39 -0 .13В

5 173 0.018 - 0 . 0 9 0

6 807 0.962 0 .274

Б 397 0.269 - 0 . 9 4 7

6 489 0.046 - 0 . 1 2 3

6 316 0.027 - 0 . 1 1 7

0.005 -О.Б80 -

D.726 -

•0.010 -0 .026

•0.091 - 0 . 1 5 4

0 .794 0.590

•0.598 0.796

0.012 -0 .004

•0.027 - 0 . 1 7 6

0.778 0.614

•0.627 0.769

Table 2,h : RPC-perturheri wave-function?; fnr the positive parity states

I E fkeV] a 3 '

4 365 0 .986

4 151 0 .165

5 506 0 .974

5 269 0 .226

5 17 0 .004

6 674 0 .964

6 412 0 .266

6 164 0 .007

7 B69 D.956

7 580 0.294

7 335 0.010

°4 0.165 -0.966 0.226 -0.974 -0.033 0.265 -0.963 -0.049 0.294 -0.954 -О.0БЗ

0.007 -0.033 0.999 0.012 -0.049 0.999 0.012 -0.064 0.99B

-ü4-

fable 3 : Calculated and experimental relative intensities for the vJ=5 and 2 bands

" i X f E f c a l c . exp.

5 173 3 D 0.018 <0.05

4 97 1.0 1.0

4 114 0.16 0.51

3 316 4 97 0 .1 0.06

4 114 0.013 <0.03

5 173 1.0 1.0

5 237 0 .22 <0.16

? 270 3 0 1.0 1.0

4 97 0.019 0.005

4 114 0.002 0.129

i ЗБ0 3 D 11.1 2 .0

4 97 2 .0 0.07

4 114 0 .58 0 .46

5 173 0 .003 <0.06

5 237 0 .01 <0 .2

2 270 1.0 1.0

5 292 З х Ю ~ 6 <0.36

4S0 3 0 2 .9 0 .68

4 97 5 .1 0 .87

4 114 0 .76 0 .08

5 173 0 .72 0 .1

5 237 ЗхЮ - 1 * 0 .21

2 270 0.67 0 .35

5 2S2 0 .30 <0.08

6 316 3x10 _ t t 0 .30

3 360 1.0 1.0

6 396 3x10_ t* <0.34

5 6 u

486.3

6Z_JM« 778.6

3-_70Z0

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5 - 628/. *

-Лаз

>- 480.0

785.0

.»659.в

- - 565.7

, - 4914

12)-

5^ 782.0 f 777(d,p) 2~ 7403

MS.S 3- 7/9.6 3~ 702Ü

, --?^ 666.0 „ n r

-659.6 4 5" Q-

~3A~

-649 S28.4

-584(d.p) -565.7,

к -547,1 -S1SJ

SS9(d.p)

.4918,

443.6 679JB

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396,3

5- гэга SZ~2ÏZ3

36 OS

зил 270.4

.36 OS

6 t — , ? 7 7 f ó p ; 5~- 293.0 2' 270.4

5Z 237.3

97.8

, - 0.0

,-114.3

1732

Fig, 1,a. Level schema of the negative-parity

states in Ta. At the right are

given the f ina l proposals of re f , l1)

and (3)

.173.4

.114.3 • 97.8

-fiO

p 7/2+[40д] p 7/2*[«K] p7/2*(4Q<] p5/2+[«02] p 5/2+ |Ï02]

n 1 / 2 " [ 5 t 0 ] n3/2*[512] n7/2"[503] n 1/2~ pW] p 3/2~ [512]

HL 71 а Er 64

•>* 73 ft/

F i g . 1.Ь. Lev/el scheme of the p o s i t i v e

p a r i t y states i n 1 8 2 T a . At the r i g h t агв given the f i n a l

proposals of r a f , [1) r- 580.2

•,+ 335.3

r+ 412.0

-+ 26-59

r * 163.9 6 4*_15ЛЭ

6 / 3 /

r+ S0S.3

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,+ 250.7

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,* 57V

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,+ t02.S

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,±J1M 2.5* i+

„586.6 57 IS

5* „5054 3* i7i.4

2.5* 2t 6*s—

Л 23.5? _i02.S

39/3

7t 5*'

331.S 331.3

3+ .250.2

6t 4*'

/63.3 ~1S0.i

17.0 15S

P U/2" [51t ] P 9 / 2 - [ 5 U ] p 7 /2 + [ t 0 t ] p 7/2+ [uoi,] 7 1 HL a

n 1 / 2 " [ 5 t 0 j n 3/2" [512] n 11/2+[615] n 9/2+ [б2А] s „ • -• л л t

- 6 7 -

Proton Neutron

1/2-[5А1] 7/2-&03]

5/2+[^02] _ 11/2+[615]

3/2'[512]

9/2"[5u] 7/f[t.0U] F 1/2" [51 0]

l /2+ [AH] g / 2 + [ 6 2 / > ]

7/2"[5U]

7/2 [523]

5/2" [512]

F i g . 2. N i l sson-s ta tes f o r the proton and neutron near

the Fermi-surface

-68-

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-69-

Chaimel spin interference and potential

capture of neutrons

K. Abrahams, J. Kopecky, and F. Stecher-Rasmussen

FCM-RCN Nuclear Structure Group, Petten (N-H), The Netherlands.

Interference of channels with spin J c = Jj- + k_ has been found for capture

of slow neutrons П~3]- I n c ? s f ! n ^ polarized neutron capture, the extreme

value R of Lhe circular polarisation of fh» emitted dipole radigtinn is tip-

fined by 4R-1 • Зсоз(2ф-Ф), Here cos2<f> is the relative rate of the

Iraiisi tinn, which proceeds via channel spin JQ - 'Tt+I- ТГвпяЦу the гввипяпгс

energies are. high pnough, and the fase angle ф is real , Tn figure 1 the el­

l ipt ic functions R(cos-(ji) ягн shown fur nil relevant oonnbiuatinns of ihe

spins J t and Jf of target and final s ta te , which determine Ф.

If the j-fiHur.ed (n,y) strength is highly correlated with the (г1»р) .чрeel'ens-

cop ic factor for p levels, i t can be shown that R = (sf/2 ~ 0.5во/2)/е2 (Sftfi

appendix).

Har?, fly. i s the pi/2 reduced width, e | , , the p3/2 reduced width, and B? =

8?/2 + Q^/2' ^ n t n - e last expression for R the spins J t , Jc a n d Jf n o longer

show up, and ii_ appears that one may derive а|/2 a n d °|/2 ^ o r е а с ^ final

state by measuring R. Such я Tiie.asnrement can be used to estimate the spin

orbit spli t t ing for even A nuclei, This is de.rnnns traied in figs. 2 and 3,

for a few nuclei, for which R values have heen itieasured in Petten. Here

S = (2Jf+l)e2;

For the odd—odd nucleus ^Kn the f i rs t p£ level appe.yts rather close to the

ground state , just as for the odd A nuclei in this mass region. Another

group of p | levels is found at higher excitation energy, just as for the

odd A nuclei. For all measured odd К nuclei in the mass region 48<A<62

such a pl/2-p3/2 doublet has been found (see fig. 3).

An even mote convincing example is the even—aven nucleus Fe, for which

the relative pi /2- and p3/2-streiigtu5 have been determined for 15 levels

j>]. Figure 2 shows that the pi/2 levels appear 1-2 MeV above the strongest

p3/2 level.

-70-

Referenees:

[J] A. Fergusson, Angular correlation methods in yray spectroscopy, (North Holland, Amsterdam, 1965).

[2] A.M.F. Op den Kamp, J. Kopecky, F. Stecher-Rasmussen, K. Abrahams, and P.M. Endt, Phys. Lett. 29B (1972) 204.

[3] J. Eonzatko and J. Kajfosz, Phys. Lett. 32B_ (1972) 4A9. E.R. Reddingius, J.J. Bosman and H. Postma, Phys. Lett. 41B (1972), 301.

[4] J, Kopecky, K. Abrahams and F. Stecher-Rasmussen, Contribution to this conference.

Appendix:

According to ref. [1] p. 100 one finds:

l с В' W<è4b';al) \ (Iblb' ;cl)Rca

R = ^ (1) I S Б' W(|b£b';a0) Z,(lblb';c0)Rca

bb*

Here a = J t , b = Jt±l, b ' = Jt±i» and с = Jf. As usual S = (2b+l)*.

For pure channel capture to &n(dp) = 1 l eve l s К^а i s p ropor t iona l to the following sum over j = l / 2 ( p t / 2 ) and j = 3/2(p3/2) s ingle p a r t i c l e s t a t e s ;

R c a « I (a J b | ! H ( l ) И a j c) (a I b ' | ] H ( ! ) (J a j ' c ) < b j j i | a >

ii1

<b'Ml|a> - I t(-l) a + i+ b + 1 В И Г C2c+1) {J I [} {I £ <} 6,

By <b] |i ja> <b ,Hi|a> (2)

For p o t e n t i a l capture the coef f ic ien t s <b|]A|a> and <b ' | | | ] a> are equal .

By s u b s t i t u t i o n and use of seme Racah algebra one f inds the express ion:

R- (e] / 2 - о . 5 в | / 2 ) / (ef /2 + e | / 2 ) (3)

For channel capture the necessary condition for the validity of this ex­pression follows from <b'|j|Ja> = <b||j|a>, which is found in case that the reduced (n,v) strengths are proportional to the (d,p) spectroscopic factors.

- 7 1 -

ч*

И - г?

т il

il

II

м 00 II »-< Рч

.X?

о о и

1 2 SU 53л 55_ Cr, Cr, Fe

ni-Jzt2

II 51

J rW WO-w 2 S H

-siT' 55 UbL 63 i*

V , 1 1

3 MeV

56 Mn

]I i(i—tbirT~'rff

1 2 MeV Excitation energy >

4 MeV

Fig. 2

- 7 3 -

58 Fe

т, f*'

%

—I

e ь

_ i

1 _ i 3 О 1 2 3 4 5 MeV

»Exe r t a t i on above ground state -»

Fig. 2a

-1MeV О 1 О -»->-Excitation above first p1/2 level

1MeV

Fig. 3

- 7 5 -

THE 5 7 F e f n , y ) 5 9 F e REACTION

J. Kopecky. К. Abrahams and F . Stecher-Rasmussen

FCfrbRCN Nuc lea r S t r u c t u r e Group, Reac to r Centrum Nede r l and ,

P e t t e n , the N e t h e r l a n d s

NUCLEAR REACTION 57 Fe (polarized n,y); E = thi armal; measured Ey5 yi> У-CP; deduced Q; 5 8pe levels deduced J. Enriched target.

, , ,

-7ó-

1. Introduction

The energies, spins and parities of the excited states of the even-even

nucleus 5BFe have been studied extensively during the last years.

The spin values adopted in Nuclear Data | ] | maninly result from y-y angular

correlation measurements on y-ray cascades following neutron capture

|2.3|.

In order to confirm and extend these spin assignments, the circular

polarization of y-rays from the capture of polarized thermal neutrons has

been measured.

It has been concluded in ref. |2,3| that the shell model is more suitable

for a description of the levels with excitation energy below 3 MeV than the

vibrational model.

The possible correlation 15—T J between the reduced (d,p) strength (2J+1)S

and the reduced (n,y) strength Iy/Еу3, for primary y-rays leading to the same final states with I = 1» has been analysed.

2. Experimental Method and Data Analysis

In refs. J8,9[ the experimental set-up and data processing technique have been described. A sample in the form of isotopically enriched oxide (10 g, on loan from US-AEC, loan contract EU/L/24) has been used in the present work. In table 1 the isotopic analysis of this sample is presented.

The polarization spectrum is shown in fig. I. The polarization function R (see e.g. ref. |8J) has been determined from the measured polarization spectrum for the strongest primary transitions and for several secondary ground-state transitions. The results are given in table 2.

It has been generally assumed J8|, that the primary transitions to the odd Z (d,p) states were pure dipole transitions. In that case R is only a function of the -pin J of the final state and of the admixture a of the two coherently interfering spins J = J +{ in the capturing st particular. The function R is then defined by interfering spins J = J +{ in the capturing state for each transition in

R * aR +_ 2R° / a(J-a) + R ,

-77-

where J is the spin of the target nucleus, and where the functions R j, R and R are defined in ref. | 101. The variable a can range from

2 0 to 1, with ot = -T—T—2> where л is defined |llj as

pJ t+3\i <J|L||J t+l><J t+i| I 1 |J t>

In f i g . 2 R i s given as a function of a together with some experimental points (ct-values from ref . | 3 [ ) . The spins derived from the experimental R-values can be found i n tab le 2 . They are based on a 99.9% confidence l im i t corresponding to the r e j e c t i o n of a l l other spins i f R d i f fe r s more than approximately three standard deviat ions from the t h e o r e t i c a l va lue .

The y-ray spec t ra obtained in the po l a r i za t i on measurements have also been used to determine the energies and i n t e n s i t i e s of the t r a n s i t i o n s . The pos i t ions of the peaks were determined by f i t t i n g a Gaussian function to the experimental p o i n t s . For the energy ca l ib ra t ion some prominent y-rays from the 2 7 Al(n ,y) ( ref . | l l j ) and 5 6Fe{n,y) (ref. | l 2 | ) react ions were used in combination with the energy d i f ferences between ful l -energy and escape peaks. The e r ro r s in y-ray energies a lso include a systematic e r ror of 100 ppm.

I n t e n s i t i e s were ca lcula ted with the e a r l i e r obtained | 9 | experimental eff ic iency curves for fu l l - energy , s i n g l e - and double-escape peaks. The values l i s t e d i n tab le 2 for the r e c o i l corrected ene rg ies , E , and the i n t e n s i t i e s , I , are the weighted averages of those deduced from the ful l -energy and escape peaks. The sum of i n t e n s i t i e s of primary y-rays was normalized to the value of 93% taken from the measurement described in ref. | 2 | . An est imated systematic e r r o r of 10% in the eff iciency curves has been included in the i n t e n s i t y e r r o r s .

Because some secondary t r a n s i t i o n s have been measured too , some two step cascades were included in the ca lcu la t ion of the Q-value.

Most of the e x c i t a t i o n energies have been calcula ted from the Q-value and the measured energies of primary t r a n s i t i o n s . If secondary ground-state t r a n s i t i o n energies were measured, t h e i r values were a l so taken in to account

-7Г-

3. Experimental Results and Discussion

Table 3 shows s i x cascades, which were used to ca l cu l a t e the reaction. Q-value. In ref. J2| these cascades were e s t ab l i shed from coincidence measurements. Because of good i n t e r n a l consis tency, the systematic e r ro r of 100 ppm has been used for the f i na l e r r o r , which gives Q = 10044. 6jH.O keV.

Spin assignments l i s t e d in table "2 are based upon measured R-values, I values from ref . I13I and a-values determined for some t r a n s i t i o n s i n n •

ref, |з|. Where a secondary transition to the J = 0 ground state has been established on the basis of coincidence measurements |2|, a J = 0 assignment can be ruled out. For the following discussion of some levels we refer to table 2 and fig. 2. E =_ 0_kgy.For known 1 -»• О primary unmixed El ground state transition the experimental value R = 1.05_+0.12 is in accordance with the theoretical value R = 1. E f_°i8Ij !i62 and. 3-08 MeV. The value R = -0.5 (expected for a = 1) for „х- - _ _ ^ + the primary transitions to these J = 2 levels is well reproduced by the measured R-values. E = 2.78, 3^54_and_3_.63 HeV. Because of the negative R-values for the primary transitions populating these Я = 1 states, J = 1 or 2 could be assigned to these levels. The work of ref. J3| excludes the J = 2 assignment for the 2.78 MeV and 3.54 MeV levels. E = 3.88, 4.14, 4,44, 4.55 and 5.00 MeV. All transitions to these A =

TF + + 1 or 3 levels have R и 1, and hence all spins but J = 0 or 1 can be ex­it + eluded. The J = 0 assignment can be excluded because all levels decay to the ground state |2J, Therefore a spin assignment J = I can be made for these four levels. . evidence for a J = 1 assignment of the 3.88, 4.55 and 5.00 MeV levels follow from the angular correlation measure-nvrits of refs. J2, 3J.

-x~~---~-±--------~^-Q-^¥- Ttie R - V a l u e s £or these transitions cluster

around zero, so that the unique assignment J = ] can be made.

This assignment is purely based on measured R-values (see fig. 2) for

these I (d,p) = 1 levels the knowledge of the parameter a is not needed

and in fact one can determine a from the ellipse in fig. 2.

-79-

In the last column of table 3 a-values determined from the present

measurement are listed. Where the projection of R on R, (a) has no •л + ÊXp theor

solution and one knows that J = 1 , the asymptotical value has been

taken as the most probable one. The positive (negative) sign of a cor- 5

responds to the constructive (destructive) interference between two

possible J components.

4. Discussion of the (d,p)-(n,v) Correlation

I t has been concluded in ref. |2j , that the shell-model j14| description

is most suitable for the levels below 3 MeV excitation. This observation

is important for the following discussion, since the existence of rather

pure single-particle p-components in Che wave functions is a preliminary

assumption in the theory of Lane and Lynn |5 ,7 | .

According to this theory the (d,p) single-particle widths Г and the

partial (п,у) widths Г . for the same final states are correlated in the

mass region A = 40 - 70. This correlation is connected with an enhancement

of El transitions to the single-particle 2p states. Because of the relatively

low excitation energy of these states in this mass region, the enhanced high-

energy part of the (n,y) spectrum generally deviates from the shape predicted

by the statistical model J4|.

The shape of the S7Fe(n>Y) spectrum» however, shows very l i t t l e anomally,

which seems to be common to al l even-even product nuclei in the mass region

A = 40 - 70.

A correlation analysis based upon the present results can be found in table

4. The linear correlation coefficient p (see the definition in footnote in

table 4) has been calculated for all known Л = 1 levels and also as a func­

tion of the excitation energy. A t- test has been applied with a 95% confidence

level as criterium for a statistically significant correlation.

A significant correlation between S and Г has been found for this nucleus n Y and especially for the I = 1 states below E - 3 MeV. In fact the highly r n x

significant value of p =0.99 is in contradiction to the tendency for p to be smaller for odd A target nuclei |7J. With the increasing excitation energy the correlation remains significant and is not confined to the lowest £ = 1 levels, as is the case for even-odd nuclei [l5J.

-80-

5. Conclusion

In the present work several spins have been assigned to excited states of 58Fe. For some transitions the ratio a of the two components, J = 0 and

1 , in the capturing state have been determined. The strong correlation

between the primary (n,y) strength and the (d,p) reduced width has been

found for p-levels with excitation energies between 0 and 5 MeV.

It is a pleasure to thank Prof. P.M. Endt, Dr. C. van der Leun and

Dr. H. Gruppelaar for their interest in this work and for their critisism

of the manuscript.

The authors wish to acknowledge the technical assistance of Mr. P. Snip.

- 8 1 -

REFERENCES

S. Raman, Nuc lea r Da ta B3 No. 3,4 (1970) 145.

U. F a n g e r , W. I c h a e l i s , H. Schmidt and H. Ot tmar , Nucl . Phys . A128

(1969) 6 4 1 .

H. Schmidt , W. M i c h a e l i s and U. F a n g e r , N u c l . P h y s . A136 (1969) 122.

J.M. B l a t t and V.F . Weisskopf, T h e o r e t i c a l n u c l e a r p h y s i c s

( John Wiley and Sons , New York , 1952) .

J . E . Lynn, The Theory of Neutron Resonance Reac t ions (Clarendon

P r e s s , Oxford 1968) .

A.M. Lane, C o n t r i b u t i o n t o t h e I n t e r n a t i o n a l Conference on S t a t i s t i c a l

P r o p e r t i e s of N u c l e i (Albany , New York, 1971) .

A.M. Lane , P r o c e e d i n g s of t h e I n t e r n a t i o n a l Symposium of Neutron

Capture Gamma-Ray Spec t ro scopy ( S t u d s v i k 1969) >p. 5 1 3 .

F. S t eche r -Rasmussen , К. Abrahams and J . Kopecky, N u c l . Phys . A181

(1972) 2 2 5 .

J . Kopecky, K. Abrah atns eind IT. S tschsT~R&sraussen, NucX. Phys . A1S8

(1972) 535 .

K. Abrahams, C o n t r i b u t i o n t o t h e Conference on N u c l e a r S t r u c t u r e

Study w i t h Neu t rons (Budapes t , August 1972) , c o n t r . A21.

A . J . F e r g u s o n , Angular c o r r e l a t i o n methods in y - r a y s p e c t r o s c o p y ,

( N o r t h - H o l l a n d , Amsterdam, 1965) .

A.M.J . S p i t s , A.M.F. Op den Kamp and H. G r u p p e l a a r , Nuc l . Phys .

A145 (1970) 449.

J . R a p a p o r t , A, T r i e r , T,A. B e l o t e and W.E. Dorenbusch,

N u c l . P h y s . A187 (1972) 25.

J . B . McGrory, P h y s . L e t t . 26B (1968) 604.

J . Kopecky, RCN R e p o r t , t o be p u b l i s h e d .

G.A. Bartholomew e t a l . , Nuc lea r Data A3 (1967) 374.

- 8 2 -

Table I. I so top ic composition of the sample s tud ied .

Isotope Tsotopic ana lys i s (atomic percent) ° t > > a>

Contribution o\ ^ in % t o t

S^Fe < 0. I 2 . 3 < 0.1

56F e 6.14+0.1 2 .7 6 .6

57 F e 93.63+0.1 2 . 5 93.2

5Spe 0.22+0.05 1.2 0 . 1

Ref. j 16 |

±dU 1С i . LJL>AII uc(.exiuj.uctLi.viia u i i e i e vci_a

X (KeV)

E Y

(KeV)

I ï

m

l

b)

P rev ious J

d e t e r m i n a t i o n с) 0 )

Thi s work X (KeV)

E Y

(KeV)

I ï

m

l

b)

P rev ious J

d e t e r m i n a t i o n с) 0 )

R J* d) a

0 10044.1+1.2 2 .7+0 .5 1 °: 1 +1.05+0.12 et 810.9+1.0 9233 .7+1 .0 2 .2+0.4 1+3 2 +

2 1 -0 .50+0 .10 2^

1674.9+1.0 8369.7+0.9 11.8+1.5 l + (3) 2 + 2 1 - 0 , 4 i + 0 . 0 5 г\ 2782.4+1.С

3083.9+"l.O 7262,2+0.8 6960 .7~0 .7

11,4+1.2 IO.5T1.O 2

>. 2410.14

••09*0:'09

> 90

- 0 . 5 0 + 0 . 0 5 - 0 . 4 6 + 0 . 0 5 %

+0,3510.15

+0 .3 +0.2 - 0 . 7 +0.3 - 0 . 0 2 + 0 . 0 2

3538.2+1.0 Э630.3Т1.0 3881.6+1.0 4015.9+1.0

6506 .4~0 .7 6414. ЭТО.7 6163.1+0.6 6028.7+0.6

6 .8+0 .8 1.6+0.2 3 .3+0 .3 1.2+0.2 1+3

1+ С

>. 2410.14

••09*0:'09

> 90

- 0 . 4 2 + 0 . 0 6 - 0 . 6 То .2 +0.95+0.11 +0.2 ±0.2 t

+0,3510.15

+0 .3 +0.2 - 0 . 7 +0.3 - 0 . 0 2 + 0 . 0 2

)

+ 0 . 9 6 l 8 : 8 ? 4139.0+1.1 5905 .6+0 .7 2 .5+0 .3 1 +0,97+0.14 i + - 0 . 7 1 0 . 3 4297.6+1.0 5747.0+0.6 2 ,4+0 .2 - 0 , 5 8 + 0 . 1 5

+0.90+g: (?§ + 0 . 8 7 + 0 ; ^

4322.8+1.0 4353.0+1.0 4444.4+1.0 4550.7+1.0 5000.6+1.0 5220.7+1.1

5721.8+0.6 5691.6+0.6 5600.2+0.6 5493.9+0.6 5044.0+0.5 4823.9+0.6

2 ,5+0 .2 2 .5+0 .2 1.1+0.2

10.9+0.9 10.7+0.8 2 .4+0 .2

1+3 1+3 1+3

1 1

1<*> С Г С

.23+0.20

+0.02T0.16 - 0 . 0 4 + 0 . 1 2 +0.9 + 0 . 3 +0.85+0.08 - 0 . 9 7 + 0 . 0 3 - 0 . 1 7 + 0 . 1 7

- 0 . 0 +0.02 +0.01+0.02 - 0 . 7 0 + j b | -о.35+р."Д9 - 0 . 7 W.r

+0.90+g: (?§ + 0 . 8 7 + 0 ; ^

5294.8+1.1 4749.8+0.6 3 .0+0.2 +1.1 То .2 5418.1+1,0 4626 .5+0.5 .

5001.0+0.7 a ; 4322.1+0.6 a ' 4298.1+0.6 a ( 4139.9+0.7 l 3881.8+0.7 '

3.3+0.2 +0,74+0.15 5000.6+0

4626 .5+0.5 . 5001.0+0.7 a ; 4322.1+0.6 a ' 4298.1+0.6 a ( 4139.9+0.7 l 3881.8+0.7 '

1.5+0.2 +0.7 +0.4 4322.8*0

4626 .5+0.5 . 5001.0+0.7 a ; 4322.1+0.6 a ' 4298.1+0.6 a ( 4139.9+0.7 l 3881.8+0.7 '

2 ,8+0 .3 +0.5 +0 .2 4297.6+0 4139.0+0

4626 .5+0.5 . 5001.0+0.7 a ; 4322.1+0.6 a ' 4298.1+0.6 a ( 4139.9+0.7 l 3881.8+0.7 '

0 .8+0 ,2 2 .1+0 .2

- 0 . 2 +0.4 - 0 . 5 +0 .3

3881.6+0

4626 .5+0.5 . 5001.0+0.7 a ; 4322.1+0.6 a ' 4298.1+0.6 a ( 4139.9+0.7 l 3881.8+0.7 ' 1.2+0.2 - 1 . 1 +0.5

a) The secondary ground-state transitions. b) Ref. |I3|. c) Refs. |2,3[. d) Eased upon R, I , a and J=0 rejection from c).

e) The projection of Rexp on R t h e o r(a) has no solution, the asymptotical value is taken as the most probable one.

-84-

Table 3. Determination of the 57Fe(n,y) reaction Q-value

Cascade (E in keV) E (keV) a )

10044.Ï 10044. HO. 6

6163- 1-38S1.S 10044.9+_0.5

5905.6-4139.0 10044.6+0.6

5747.0-4298.1 10045.1+0.4

5721.8-4322.1 10043.9+0.4

5044.0-5001.0 10045.0+0.5

weighted average: 1 0044.6+0.2

adopted value : Q = 10044.6+1.0

a) The errors are purely statistical,

b) See text.

Table 4 . C o r r e l a t i o n be tween t h e ( d , p ) Jt *= 1 reduced width (Г •v S (d ,p>) and the pr imary (a,y)

p a r t i a l w i d t h (Г .VE / E 3 . ) as r e l a t e d t o energy s e p a r a t i o n . Yl Y Y1

1 l e v e l s ДЕ -vO - 2 MeV ДЕ -v. 1.5 — 3.5 MeV -1-3.5 - 6 . 5 MeV Nucleus

p P ДЕ x

(MeV)

N p P ДЕ x

(MeV)

P fiE N p x

(MeV)

P ЛЕ x (MeV)

Fe 23 0 .53 99 0 - 5 . 0 6 0 .99 99 0 - 2 . 9 8 0 .72 96 2 . 9 - 4 . 1 9 0 .80 99 4 . 1 - 5 . 0

The c o r r e l a t i o n c o e f f i c i e n t p i s d e f i n e d by

Hi r / v y i у

E (Г° - f ° ) 2 E (Г . - Г ) 2

j п . и . Y i Y 1 1 1

where Г and г are average values. The S(d,p) values have been taken from ref. |I3|. and I from the present work.

Y N is the nuirber of levels. ЛЕ is the range of excitation energies considered.

S'c,_ J&t

^4*3W^tv^*jwCw^*!ï^?i ,v 'fw »• •••*

Feta. j f F e

ь"Ъ8*>

(fflefcfiee spectrum

К ^ ^ ^ * ^ ^ . ^ Л 9 Ц tfV,

бит доеЬшп W w i ^

яРви^

шкзЖЩяйМ 'Fe ,"»*J •«* ,

ffi.-...,,JU

(Jffletence Cfrtctrum

A-XIULJloütLL. - i c j l r T «Опил ™ — " ' - " » " — _ Д . _ _ ~™_.JL„ . Ji

Л.

7 ' "Fé " « у '

sum spectrum

9S0O

,„.A„,

Fig. I Circular-polarization spectrum of the s7Fe(n,Y)s8Fe reaction. Two spectra, accumulated for opposite neutron spin directions, are presented by their difference and sum. The measuring time was 550 hours.

- 8 7 -

C—5.00 MeV С —4.55 MeV

/

C~~OMeV С — 3,88 MeV

C-*3.54\(VleV С—2.78 MeV

0.5

С —1.67 MeV С—3.08 MeV

С — 0.81 MeV

-»-Ot

The polarization function R for primary dipole transitions to a level with spin J, presented as a function of a (the fraction of the J = 1 spin in the capturing state) together with some experimental points; the spin of the target nucleus is J = 5/2

- 8 8 -

57 Fe+n 10045

1 - T

T In (d,p)

0 - , 1 г

S * o « r Ф < # с о о > Ф г - « о 2 ^ , З Я О » -О С М Р Э О 1 0 ) l 0 4 t T - O 5 r ^ N O I 0 4 f O C 0 p : ©

5295 5418

5221 5001

4444 4551

4323 4353

4139 4298

3882 4016

3538 3630

3084 3244

2782

1675

811

M S OD GO N

П И Й « 5 51 9 O r-

o 5?

58 Fe

T*0

1+

- 1 + _ - 1+— -T*0 — - 1 * _

I t 2 *

0 * 2 + -1 +

Fig. 3 The 5 7 Fe(n ,v) S 8 Fe t r a n s i t i o n s discussed in t h i s a r t i c l e . A more complete decay scheme is given in r e f s . J2| | 3 J .

- 8 9 -

Ш ESTIMATE OF THE HINDRANCE FACTORS FOR y-TRANSlTIONS NEAR THE NEUTRON

BINDING ENERGY FROM THE REACTION l t t 3 N d ( n , v a ) 1 4 0 C e .

"f.I, Furman, K. N iedzwied iuk , Yu.P . Popov, R.F. Rumi, V . I . S a l a t s k y ,

if.G. T i s h i n , P . Win iwa r t e r

Labo ra to ry of Neu t ron P h y s i c s

J o i n t I n s t i t u t e fo r Nuc lea r Research

Dubna, 1972

The r e a c t i o n l t t 3 Nd(n ,Ya) 1 4 0 C e has been d e t e c t e d in the resonance of 55 .3 eV.

A t h e o r e t i c a l a n a l y s i s h a s been c a r r i e d o u t , y i e l d i n g lower l i m i t s for t h e

h i n d r a n c e f a c t o r s of y - t r a n s i t i o n s between h i g h l y e x c i t e d s t a t e s c l o s e to

the n e u t r o n b i n d i n g ene rgy . Some ev idence f o r t he predominance of Ml

t r a n s i t i o n s i n t h i s energy r e g i o n was found

The p r i n c i p a l i n f o r m a t i o n about y - t r a n s i t i o n s a v a i l a b l e a t p r e s e n t concerns

e i t h e r t r a n s i t i o n s between d i f f e r e n t low l y i n g l e v e l s or t r a n s i t i o n s between

h i g h l y e x c i t e d s t a t e s of a compound n u c l e u s and l e v e l s wi th sma l l e x c i t a t i o n

energy (or t h e r e s p e c t i v e ground s t a t e ) .

For t h e d e s c r i p t i o n of t h e second ca se u s u a l l y s t a t i s t i c a l methods a r e

u sed , s i n c e t he s t r u c t u r e of t h e h i g h l y e x c i t e d s t a t e s i s q u i t e complex.

For a comparison of e x p e r i m e n t a l and t h e o r e t i c a l Y - t r a n B i t ; i - o n p r o b a b i l i t i e s

a h i n d r a n c e f a c t o r HF i s used i n r e l a t i o n t o t h e s imple Weisskopf e s t i m a t i o n

f o r s i n g l e p a r t i c l e t r a n s i t i o n s | l | .

An unique method f o r r e c e i v i n g i n f o r m a t i o n about Y ~ t r a n s i t i o n s between

h i g h l y e x c i t e d s t a t e s i s the s t udy of t he (n.yct) r e a c t i o n . I n t h i s p rocess

a t w o - s t e p d e - e x c i t a t i o n of a n e u t r o n c a p t u r e s t a t e t a k e s p l a c e , i n v o l v i n g

an e l e c t r o m a g n e t i c t r a n s i t i o n t o lower l y i n g s t a t e s (E ^ 2 MeV) fol lowed

by c c - p a r t i c l e e m i s s i o n . The nuc leus l u 3 N d i s an i d e a l t a r g e t f o r t h e

d e t e c t i o n of t h i s r e a c t i o n , s i n c e the c t - p a r t i c l e e n e r g i e s expec ted fo r t he

(n,ya> p r o c e s s l i e between t h e e n e r g i e s of two a - p a r t i c l e s groups from the

-90-

(n,a) r eac t ion , leading to the f i r s t excited s t a t e (сц) and the ground s t a t e (cc0) of the f ina l nucleus l l t 0 Ce, separated by an energy gap of about 1.6 MeV,

Macfarlane J2J has reported the detect ion of the r eac t ion -14 3Nd(n,yet) l t | 0Ce with thermal neut rons . The thermal cross sec t ion i s due to civ brmnd s t a t e of 14t+Nd with the spin and p a r i t y 3 .

We have car r ied out an experiment with resonance neutrons on the fas t pulse reac to r s IBR-30 using the t ime-of - f l igh t method and r e g i s t e r i n g a - p a r t i c l e s with an ionisa t ion chamber | з | in the resonance of 55.3 eV with J = A . An enriched 43Nd sample (83.2%) with a thickness of 2.2 mg/cm2

was i r r a d i a t e d for 250 hours.

The ot-part icle spectrum for the resonance 55.4 eV a f te r deduction of back­ground i s shown in F ig . 1. The r e l a t i v e bad energy reso lu t ion i s mainly due to the thick sample, which had to be used because of the small cross sec t ion of the reac t ion under cons idera t ion . Due to the spin and p a r i t y requirements imposed on a—decay, the t r an s i t i on from the k resonance to the 0 ground level of 1 ^Ce is forbidden. As a consequence the spectrum contains only a i - p a r t i c l e s from t r a n s i t i o n s to the f i r s t exci ted s t a t e of

^Ce with an energy E a and a - p a r t i c l e s which are a t t r i b u t e d to the (n,ya) r eac t ion . The experimental spectrum has been analysed by a l e a s t square f i t program, using the experimental shape of the a.\~ spectrum and the t h e o r e t i c a l shape of the a-spectrum from the reac t ion * %d(n,ya) 1 ^"Ce. The influence of the sample thickness and the reso lu t ion of the de tec tor have been taken i n t o account. The parameters for these ca lcu la t ions have been received by analysing the spectra of a - p a r t i c l e s from the (n,ct) r eac t ion with thermal neut rons . The zero hypothesis of a t t r i b u t i n g the en t i r e experimental spectrum to the (n,a) reac t ion only was re jec ted on a leve l of confidence of 1%. Detai ls of the experiment and the above ana lys is are reported in paper [ 4 | . The f i na l r e s u l t s in terms of p a r t i a l widths are given in Table 1.

- 9 1 -

ТаЫе 1

E eV n

J17 Г eV Г eV yet

5 5 . 3 4~ ( 0 . 6 ± 0 . 4 ) . l ( f 7 ( 1 . 1 + 0 . 8 ) . 1 0 ~ 7

Bound l e v e l 3~ - ( 0 . 8 ± 0 . 2 ) . 1 0 " 7 Ж )

Value obtained from the r e s u l t s of paper [2| using On,ao and Г from paper | 5 J .

]_: Alpha-par t i c le spectrum from the resonance 55.3 eV of 14I,Nd. n -channel number, E - energy of a - p a r t i c l e s [MeV] , N - counts per channel, histogram - experimental count curve a - alpha p a r t i c l e s from the r eac t ion (п ,сц) , . curve b - alpha p a r t i c l e s a t t i bu t ed to the reac t ion (п,уи) , curve с - sum of a + b .

-92-

On the basis of the R-matrix theory the theoretical spectrum of a-particles

W (E ) from the reaction (n,ya) has been calculated using the following yctv a

assumptions (see Ref. |4 [ ) : 1) Between the neutron capture state and the intermediate state emitting

an a-particle only one y-transition takes place.

2) The total widths of the intermediate states are equal to the average

experimental gamma width at the neutron binding energy.

3) Absolute values and energy dependence of a-widths have been calculated

on the basis of the optical model.

4) The par t ia l widths for gamma transitions from the neutron captare state

to an intermediate state are expressed in terms of Weisskopf units

divided by hindrance factors HF.

So

va v оГ 2тгГ (В ) i у П

^ ( ^ , Л ^ н ^ Х ) / н г ^ Х ) 1 5 Т пл ^ ( Е „ ) (1)

J a a

where J. are the spins and parities for the neutron capture state and thie Л. л,

intermediate states \^~; E the mean energy of alpha particles from the (п,усО reaction in a small energy interval U<<E , Г (В ) the average total gamma width at the neutron binding energy В , S the Weisskopf estimation for y-transitions with the energy from the neutron capture state with J. to a final intermediate state with J,^.» EX stands for electric and MA for

Afi' magnetic transitions with the multipolarity A; HF are the hindrance factors for the respective y-transitions and TjAfi the transmission coefficients for a-particles with angular momentum £. and energy E . The theoretical spectrum W ( E ) includes the sum of transitions with different multipolarity

of the electric or magnetic type, since the intermediate states Xfi can be

of any spin and parity. But one makes a certain selection, comparing the shape

of the experimental spectrum from work \ l \ , which has a good energy resolution,

with the theoretical spectrum W ( E ) calculated under different assumptions

for the type of y-transitions. As a result of this comparison one may con­

clude that only El and MI transitions give an important contribution.

Г3-Comparing the experimental value of the ratio W = Jf=-, obtained from Table 1

yet (0.3<W <3) with theoretical values calculated under the assumption of

P FT Ml only El transitions <X.-5) and only Ml transitions (W™, =0.8) one may con­clude that the majority of transitions are of the Ml type.

-93-

Using W (E ) from formula (J) integrated over E and experimental data yet a a of Table 1, lower limits for the hindrance factors HF have been calculated under the assumption that y-transitions are only of the El or Ml type. The results are given in Table 2. The uncertainties connected with the above-mentioned assumptions and the choice of parameters used in optical model calculations may change the values of HF by about one order of magnitude.

Table 2

J* HF(E1) HF(M1)

3"

4" 2x106

4xl05 2х10ц

lxlO4

A comparison of our results with the results of Lobner [6J for y-transitions between low lying levels (HF(E1) = 102+10^) yields, that at least for El transitions the hindrance factors in a region of high level density seem to be stronger than in the region of small excitation energies. Nevertheless, the deduced values of hindrance factors seem to be reasonable from the point of view of the new semimicroscopic approach to the structure, of neutron resonances, developed by V.G. Soloviev at al. [7

- 9 4 -

R E F E R E N C E S

J . B l a t t and W. Weisskopf, T h e o r e t i c a l Nuc lea r P h y s i c s , New York, 1952.

N . S . Oakey and R.D. Macfa r l ane , P h y s . L e t t . , 26B (1968) 662.

Yu.P. Popov, M. P r z y t u l a , K.G. Radionov, R.F . Rumi, M. S t e m p i n s k i ,

W.I . Furman, J a d e r n a j a P h y s i c a , _1_3 (197) ) 9 1 3 .

P . Win iwar t e r , K. N iedzwiedz iuk , Yu .P . Popov, R.F . Rumi, V . I . S a l a t s k y ,

V.G. T i s h i n , W.I. Furman, Report JINR, Dubna, P3-6754 (1972) .

K. Okamoto, N u c b P h y s . Al4l (1970) 193.

K.E.G. Lobner , P h y s . L e t t . , _26B (1968) 369.

V.G. Soloviev, L.A. Malov, "Particles and Nucleus", vol. 3, part 4,

Dubna, 1972.

- 9 5 -

THE MASS DISTRIBUTION OF NEUTRON INDUCED FISSION

239 FOR ^ 7 P u AT THE 0 . 2 9 7 eV RESONANCE

P.H.M. VAN ASSCHE (S.C.K./C.EJ., Mol) G. VANDENPUT, L. JACOBS, J.M. VAN DEN CRUYCE and H- SILVERANS

(Physics Department, University of Leuven)

1. INTRODUCTION

In this experiment it has been tried to determine the mass distribution of the fission products from the neutron induced fission

239 of Pu at the 0.297 eV resonance. This has been achieved by com-239

paring the gamma intensities of Pu targets activated in respecti­vely thermal and epi-Samarium neutron fluxes- The identification of fission products reposes only on the observed gamma energies and half-lives, without applying any chemical separation on the Pu-targets.

2. EXPERIMENTAL METHODS

The epi-samarium irradiation has been performed under a 2 0.29 g/cm Sm cover; according to ref. (68 PS) this results in a cut-off around 0.25 eV, with more than 90& of the fissions being due to the 0.297 eV resonance.

The samples are 10 mg Pu/Al alloys with 2.Ш Pu-metal with 239 8

SJ>% enrichment in Pu. A fission density of 7 x 10 has been reached. 3 Gamma spectra are taken with a 20 cm active volume coaxial

Ge(li) detector, made by Dr. P. Fettweis (S.C.K./C.E.N.); an energy resolution of 1-6 keV at 100 keV and 2-7 keV at 1 MeV has been obtained. The intensities are measured at different moments after the end of the irradiation, starting from 10 m decay time until a few weeks decay time. The variations in mass distribution are deduced then from the comparison of these intensities; both the thermal and epi-Sm experiments are performed in absolutely identical conditions, as concerning the targets, gamma detectors, activation and measuring

tines etc. This way any correction, th.it otherwise could be intro­

duced, was avoided. This method has been applied previously to the

neutron induced fission of U, see refs- (ó9 VA) and (70 PO).

5. RESULTS

At the moment fission products of following mass numbers

have been observed : 87, 88, 97, Ю 5 , 107, 111, 115, 127, 128, 129, 140 and 149. Following information is also present in the data but has not been analysed at the moment :

- fission products with gamma energies below 170 keV - gamma spectra taken after more than 4 days decay time - most information on mass numbers with a thermal fission yield

larger than 2#. Table 1 contains detailed information on the observed mass

numbers; for each of them the fission products (column 2), the half-life (column 3) the observed gamma transitions (column 4) and the ratio Ïepi-Sm/Yth (column 5) are given. The latter ratio has been normalised

to unity for A = 97- The results are displayed in Fig. 1, together 239T with the mass distribution for the thermal neutron fission of

taken from (70 FL).

Pu,

TABLE 1 : The variation of mass distribution for neutron resonance.

239 Pu at the 0.297 eV

Mass number Fission product Half-life EY (keV) Yepi-Sm EY (keV) Tth

37 Kr 81 m 402-7 0.899 ± 0.030 38 Kr 3 h 196.2 0.973 i 0.038

97 Nb 74 m/17 h 65&-2 Zr 17 h 743.3 1.000 £ 0.012

105 Rh 36.5 h 306.2

Eh 4.5 h 724.4 0-992 +_ 0.014

107 Rh 21 m 302.6 0.935 +. 0.037

111 Ag 6.7 d 341.0 0.771 ± 0.025

115 In 35 h/4.5 h 336.0 0.659 ± 0.045

127 Sb 3.9 d 685.7 0.819 ± О.О56 128 Sb 50 m/10 m 754.2 0.940 + 0.033 129 Sb 4.4 h 812.6 О.998 + 0.025 i4o La 12 a/4 o h 487.2,1595-3 1.010 _+ 0.025 1 9 Pm 2.2 d 284.8 O.980 +_ О.О36

-97-

k. DISCUSSION

Significant variations of the mass-distribution for epi-Sm 2^9 induced fission of ' Pu are already observed for at least 6 mass

numbers. Detailed information is present for the change in symmetric fission yield. A decrease in symmetric fission by about a factor of 2 has been observed in (71 TO) with a fragment kinetic energy detection; due to its inherent mass resolution such an experiment cannot be compared directly to our results, but the observed effect goes at least in the same direction. Besides, this experiment determines a "post-neutron" mass distribution while a fragment kinetic energy measurement leads to a "pre-neutron" one. A relative radiochemical determination

115 of the Cd yield at the 0.297 eV neutron resonance by Regier et al. (б0 RE) showed a decrease of a factor of 3; here again the effect is in the same direction. The Sm cut-off energy depending sensitively on filter thickness_and reactor spectrum, it may at least be stated that

(Sr¥nel the differemeWariations in the mass 115 yield in both experiments is

partly due to these experimental conditions.

The results from this experiment also point to a narrower

mass distribution at the 0.297 eV resonance. This can be related

to the increase of 0.75 ,+ 0.05 MeV in average total kinetic energy, "™ 239 observed in (71 Ï0) for the Pu fission by Sm-filtered neutrons.

R.B. Regier, W.H. Burgue, R.L. Tromp and B.H. Sorensen, Phys. Rev. j m (1960) 2017

F. Pistella, Nucl. Sci. Eng., 3^_(1968) 329

P.H.M. Van Assche, M. De Coster and CI. Brandt, in procee­dings of the International Conference on Radioactivity in Nuclear Spectroscopy, ed. J. Hamilton (Nashville, 19^9) 573-

70 FL K.F. Flynn and L.E. Glendemin, A.N.L. - report 77^9 Ü970)

71 TO J. Toraskar and E. Melkonian, Phys. Rev. 4C_ (1971) 2б7-70 PO P. Popa, M. De Coster and P.H.M. Van Assche,

Nucl. Science Eng. 3>9 (1970) 50.

REFERENCES

60 RE

68 PS 69 VA

- y t -

Pigure caption

F i g . 1. : Up£.e£ 2,art__: raass d i s t r i b u t i o n of f i ss ion products 239 for Pu f i ss ion with thermal neutrons;

JLower. J>art__: r e l a t i v e change of t h i s mass d i s t r i b u t i o n

for f i s s ion with epithermal neu t rons .

10 ,

10 Mass 1 I distribution IV.) 239

Pu(n,h .f) | .« • •

• • • ••

•

4

•

• t

•

• «

• • • •

•

» •

• *

• •

• *

*

*

•

• *

•

at ' at • • •

•

• • *

* • • •

• , , Yepi-Sm (u297eV)

Ylh •

u •

u

1J0

0.9

m

1

u

1J0

0.9

1 1

{ { 1

08 -f I

07

I I Mass number

f 1 — ^

-J 00-

NEUTRON MULTIPLICITY MEASUREMENTS ON RESOLVED FISSION 2 3 S 2 39

RESONANCES OF U AND P u J. P . Theobald , J, A. War t ena , H. Weigmann, R. Werz Cen t ra l Bureau for Nuc lea r M e a s u r e m e n t s , Geel (Belgium)

F . P o o r t m a n s SCK-CEN, Mol (Belgium)

ABSTRACT Neu t ron induced f i s s ion events emi t t ing 2, 3, 4 o r 5 n e u t r o n s have different cont r ibu t ions to f i s s ion y ie lds r e c o r d e d with double and t r i p l e neu t ron co in­c idence s igna ls a s a function of incoming neu t ron ene rgy . Th i s fact can be u sed to s e a r c h for v a r i a t i o n s of n e u t r o n mul t ip l i c i t i e s in f i ss ion r e s o n a n c e s , in p a r t i c u l a r in r e s o n a n c e s of different channel sp ins .

*> V С

In the case of U no difference in fission neutron numbers for 3 and 4 levels has been detected above the experimental e r ro r of ± 1. 5%.

239 In the case of Pu there is also no clear correlation with the spin but a trend, that a lower neutron multiplicity goes with small Г, values, an effect already found by D. Shackleton et ai .

— 101 —

INTRODUCTION

Since about 19 68 the i n t e r e s t of e x p e r i m e n t a l i s t s and t h e o r i s t s concerned with n u c l e a r f i s s ion i s d rawn to the s tudy of shel l ef­fec t s , which V. St ru t in sky had p r ed i c t ed in his t h e o r y of nuc lea r deformat ion . These deve lopment s switched e m p h a s i s away f rom inves t iga t ions in the e a r l y s ix t i e s , which a t t empted to find a d e ­pendence of the f i s s ion f r agmen t m a s s , the i r k inet ic ene rgy and the i r exc i ta t ion ene rgy d i s t r i bu t i ons upon the spin of the incoming neu t ron channel . The c o r r e s p o n d i n g m e a s u r e m e n t s however yielded conflicting r e s u l t s and th is s i tua t ion h a s not changed, although r e ­cent ly in s e v e r a l l a b o r a t o r i e s t h e s e s tud ies a r e rev iv ing .

The idea behind t h e s e e x p e r i m e n t s was A. B o h r ' s sugges t ion that a nuc leus caused to f i s s ion by neu t ron cap tu re m a y u s e up m o s t of i t s exc i ta t ion e n e r g y in deformat ion , leaving only a few p o s ­sible quantum s t a t e s - ca l led f i s s ion channels - ava i l ab le at t he top of the f i s s ion b a r r i e r of the t r a n s i t i o n compound nuc leus . It •was a s s u m e d that these f i ss ion channe ls d e t e r m i n e m a s s and ene rgy d i s t r i bu t i ons of the f i s s ion f r a g m e n t s . If neu t ron induced f iss ion r e s o n a n c e s of different spin decay through different f i s ­sion channe l s a spin dependence of f ragment m a s s , k ine t ic , and exci ta t ion e n e r g y d i s t r i bu t ions i s qua l i ta t ive ly pos s ib l e . In A. B o h r ' s p i c tu re the t r a n s i t i o n s t a t e s at the top of the f iss ion b a r r i e r r e s e m b l e low-ly ing s t a t e s of the unexci ted compound n u c l e u s . They a r e e s s e n t i a l l y c h a r a c t e r i z e d by the i r K-quan tum n u m b e r s . If t h e r e is a c o r r e l a t i o n be tween the r e s o n a n c e spins (I ± 1/2), w h e r e I is the t a r g e t n u c l e a r spin, and the К quantum n u m b e r s of the t r an s i t i on s t a t e s , the above ment ioned spin d e ­pendence of m a s s k ine t ic , and exci ta t ion ene rgy i s in p r inc ip le a c c e s s i b l e for c a l cu l a t i ons .

The d i s c o v e r y of the double humped f iss ion b a r r i e r p red ic t ed by V. S t r u t i n s k y h a s however weakened the i m p o r t a n c e of the t r a n s i t i o n s t a t e s on the top of the f i r s t f i ss ion b a r r i e r . It is quite p o s s i b l e tha t compl i ca t ed n u c l e a r s t a tes built upon the s e c o n d a r y m i n i m u m cause a s t rong К band mixing and that t r a n s i t i o n s t a t e s on the top of the second b a r r i e r , which i s s e v e r a l 100 KeV lower t han the f i r s t , have a c o n s i d e r a b l e h igher l e v e l dens i ty . This s i tua t ion i s ske tched in f igure 1.

With t h e s e p r e l i m i n a r i e s taken c a r e of i t is quite unde r s t andab le that the e x p e r i m e n t a l data show a m u c h lower spin dependence of f ragment p r o p e r t i e s t han it w a s a s s u m e d before 19 68,

- 102-

EXCITATION ENERGY AND NEUTRON MULTIPLICITIES

V a r i a t i o n s in the r a t i o s of k inet ic to exc i ta t ion e n e r g i e s of the f i s s ion f r agmen t s r e f l ec t t h e m s e l v e s in v a r i a t i o n s of the i n t en ­s i t i e s of deexc i t a t ion p r o c e s s e s after f iss ion. One of t h e s e p r o ­c e s s e s i s the n e u t r o n e m i s s i o n . It is however not c l e a r , if it is the m o s t s ens i t i ve one. N e v e r t h e l e s s , if t h e r e i s for a given i so tope a sample of sp in a s s i g n e d neu t ron r e s o n a n c e s , it is p o s s i b l e to i nves t i ga t e the ques t ion , if for the two r e s o n a n c e spin f ami l i e s the p r o b a b i l i t y d i s t r ibu t ion of f i ss ion even ts emi t t ing n =0, 1,2,3,4,or 5neutrons i s different or not . To th i s end two types of m e a s u r e m e n t s come into cons ide ra t i on :

1) the count of al l n e u t r o n s emi t t ed in a f i s s ion event) 2) the count of n e u t r o n co inc idences r e c o r d e d pe r f i s s i o n ) ^ . the l a t t e r method h a s been used at the CBNM l i n e a r a c c e l e r a t o r l a b o r a t o r y , b e c a u s e a m u l t i c h a m b e r f i s s ion n e u t r o n d e t e c t o r has been u s e d t h e r e s ince s e v e r a l y e a r s for t ime-o f - f l igh t e x p e r i m e n t s . This i n s t r u m e n t i s sui ted for neu t ron mu l t i p l i c i t y m e a s u r e m e n t s , in p a r t i c u l a r , a s i t s p r o p e r t i e s a r e wel l known f rom p rev ious work .

THE M U L T I P L E COINCIDENCE METHOD

F i s s i o n yie lds a r e r e c o r d e d a s a function of neu t ron t ime-o f - f l igh t , The s top s igna ls a r e given by double and by t r i p l e neu t ron coin­c idence s igna l s . In th i s way two f i s s ion s p e c t r a a r e obtained, which differ if the n e u t r o n mul t ip l i c i t y is not cons tan t ove r the r e s o n a n c e s with different s p i n s . R e s o n a n c e s with m o r e n e u t r o n s p e r f i s s ion a r e enhanced in the run r e c o r d e d with the t r i p l e c o i n ­c idence s ignals r e l a t i v e to those with l e s s n e u t r o n s than the a v e ­r a g e . In o r d e r to d e s c r i b e t h i s method in a m o r e quant i t a t ive m a n n e r one has to c a l cu l a t e two th ings

1) the p robab i l i ty d i s t r i bu t ion of f i s s ion events emi t t ing n n e u t r o n s (n = 1, 2, 3, 4, 5) for the two i so topes 235u a n d 239 p u c h a r a c ­t e r i z e d by the i r v v a l u e s , the a v e r a g e n u m b e r of n e u t r o n s emi t ted p e r f i ss ion,

2) the p robab i l i t y to de tec t an s fold co inc idence in к d e t e c t o r s with a to ta l efficiency с p e r neu t ron , when n n e u t r o n s a r e impinging upon t h e s e d e t e c t o r s .

The f i r s t d i s t r ibu t ion i s g iven by T e r r e l l ' s r e l a t i o n s h i p )

(n -v + r + Ь) . а

pn-:5-=r / -»(-£>*• a)

-103-

in which a measures the width of the total fragment excitation energy distribution and b is a small correction. Their values have been obtained by a fit to experimental data: a = 1.08, b « 10- 2 . The latter quantity has been derived in a special report ) . It is expressed by the formula

n r j ] Р(пД, s | e ) = Г S( j j S j k) C(n, j) •* (2)

with H = — and J j ] = ( H ) j : £ j

C(n, j) gives the number of combinations, when distributing n neutrons in j detectors

c(n,j) = (. _1): Jr I - D V ; ^ - ! ) 1 1 * 1

L = 0

S(j, s,k) is the probability to detect in the case of e < 1 s coincidences out of j possible ones.

S(j .s ,k) = {*) - -( •*_-?_> -s Г к 1

я

For the CBNM multichamber neutron detector к = 4 and e = 13. 3%. For this case the contributions of fission events emitting 2, 3, 4 and 5 neutrons to the double (D) and triple (T) coincidence runs have been calculated by a convolution of formulas (1) and (2). The result is shown in figure 2 for the two isotopes considered. The multiple coincidence method in the present form allows to detect variations of "v from resonance to resonance i n the order of A"v /~v = 3%. If many resonances are spin assigned this r e ­lative e r ro r will be considerably smaller.

RESULTS OF THE MEASUREMENTS

с As experimental details will be published elsewhere ) , only some resul ts of the measurements are presented here . For several resonances labelled by the index i resonance integrals

J . = / fff (E) dE

- 3 0 4 -

have been computed for the D and the T runs and r a t i o s

J- <D) R. = —

1 J . ( T )

have been d e t e r m i n e d .

!Г31_е_Е^??-0-.£--?-У-+11- ( s e e Table I ) F o r some r e so lved r e s o n a n c e s below 40 eV incoming neu t ron ene rgy the channel spin J = I + 1/2 i s known by p rev ious e x p e ­r i m e n t s )6, 7. In co lumns A and В the r a t i o s R^ n o r m a l i z e d with R a r e given. In co lumn A the r a t i o s have been d e t e r m i n e d af ter for each r e s o n a n c e a base l ine has been sub t r ac t ed i n t e rpo l a t ed f rom the r e s i d u a l f i s s ion be tween the r e s o n a n c e s . In column В the s u b t r a c t e d b a s e l ine i s the background m e a s u r e d with the black r e s o n a n c e technique . The r e s u l t s in both co lumns a g r e e within the e x p e r i m e n t a l e r r o r . Unre so lved r e s o n a n c e s and r e s o n a n c e s , for which t h e i r e r r o r on R./K- caused by the sub t r ac t ion of the base l ine in the D run exceeds 0. 0 5 have been omi t ted . Taking the r e so lved r e s o n a n c e s to which the spin h a s been a s s igned , the weighted a v e r a g e of R . / R . can be d e t e r m i n e d for the two channel sp ins J

J71 R. l

R .

A В

з" 0 .9988+0.0084 0.9921+0. 0099

4" 1. 00 54+0. 009 5 1 .0146+0.0086

It t u r n s out that the r a t i o s a r e equal within 1. 5%. This e r r o r is due to the s m a l l number of r e s o n a n c e s to which the spin could be a s s igned with m e t h o d s independent f rom the f iss ion neu t ron mul t ip l i c i t y and due to th& e r r o r caused by the d e t e r ­mina t ion of the b a s e l ine under ly ing the r e s o n a n c e s b e c a u s e of background and r e s i d u a l f i ss ion con t r ibu t ions .

-105-

239 The c a s e of Pu+n

R e c e n t l y D .Shack le ton et a l . ) have r e p o r t e d on fluctuations of the f i s s ion n e u t r o n mul t ip l i c i ty and p rompt у - r a y ene rgy for r e s o n a n c e neu t ron induced f iss ion of ' P u . They obse rved an a n t i c o r r e l a t i o n be tween f luctuat ions of these two p a r a m e t e r s , which they a t t r i bu t ed to the ro le of the (n, у , f) r eac t ion . This p r o c e s s i s p ronounced in r e s o n a n c e s , for which the total f iss ion wid ths Tf is so s m a l l a s to be c o m p a r a b l e with the width Г of the (n, у , f) r e a c t i o n . In the appendix to th i s paper the Г * va lues a r e e s t i m a t e d for the 1 r e s o n a n c e s to be about 4 meV. In o r d e r to t e s t Shack le tons ' r e s u l t s with the p r e s e n t method the r a t i o s I . (T) / l j (D) (unfortunately we took the r e c i p r o c a l va lue of that u sed in the case of ^35xj) have been de t e rmined . In f igure 3 the r e l a t i v e dev ia t ions of R^ = I ^ T j / l ^ D ) from the a v e r a g e < R^ > , tha t i s to say (Rj - < R i > ) / < R . > i s plot ted aga ins t p£. T h e r e i s obviously a t r end that the lower neu t ron mul t ip l i c i ty goes with s m a l l If va lue s , but t h e r e a r e r e s o n a n c e s with sma l l Tr v a l u e s , for which I^(T)/l.(D) i s r e l a t i v e l a r g e . Consequent ly the p r e s e n t e x p e r i m e n t suppor t s the r e s u l t s ob ­ta ined by D .Shack le ton only to some extend. It should however be e m p h a s i z e d that h i s me thod i s the counting of a l l neu t rons af ter a f i s s ion event in a Gd loaded liquid sc in t i l l a to r tank. This me thod should be m o r e r e l i a b l e , if s y s t e m a t i c e r r o r s could be excluded.

A spin dependence of the r a t i o s I-(D)/l-(T) could not be d e ­duced f rom the p r e s e n t e x p e r i m e n t . The r e s u l t depends on the type of spin a s s i g n m e n t that i s u s e d . If one takes only 0 l e v e l s into account , for which Г > 350 meV and 1 + l eve l s , for which Г < SO m e V , the neu t ron mul t ip l i c i ty s e e m s to be s l ight ly h i g h e r for 0+ l e v e l s .

CONCLUSION

Spin effects on f i s s ion neu t ron mul t ip l i c i t i e s a r e ce r t a in ly v e r y weak. F r o m t h e o r e t i c a l point of view s t rong К mixing of diffe­ren t t ypes of " t r a n s i t i o n s t a t e s " or a lack of c o r r e l a t i o n between the neu t ron channel spin J and К quantum n u m b e r of the t r an s i t i on s t a t e s could be the r e a s o n s . Most p robab le t h e r e i s s o m e evidence for the (n, у , f) p r o c e s s f rom n e u t r o n mu l t i p l i c i t y m e a s u r e m e n t s a s pointed out by Shackle ton et a l .

-106-

APPENDIX

•f 239 E s t i m a t e of the Г ,- v a l u e s for 1 l eve l s in P u + n li

240 Below the neu t ron binding e n e r g y В of P u t h e r e a r e two t r a n s i t i o n s t a t e s , which a r e of i n t e r e s t in the p r e s e n t context , when one c o n s i d e r s у - с * е с а У 8 °^ ЪЪ.е E l type f rom 1 + l e v e l s into f i ss ion channe l s )9

TT TT -• ** ^ » 1) the ( K ; I ) = ( 0 ; 1 , 3 , 5 ) m a s s a s y m m e t r y v i b r a t i o n a l

s t a te , about (дЕ) °~ ~ 1 MeV below В and 2) the ( K ; l ) = ( l ; l , 2 , 3 ) bending v i b r a t i o n a l s t a t e ,

about ( Д Е ) 1 - = 0. 5 MeV below В . n

If we a s s u m e a (2 I + l ) dependence of the l eve l d e n s i t i e s and t h e r e b y of the width Г f for populat ion of the definite I - s t a t e s the E l t r a n s i t i o n s T r o m 1 + l e v e l s have the s t a t i s t i c a l weights

(2 I17 + 1) = 1 3 and 5 for ITT = o- 1- and 2~ In the K n = 0 f i ss ion channel band 0 and 2 l e v e l s do not exis t , and the 1+ -» 1- t r a n s i t i o n h a s the weight 3 : 9 = 0. 3

F o r the (К11" ; I ) = ( 1 " ; I n ) f i s s ion channel I71 = l " , 2" , 3" , . . . l e v e l s do ex is t , but only the 1 and 2~ l eve l s a r e populated by E l decays f rom a 1 + s t a t e . Consequent ly the 1 -» ( l~ , 2") t r a n s i t i o n s have the s t a t i s t i c a l weight 8 : 9 = 0, 89 .

239 The P u to ta l r a d i a t i v e n e u t r o n cap tu re widths is of the o r d e r p = 42 meV. F r o m the above c o n s i d e r a t i o n s i t follows that t h e components of the r a d i a t i v e wid ths populating К = 0" and 1 bands a r e

Г Y (K= :0-•!; = 0. 3 г = 14 meV

and Г

Y (K= = 1" ) = 0. 89 Г

Y = 37 m e V

As the у -decays into the f i s s ion channe ls do not cover the e n e r g y r ange of the n e u t r o n binding ene rgy l ike the u s u a l c a p t u r e y-va.ys, but r a t h e r the ene rgy r a n g e s

(ДЕ)° = 1 MeV and

( Д Е ) 1 " = 0. 5 MeV, the e n e r g y dependence of the у t r a n s i t i o n s and level d e n s i t i e s have to be t aken into account . This i s done -with the he lp of the cons tan t t e m p e r a t u r e s t a t i s t i c a l mode l , in which the cap tu re width is equal

-107-

V C " / f № ) ' P("-Od« (I)

with p (U) = exp ( — )

U is the binding energy minus the pairing energy gap and T is the nuclear temperature U and.T a r e estimated with T. 5\ Newton's level density formula J1 ° to be

U = В - 1. 34 MeV = 5 . 1 1 MeV and n T = -г - | U . b with

b = 2. 26 |MeV, consequently T = 0 . 4 5 MeV

"With these quantities formula I yields Г = с • 0. 242

Y 0 -If the integral is taken over ( ДЕ) = 1 MeV instead of U

Г° " = с . 0.0453 = 0. 187 Г Y

and over (ДЕ) = 0 . 5 MeV

Г = с • 0.00652 = 0. 027 Г Y v

Under the assumption that after the у -decays into the fission channels, fission occurs necessari ly, one can identify the com­ponents of Г ° " and Г populating К = 0" and 1" bands with the corresponding Г f values and gets

Г у £ (K=0-) = 0. 187 • Г (K=0-> = 2. 6 meV

and

r Y f ( K = l " ) = 0 . 0 2 7 - Г у ( к = 1 _ ) = 1 . 0 m e V

From which follows, that Г , ca 3.6 meV.

Yf

-108-

R E F E R E N C E S

1) H. R. Bowman and 5. G. Thomson Univers i ty of Cal i fornia Repor t , UCRL-5038 (19 58).

2) L . W . W e s t o n and J. H. Todd P r o c e e d i n g s of the 3rd Conference on Neut ron C r o s s 5ec t ion and Technology, p. 861, (1971).

3) J. T e r r e l l , P h y s . Rev. 108, p. 783(1957) .

4) J . P , Theobald, J . A. War t ena , and W. Kola r R e p o r t EUR 4829e, B r u s s e l (19 72),

5) J . P . T h e o b a l d , J. A. War t ena , R . W e r z and F . P o o r t m a n s , Jou rna l of Nucl . Energy , in p r e s s .

6) F , P o o r t m a n s , H. C e u l e m a n s , E. Migneco, and J. P . Theobald , 2nd IAEA Conference on Nuc lea r Data for R e a c t o r s , Hels inki , p . 449, Vol. I (19 70).

7) F , Corvi , M. Stefanon, C. Coceva, and P . Giacobbe, P r o c e e d i n g s of the E u r o p e a n Conference on Nuc l ea r P h y s i c s , Aix en P r o v e n c e , paper I. 18, (19 72).

8) D. Shackleton, J. Trochon , J . F r é h a u t , and M. Le B a r s , P h y s . Le t t . , 42B, p . 344(19 72).

9) J . E. Lynn, Neu t ron Resonance R e a c t i o n s , Oxford 19 68, p, 39 6.

10) T. P . Newton, Can. J. of P h y s i c s , 34, p. 804(19 56).

-109-

TABLE

E R i / R i

(£fr) A

8.79 1 . 04 + 0 .05

12.39 1 . 00 + 0.02

15 .40 1 . 00 ± 0.03

16. 08 1 . 04 ± 0.03

16. 69 1. 05 ± 0.03

18.07 0.99 + 0.03

19.31 0.99 ± 0. 02

2 1 . 08 1 . 03 ± 0.04

22.94 1. 00 ± 0.02

23.42*1 0 .97 + 0. 03

23. 6 5 i

24.32 0,98 + 0.03

2 5 . 2 0 1 0 .95 + 0 .04

25. 50 J 26.48 0.99 + 0.03

27 .84 1. 07 ± 0.04

30. 6 "1 0.9 3 + 0. 04

30.85 J 32. 07 0 .98 + 0.03

33. 53 0 .98 + 0. 03

35 .20 1.06 ± 0. 03

39 .40 1 . 00 + 0. 03

J Б

1. 01 + 0. 05

1. 00 + 0 . 0 2

0. 99 ± 0 . 0 3

1. 01 ± 0 . 0 3

1. 04 ± 0 . 0 3

0. 9 4 ± 0. 03

1. 00 ± 0. 02

1. 03 ± 0. 04

1 04 ± 0 . 0 2

0 9 5 ± 0. 03 4

0 .96 + 0. 03 3

1. 00 + 0. 04

1. 00 + 0 .03

1. 01 + 0. 04

0.99 + 0 .04 4.

1. 01 + 0. 03 4 ' 0 . 9 8 + 0 . 0 3 4

1.05 + 0 .03 4 1.00 + 0 .03 3

— 110—

FIGURE CAPTIONS

Fig. 1: Level densities upon the fission ba r r i e r (qualitatively)

Fig. 2: Contribution of fission events with different neutron numbers to the double and triple coincidence runs

Fig. 3: Relative deviations of the rat ios of resonance integrals taken from the triple to those taken from the double coincidence run from the average ratio plotted as a function of rf values for " ° P u , (The Г, values a re these of Saclay). Because of the lower level density of 239p u

compared to 2 3 5 U the e r ro r on the data points are smaller than J; 0. 6%

- i i i -

Regions of high low high low

level densities and K-mixing

ЧУ

Fig.1 Deformation

2 • 3 ^ T 5 Number Fig.2

•112- A

О h o го

о НО

01

о о

CC < l

iet - 1 — \ 1 1—1 1 1 ! (—Г О 00 C£> чЗ* CM

О h-O

*

• e * •

~т—i—I—I—1—г -

О N v f Ю I I I

СО

ÏZ 1—(—1—г~ оо о I Т

— 113—

NEUTRON RESONANCE PARAMETERS OF 2 4 2 P u

F . Poortmans SCK/CEN, Б 2400 MOL, Bel gium

G. Rohr, J. P . Theobald and H. Weigmann Central Bureau for Nuclear Measurements

EURATOM, Geel, Belgium

G. J. Vanpraet ^ Rijksuniversi tair Cent rum, Antwerpen, Belgium

ABSTRACT: Capture, elastic scattering and total c ross section 242 measurements were performed on Pu below 1300 eV. The

neutron widths Г wereobtained for 71 resonances and the total n radiative widtKsr for 25 resonances. The s-wave strength

Y4.0 16 -4 function S =0 .89 n\i. x 10 a n c i the average radiative width _ о -0.1ч b

Г = Г 21.9 + 0. 4 (stat. ) + L. (syst . ) ] . The resonance para ­me te r s were used to calculate the fission widths Г, from the

1) fission c ros s section resul ts of G. F . Auchampaugh et al. . F rom these fission widths, the height of the second fission b a r r i e r is deduced: E n = 5. 18 MeV.

74? 74? NUCLEAR REACTIONS Pu{n, n), Pu(n, у ) ,

E = 20 eV - 1300 eV; measured CT .. a n, t n,Y

,*- deduced resonance parameters Г , Г Qnt n г п у enriched target .

-114-

1. INTRODUCTION 242 A study of the react ions of slow neutrons with Pu

is of in teres t for different r easons . The resonance pa rame te r s a re needed to establish the mass dependence of the s-wave neutron strength function Г / D above A = 240 and for the interpretat ion of the subthreshold fission c ross section r e ­sults obtained at Los Alamos ' and at Harwell . The neutron c ross sections a re also requested by reac tor designers and for the calculation o£ the production of heavier isotopes,

4) especially Curium,in reac tors

242 Little information has been published on Pu. Only

the neutron widths were obtained from total c ros s section m e a -5-8 \

surements below 400 eV ~ .

The present paper descr ibes the measurements of the

capture, elastic scattering and total c ross sections between

20 eV and 1300 eV. F r o m these experiments , the neutron

widths Г were deduced for 71 levels and the capture widths n Г for 2 5 levels .

Y Some pre l iminary resul ts were already communicated

a) at the "Nuclear Structure Conference in Budapest" (1972) . These resu l t s , however, were obtained only from capture and scattering experiments . Since that t ime, we did a more complete analysis of the data: the precision on the normalisation of the capture resul ts was improved and the scattering data were corrected for the absorption effect of the scattered neutrons in the sample. In addition t ransmiss ion experiments have been performed on a thicker sample than that previously used for the part ia l c ross section measurements , making it possible to analyse some more weak resonances .

-115-

2. E X P E R I M E N T A L DETAILS

A l l t h e e x p e r i m e n t s w e r e p e r f o r m e d a t t he CBNM

l i n e a r a c c e l e r a t o r ne t i t ron t i m e «of-flight s p e c t r o m e t e r with

a m e r c u r y cooled u r a n i u m t a r g e t a s ' he pulsed neu t ron s o u r c e .

The t o t a l amount of m a t e r i a l ava i l ab le w a s 4 .49 g ' P u O (on loan f rom USAEC) wi th the following i so topic

?%Л ?Ч*> ?Л0 compos i t i on : P u ( . 0 0 3 % ) , w P n ( .013%), P u (. 033 %), ~1 A *\ T А *Ъ ^\ Л A

P u (. 09 6%), ' * ' P u (99 .8%) and ' " "Pu ( < . 0005%).

The s c a t t e r i n g and c a p t u r e c r o s s sec t ion m e a s u r e m e n t s

w e r e p e r f o r m e d with the s a m e s a m p l e ( d i a m e t e r 8 3 . 1 m m , -4 t h i c k n e s s 1.82 10 a t o m s p e r b a r n ) . The s a m p l e w a s p r e p a r e d

by se t t l ing in a lcohol and canned under vacuum be tween two

a l u m i n i u m p l a t e s of a t h i c k n e s s of . 5 m m . F o r the t r a n s ­

m i s s i o n m e a s u r e m e n t , a t h i c k e r s a m p l e was used ( d i a m e t e r

14 m m , t h i c k n e s s 6 .08 10 a t o m s pe r b a r n ) .

The da ta co l lec t ion and p r o c e s s i n g w a s done us ing

the CBNM data acqu i s i t i on s y s t e m which c o n s i s t s of an IBM 1800 c o m p u t e r to which a r e in t e r f aced different 409 6

12) channel t ime -o f - f l i gh t a n a l y s e r s

2 . 1 . Sca t t e r i ng E x p e r i m e n t s

The s c a t t e r i n g e x p e r i m e n t s w e r e m a d e on a 30 m e t e r 3

flight pa th . The d e t e c t o r s y s t e m cons i s t ed of s ix He high

p r e s s u r e g a s e o u s s c i n t i l l a t o r s (LND type 800). The sample

was p laced in a tube which w a s filled with he l ium in o r d e r to

avoid n e u t r o n s c a t t e r i n g by a i r . The d e t e c t o r s w e r e placed a

at an angle of 102 . The m o s t i m p o r t a n t fac tor in the t ime-of -

flight r e s o l u t i o n was the flight path unce r t a in ty , due to the s ize

of the s a m p l e so that _\ E (F . W. H. M. ) / E is app rox iamte ly

2 x l 0 ~ 3 . The s c a t t e r i n g c r o s s sec t ion w a s m e a s u r e d r e l a t i v e

to Pb for which ,- = 1 1. 28 + 0. 6 ba rn ' . n —

- П 6 -

The backg round was m e a s u r e d with the b lack r e s o n a n c e

technique» Na (2 .8 keV r e s o n a n c e ) was u s e d a s a p e r m a n e n t

f i l t e r . The to ta l background v a r i e d f r o m 20% to 50% of the

s c a t t e r i n g yield due to the po ten t i a l s c a t t e r i n g of " Pu , O and

the Al canning . The r a w da ta a r e shown in fig. 1

T h e s e da ta w e r e c o r r e c t e d for self s c r e e n i n g and for

a b s o r p t i o n of the s c a t t e r e d n e u t r o n s . F o r th i s c o r r e c t i o n it w a s

a s s u m e d tha t any second i n t e r a c t i o n w a s an absorpt ion» The

s a m p l e w a s thin enough that t h i s a p p r o x i m a t i o n i s va l id except

for a few s t r o n g s c a t t e r i n g r e s o n a n c e s below 400 eV.

2. 2. Cap tu r e M e a s u r e m e n t s

The ca.pture m e a s u r e m e n t s w e r e p e r f o r m e d at a 60 m e t e r

flight path s t a t ion us ing a .Moxon-Rae type d e t e c t o r . The nomina l

r e so lu t i on v a r i e d be tween 1. 5 n s e c / m and 5 n s e c / m for di f ferent

e n e r g y r a n g e s .

The e n e r g y s p e c t r u m of the n e u t r o n s at the de t ec to r s ta t ion was m e a s u r e d with а В s lab v iewed by a Nal c r y s t a l ; the В

7 * - 1 / 2 (n, a ) Li c r o s s sec t ion i s a s s u m e d to v a r y a s E in the

e n e r g y r a n g e of i n t e r e s t . The abso lu te c a l i b r a t i o n of the p roduc t

d e t e c t o r efficiency t i m e s neu t ron flux w a s done by o b s e r v i n g

c a p t u r e in "b lack r e s o n a n c e s " at 5 .2 , 1 6 . 3 , 51 .4 and 70.9 eV

from a Ag s a m p l e . The r e s u l t of this ca l ib ra t ion is conf i rmed

by the good a g r e e m e n t be tween the r e s u l t s f rom the t r a n s m i s s i o n

m e a s u r e m e n t s and the cap tu re m e a s u r e m e n t s for s m a l l r e s o n a n c e s . As the a r e a under a r e s o n a n c e peak in the c a p t u r e c r o s s

sec t ion is p r o p o r t i o n a l to Г Г / ( Г +Г ), the neu t ron width Г n у п Y ~n

of a s m a l l r e s o n a n c e ( Г <? Г ) is d i r e c t l y obtained f rom the n у

a r e a a n a l y s i s of the c a p t u r e c r o s s sec t ion m e a s u r e m e n t . F o r all

the s m a l l r e s o n a n c e s , t h e r e is a v e r y good a g r e e m e n t between

the Г v a l u e s obtained from the c a p t u r e and t r a n s m i s s i o n e x p e r i ­

m e n t s .

-117-

Resonance analysis of the capture data was done with

a capture area analysis program due to Fröhner and Haddad '

which contains a Monte Carlo subroutine to determine the mul-

tiple scattering contribution to the capture area.

2. 3. Transmission Measurements

These experiments were done at a 30 meter flight path 3

station, using a He high pressure gaseous scintillator as trans­mission detector. The nominal resolution varied between 1. 5 nsec/m and 5 nsec/m. The total background was about 3% at 2 keV and Z% at 100 eV.

An area analysis of the transmission data was done using 15) a modified version of the Atta-Harvey program

3. RESULTS AND DISCUSSION

3. 1. Analysis of the Data

An area analysis was applied to the three experiments.

The area under a resonance peak in capture and scattering or

above a transmission dip in the transmission experiment is

independent of the resolution broadening and is a function of

the neutron width Г and capture width Г . An illustration n у

of the analysis is given in fig, 2 where the relation between Г and Г is shown for three typical resonances at 67. 6 eV

n у (Г < Г ) . 149. 6 eV (г « Г ) and 536.2 eV (Г > Г ).

n у n Y n V

The curves labeled with C, Sc and T are from the capture,

scattering and transmission experiments, respectively. The

total errors are also indicated. The resonance parameters

Г and Г are deduced from the intersection point of the two n Y

most precise curves. The errors on Г and Г are determined r n Y

so that all three experiments are consistent. These errors are

mostly larger than obtained from a pure mathematical analysis.

- 1 1 8 -

o The results from the analysis for E , Г , Г and Г = о у n ' n

Г / v E are given in table 1. The resonance energies E are deduced from the capture measurements. The weak resonances

marked with a) were only observed in one of the three experi­

ments and those marked with b) are probably double resonances.

3.2. Statistical Properties of Resonance Parameters

We obtained the following value for the average radiative

width: Г = [21.9 + 0.4 (stat. )± 1 (syst.) ] meV

This is rather low if compared to neighbouring even-even nuclei.

For instance, in U one has Г =24 meV ' *; on the other Y

hand, one has essentially the same level spacing parameter so 2

that the total radiative width is proportional to (B - Д ) (B = 18) binding energy and Д = 0. 67 MeV - pairing energy gap )

and should therefore be 12% higher for Pu than for U. Experimentally however, it is 9 % smaller.

The plot of the observed number of levels vs. energy is shown in fig. 3. If we suppose that the resonances at 504 eV and at 576 eV are single resonances, we obtain for the mean level spacing below 1 keV:

D = 17. 02 eV.

Fig. 4 shows the integral distribution for Г / Г for n n

all the resonances up to 1004 eV for which the average reduced

width Г = 1. 52 meV. Also shown on this figure are the calcu-П <y _

lated curves assuming a X distribution for Г with one and two n

degrees of freedom respectively.

As expected, the experimental data fit very well to the v = 1

curve corresponding to a Porter-Thomas distribution.

Figs. 3 and 4 both show that below 1 keV not many levels are

missed. The value of the s-wave strength function obtained

from the data is: S = r ° / D = . B 9 + ^ : f x l O - 4 о n -0. 1**

-119-

The e r r o r s define the 68% confidence i n t e rva l and w e r e c a l -19)

cu la ted a c c o r d i n g to ref. ' . F i g . 5 shows the sum of reduced

n e u t r o n wid ths E Г in function of energy , t oge the r with the s t r e n g t h function S = 0.89 x 10 . P r e v i o u s r e s u l t s obtained for S w e r e :

° - 4 4 (0. 72 + 0 .25) x 10 * (ref. 6), (0.9 5 + 0. 4) x 10~* (ref. 7), (0.99 + 0 .44) x 1 0 ' 4 (ref. 8).

The v a l u e s of the s t r e n g t h function for 230 £ A s 240 -4

a r e m o s t l y s l ight ly l a r g e r t han 1 x 1 0 . Opt ica l mode l c a l c u -20)

l a t i o n s p r e d i c t a peak in the s -wave s t r eng th function a round 242

A = 235 . The r e s u l t s for Pu give ex t r a weight to th i s p r e d i c t i

a l though the e r r o r s a r e s t i l l too l a r g e to r e a c h a definitive con­

c lus ion .

3 . 3 . F i s s i o n Widths Г, for the R e s o n a n c e s

G. F . Auchampaugh et a l . have m e a s u r e d the neu t ron i n -242 duced sub th re sho ld f i s s ion c r o s s sec t ion of Pu using an

u n d e r g r o u n d n u c l e a r explos ion a s neu t ron s o u r c e . These

a u t h o r s have publ i shed the f i s s ion r e s o n a n c e i n t e g r a l s Г Г

Af = 2 n 2g ) [

2 - L l , г т Г п + Г ^

(g i s the s t a t i s t i c a l weight f ac to r and X is the neu t ron wave length in uni ts of 2 тт ). The p r e s e n t e x p e r i m e n t a l lows us to

deduce f rom t h e s e f i s s ion a r e a s A-, the c o r r e s p o n d i n g f ission widths us ing the Г and Г da ta f rom tab le 1. The r e su l t i ng

n у Г , v a l u e s a r e plot ted in fig. 6 a s a function of neu t ron ene rgy

E . T h e r e is ev idence for two groups of f i ss ion r e s o n a n c e s

below 1 keV enhanced by c l a s s II l e v e l s at about 475 eV and 3) 762 eV. The l a t t e r l eve l was a l r e a d y found by G. D. J a m e s

F r o m ref. 1), one ge t s the m e a n l eve l spacing of the

c l a s s II l e v e l s — ,nn + 190 eV DTT = 600 , , - v

II - 1 1 ? cv

-120-

It is i n t e r e s t i n g to know the decay and sp read ing wid ths Г '

and Г * of the c l a s s II l eve l s in o r d e r to ca l cu l a t e the height 243 E of the second f i s s ion b a r r i e r for Pu, t he t h i c k n e s s of

B 21)

which i s known f rom s y s t e m a t i c s tud ies to be :

-Нщ « 0. 5 MeV (1)

T h e s e s t u d i e s a l s o had as a r e s u l t tha t in the m a s s r a n g e around 243 Pu the f i r s t b a r r i e r he ight Е д > E and А J3

I г • > r In th is c a s e '"'' /J the f i ss ion widths Г , о ' the compoun n u c l e a r s t a t e s u, ( c l a s s I l eve l s ) a r e given by:

Г = _ 7^-z ; у |j, = 1 . . . к (2) a f 2гг ( E _ E I x ) 2 + I ( r T ) 2

u, о ' 4

DT = c l a s s I l e v e l spacing к

Г ; = £ r , (3)

The l a r g e s t among the f i ss ion width of the c l a s s 1 l e v e l s c l o s e

to E = E i s app rox ima ted by:

from which it follows that

2DT _i

F r o m eq. (3) and (5) we obrain the following r e s o n a n c e p a r a

m e t e r s of the c l a s s II l eve l s at 475 eV and 762 eV:

E 1 1 = -J75 eV r' = 16 + 9 eV Г1 = 1. 4 + 0. 8 m e V о — —•

E n = 7 6 2 e V r f = 1 2 + 7 . eV r ' = 37 + 2 2 m e V о — —

-121-

Fig. 6 also shows the Lorentzian computed by using equations 2, ,?, 5- The curves have been normalized to the fission widths of the resonances at ^75 e^ and 7^2 eV and centered at these energies. -he individual Г .-values are expected to fluctuate

uf ground the Lorentzians according to Porter-ThoMas-distributions.

The Hill-Wheeler formula гп4Щ-~ л- (5-

together with В = 5-037 MeV = neutron binding energy for Pu yields the following value for E_:

E_ = 5.18 MeV В

This result is in good agreement with the one obtained from the 21)

systematic study (E = 5-01 MeV). As the height of the first barrier is E = 5.8 MeV, the condition E у Eg is fulfilled.

The penetrability through the inner barrier A is given by 1

PA 1 + exp '] A

The thickness of the inner barrier ft ч) can then be calculated in two ways. From statistical theory :

'. - • - m Equations (7) and (8) yield the result :

tfvO. = °-56 MeV From the mean fission width < Г „> of not enhanced fission

^ pf-' 00 resonances :

< r * > = — ^ ~ **•** ( 9 )

\ uf ' .00 о fj- А В

together with the value for P_ given by

ve find nw - О.65 MeV

-122-

Acknowledgements

The authors thank Prof. Aten and Dr. Nève de Mévergnies

for the continuous interest in this work. They are grateful to

Dr. Verdingh for the sample preparations and to the data-handling

and! linac-operation groups of CBNM. Also the technical assistance

from the electronic and mechanical engineering groups of the

Neutron Physics department of SCK/CEW and of СВГШ is very appreciated.

-123-

REFERENCES

1. G. F . Auchampaugh., J . A. F a r r e l l and D. W. Bergen,

Nuclear Physics Al71 , (19 71), 31.

2. D.W. Bergen and R .R . Fulwood, Nuclear Physics Al 63,

(1971), 577.

3. G . D . J a m e s , Nuclear Physics Al 23, (1969), 24.

4. "Compilation of EANDC Requests of Neutron Data Measure­

ments" , report EANDC 8 5 "U", April 1970.

5. R. E. Coté, L . M. Bollinger, R. F . Barnes and H. Diamond,

Physical Review 114, (19 59), 505.

6. N. J. Pattenden, Int. Conf. on the Study of Nuclear Structure

with Neutrons, Antwerp, (19 65) paper 9 3.

7. G. F . Auchampaugh, C. D. Bowman, M.S. Coops and S. C. Fultz,

Physical Review 146, (1966), 840.

8. T, E. Young and S.D.Reeder , Nuclear Science and Engineering

_40, (1970), 389.

9. F . Foor tmans , G.Rohr, J .P .Theobald , G. J. Vanpraet and

H, Weigmann, Conf. on the Study of Nuclear Structure with

Neutrons, Budapest (1972).

10. V.Verdingh, Nuclear Instruments and Methods 102, (19 72),

431.

11. A. De Keyser , S. de Jonge, Т. van der Veen, P . te r Meer "Analyzer Computer Interface", Proceedings of the Int. Symp. on Nuclear Electronics, Pa r i s 19 68.

12. S. de Jonge, EUR. report 48 3 5e (1972). F . Colling, A. De Keyser , H. Horstmann, "Multiparameter Data Acquisition with a Satellite Computer", IFIP Congress, Ljubljana 1971.

13. L. A. Rayburn and E. O. Wollan, Nuclear Physics Ь±, (1965), 381.

14. F . H. Fröhner and E. Haddad, Nuclear Physics 7±, (1965), 129. 15. W.Kolar , EUR. report 4760e (19 72).

- 1 2 4 -

16. G. Rohr, H.Weigmann, J, Winter, P roc . Gonf. Nuclear Data for Reac tors . Helsinki 19 70; IAEA Vienna 19 70, p. 413.

17. F . J . Rahn, FI. Camarda, G. Hacken, W. W. Havens J r . , H. I. Liou J. Rainwater, S. Wynchank, J. Arbo and С. Ко, P roc . Conf, Neutron Cross Sections and Technology, KnoxviUe 19 71, 658.

18. J .E .Lynn , Proc , Symp. Physics and Chemistry of Fiss ion, IAEA Vienna 19 69, 249.

19. H. I. Liou and J. Rainwater, Physical Review 6C, (19 72Ï,

435.

20. D.M.Chase , L. Wilets and A. R. Edmonds, Physical

Review, 110, (19 58), 108 0.

21 . H.Weigmann and J. P . Theobald, Nuclear Physics

A187, (1972), 305.

22. H.Weigmann, Zeitschrift fur Physik, 214, (1968), 7.

- 1 2 5 -

T a b l e 1: R e s o n a n c e P a r a m e t e r s for P u from, c a p t u r e , s c a t t e r i n g and to ta l c r o s s sec t ion m e a s u r e m e n t s

—————— E (eV)

о Г (meV) n Г ° (meV) n Г (meV)

ref. 8) 2. 68 2 . 0 J; . 0 8 1.22 + . 05

22 . 56 .31+ . 0 3 .065 + . 0 0 6

4 0 . 9 3 .47+_ . 04 .073 + . 007

53 .46 52. + 2 . 7. 11 + . 0 4 2 1 . 2 + 1. 7

67. 57 4Л + . 2 •5*t + . 0 2 23 + 3

8 8 . 4 4 . 53+ . 1 .056 + . 0 1

107. 27 17. + 1 1. 64 + . 0 1 21 + 2

1 3 1 . 3 6 . 1 + . 2 • 5 3 i . 0 2 24. 5 + 7

1 4 9 . 6 1 4 . 5 + . 5 1-l8 i . 0 4 21 + 2

1 6 3 . 3 .47+ . 0 6 .037 + . 0 0 5

204 . 7 52 + 3 3. 6 + . 2 20 + 2

2 0 9 . 7 . 4 5 + . 1 .031 + . 007

2 1 5 . 2 5 . 2 + , 3 . 35 + . 0 2

2 1 9 . 0 . 2 + . 1 .014 + . 007

232 . 6 5- + . 3 . . 3 3 + . 0 2

264. 3 . 3 + . 1 .018 + . 0 0 6

2 7 3 . 5 1 6. 6 + . 5 1.0 + . 0 3 22 + 2

298 . 6 8. 7 + . 3 . 50 + . 0 2 26 + 7

303 . 5 1 7 . 8 + . 8 1. 02 + . 0 5 22. 5 + 2

319 .9 200 + 40 1 1 . 2 + 2 . 2 22 + 3

327. 6 a ) . 5 + . 3 .028 + . 017

3 3 2 . 4 70 + 15 3. 84 + . 8 2 25 + 3

3 7 4 . 2 6 + . 3 • 31 + . 0 2

382. 2 54 + 5 2. 76 ± . 2 6 22. 5 + 2

39 6. l a ) 2. 5 + 1 • 13± . 0 5

399. 7 2 + 1 . 10 + . 0 5

410. 5 8 + . 5 .39 + . 0 2

424. 0 5 + . 4 . 2 4 + . 0 2

4 7 4 . 6 a ) . 4 + . 2 .018 + . 009

482. 3 23 . 6 + . 6 1. 07 + . 2 7 23. 5 + 2

-126 -

Tab le 1 (cont inued)

E o (eV) Г п (meV) Г ° (meV) Г (meV)

503 .9 Ъ ^ 150 + 50 6. 68 + 2 . 2 3

536 .2 100 ± 5 4. 32 + . 22 21 + 2

548. 3 74 + 3 3 . 1 6 + . 1 3 25 + 2 5 7 6 . 1 Ъ ) 30 ± 5 1 . 2 5 + . 2 1

594 .7 38 i 4 1 . 5 6 + . 1 6 2 1 + 2

599. 5 11 i i . 4 5 + . 0 4 610.7 14 + 2 . 5 7 + . 0 8 638 .2 5 ± 1 . 2 0 + . 0 4

669. 2 14 + 2 . 54 + . 0 8

69 2.9 45 + 3 1 . 7 1 + . 1 1 2 2 + 2

711. 3 130 + 1 0 4 . 8 7 + . 3 7 19. 5+ 2

727 .4 3 i 2 - 1 1 + . 0 7 7 3 6 . 6 100 + 5 3 . 68 +f . 18 7 54 .8 137 + 5 4 . 9 9 + . 1 8 2 1 . 5+ 2. 5 761.7 3. 3+ 1. 5 . 1 2 + . 0 5

788. 5 53 + 14 1.89 + . 50 79 3 . 5 85 + 40 3 . 02 + 1.42

8 2 3 . 8 2 + 1 . 0 7 + . 0 4

837. 5 38 + 2 1. 31 + . 07 2 0 + 3 8 56. 1 37 + 2 1 . 2 6 + . 0 7 2 2 + 3

865. 1 10 + 1 . 3 4 + . 0 3

8 7 7 . 6 62 + 3 2. 09 + . 1 0 2 6 + 3 8 8 6 . 2 22 + 1.5 . 7 4 + . 0 5 29 + 1 0 9 2 2 . 5 64 + 3 2. 11 + . 1 0 1 8 + 3 9 3 5 . 4 11 + Z . 3 6 + . 0 7

9 39. 6 a ) 10 + 3 . 33 _+ . 1 0

949 . 1 14 + 1.5 . 4 5 + . 0 5 2 6 + 6

977 .9 14. 5 + 1 . 5 . 4 6 + . 0 5

1004 43 + 3 1 . 3 6 + .09

1030 46 + 2. 5 1 . 4 3 + . 0 8

-127-

T a b l e 1 (continued)

1 I E (eV) o Г (meV) n Г ° (meV) Г (meVl

Y

1045 1 1 8 + 1 0 3 . 6 5 + . 3 1

1 0 6 2 . 5 33 + 3 1.0 + .09 1087. 5 200 + 10 6. 0 ± . 3 0

1117 5 + 3 . 1 5 + .09

1 1 2 9 . 5 10 + 5 . 3 0 + . 1 5

1148 300 + 100 9 ' + 3

1182.5 1 3 + 3 . 4 + .09

1197 9 5 + 6 2 . 7 5 + .17

1207 40 + 5 1 . 1 5 + . 1 4

1248 9 + 3 . 25 + . 0 8

1267 27 + 3 . 7 6 + . 0 8 1286 ! 59 + 5 1 . 6 5 + -14

a) weak r e s o n a n c e s only seer i i n one of the t h r e e e x p e r i m e n t s

b) p robab ly double resonance ; s .

-128 -

FIGURE CAPTIONS

Fig. 1: Scattering neutron yield below 1300 eV. The small bump around 300 eV is due to Manganese, present in the aluminium canning of the sample.

Fig. 2: Examples of resonance-parameter analysis for three 242 resonances of Pu. The curves labeled with C, Sc,

T a re from the capture, scattering and t ransmiss ion experiment respectively.

Fig. 3: Plot of the observed number of levels vs energy. The straight line corresponds to a level spacing D = 17. 02 eV.

F ie . 4: Number N of resonances for which x = Г / Г > x vs x. . " n ' n о о The la rges t value for Г from the 319 eV resonance 0 n was omitted. The two curves were calculated assuming

2 , о \ distributions for Г with one and two degrees of freedom respectively.

Fig. 5: Plot of S Г vs energy. The slope gives the s-wave strength function.

Fig . 6: Class I fission width vs neutron energy. The two curves represent Lorentzian distribution functions. The way these curves were calculated is explained in the text.

ID NUMBER Z09941

242 Pu

SCATTERING YIELD

. о о

kJlLJT ^ N J **JuJ

l ^ ^ W t w * ,

1000 500 200 50 E (eV)

ftj Ю * J »0 t-J t-J

»ч* Сл C i C3

ChPNNEL N0= ( X103 )

Гп = 100 i 5 meV

Гу = 21 ±2 meV

20 21 22 23 24 25 19 20 21 22 23 24 19 20 21 22 23 24

T i g , 2.

- 1 3 ! -

100-

S0 = .89 10"4

- ^ * *

—r— 200

— i — 400

—! 600 800 1000 '200 E (eV)

Fig- 4.

о Л

Ю5- calculated number V of degrees of freedom:

1.07 ± 0.10

~i 1 1—i—i—i—|—

o.i

experimental

T 1 i 1 "П 1 1 Г -

0.01 r~l— 1.0 to

F ie . 5.

Г ' X = П

Г*

(II) 762 &

E

10-

E0(II) = 475eV

r'=16eV

r ' .UmeV

0.1-

0.01-I 350 400 ASO 500 550 600 850 700 750 eoo 850 900

E Q (eV)

950

Hg. 6.

- 1 3 5 -

C0MPAR1S0N OF THE THERMAL NEUTRON INDUCED FISSION OF "*Pu

AND THE SPONTANEOUS FISSION OF 240Pu

G. WEGENER-PENNING and A.J. DERUYTTER

S.C.K.C.E.N., Mol. Belgium

and

C.B.N.M., EURATOM, Geel, Belgium

Abstract The thermal neutron induced fission of J39Pu and the spontaneous fission of 240Pu were compared in a double kinetic energy measurement with solid state detectors. The method was such that systematic errors cancelled in the comparison. Kinetic energy and mass distributions were obtained and the correlation between them was studied. The average pre-neutron total kinetic energy is found to be higher for the thermal neutron induced fission : i.e. 177.9 ± 0.04 MeV and 176.8 + 0.2 MeV for the spontaneous fission. Indicated errors are statistical. The shape of the mass distributions is similar in both cases. However the valley is deeper, the peaks are narrower and shifted towards the symmetric point over 1 mass unit for spontaneous fission. Mass distributions for several groups of total kinetic energies show that with increasing kinetic energy the peaks become narrower, the average heavy mass approaches 132 and apparent fine structure at lower kinetic energies washes out.

-136-

1. INTRODUCTION

Ths stuay of tne influence c-' tns s-:cita~io., *>-... ±\ :- c-.e conpauna nucleus on cr.a r.instic energy- ana mass cistrio^tion с- m = -insiur- -'rag-rents car gi.-э information about the mechanism of the fission process.

I- tnermal neutron induceo fissi yr :•? -J"-_ tns :;.~IG--'"2 n_cle--s has an excitation energy wnich is 5.-* MsV nighsr than - т ^ -ijcsus - ''г-_, that is Missioning spc—anes-sly i- its =.:.^з stats. • ПЙ сотос-по r.ilc-S ^o^,. iS -nose- bsca.se ;rs -sas.: ='\=nts со-1з oe done simultaneously. :"ns naif li e for- spontaneous fissiur cr -^°Ри is aDOLt 4.Ю1" tirr.es shorter than that for 2 3 9Fu, anG the thermal neutron induced fission cross section is smaller than 0.01 сэгг, whereas that for ''"Pu is aocLit 742 barns.

Witn one -issile source, containing both isotopes in selecteo proportions, B"ó tne same Si-Au detectors we stucied ooth cases : the thermal ne_tron in-

2-ce: fission witn the rsactcr ÜR1 switched or ana the spontaneous fission

o* - 1* 0PL with the reactor sh^t oown.

An analogues experiment was carried out by Mosto\,aya i1) with a double ion­

ization chamber.

Also TorasKar :2J stuaiad tne neutron-inooceo arc tne spontaneous fission,

but in two separate experiments, using an other set of solid stats detectors

ana an other fission-source.

2 EXPERIMENTAL PROCEDURES

The target consisted of 50 ug/cm2 P'_-acetate eiectrosprayec on a gold-coatec

V *' MS - •' i I™1. Z:. was orsparec' at C5Nf'1-5eel. It jorfcainea 5.3 \ of 235Pu and Э0.8 к of 2Ll°Pu. Cf- ana Cm- impurities are below the detection limit. The is^*o: • ~. composition is given in table I. ~n= s'oeri-чп-. was psrfo-гт.эо at ths nelgïan reactor 5R1, where we used a weli-therbaliceo ana .c iii^atec ngutron пезт-. Two large golo-silicon surface bar-rl~r oetsctors wore "rj".=j -a-c to -ace at the opposite sides cf the target. Detectcrs a^o s^r-e «sis ~:j_n- = j !'• э .•асит. -issicn charmer with thin Al-wi^dows "'or э^;:ап'-= ^r<j: з? ir •_,- tny neuti or osa'.i.

-•..Tthsr el£cс•-'••".:'-; rJDD- :av.s -o-'Sistea o- two charge sensitive pre-amplifiers, '•: ccubl= dslzj.. - line cliocsc amplifiers witn a clipping time of 2 us to avoid j: = -o: tic- t- \r.~ spectxa by ос-pile up, a coincidence j~iJ. vvitn a resolving

•137-

time of Б ns, a double analog to digital converter of 12G x 120 channels.

Coincident pulse-heights wars registered event by event or, paper taps-The oata were collected over a purioti of a few weeks . We registered in sequence the thermal fission when the reactor was on, and the spontaneous -ission with the reactor shut down, in order to avoid background. Systematic errors are the same far both the spontaneous and the thermal fission ano hence they cancel in the comparison of the res-ilts.

3. DATA ANALYSIS

To calculate fission fragment energies from the registered pulse heights we jsea the linear equations :

E, = A x. - 0. Ci = 1.2) i i i l

E4 eni x. are the post-neutron energy and the pulse-height of the fragment •Detected in detector i. A. and B. are calibration constants. 7c Determine them we identified the average light and the average heavy pulse neight with the corresponding post-neutron energy values, calculated from pre-neutrön values obtained by H.W. Schmitt et al. (3)

For each thermal fission run the calibration constants were determined and a slowly varying function of the time could be fitted through experimental values A. ;t) and B, (tb Values of the calibration constants for the spontaneous fission could then be obtained accurately by interpolation. From the momentum ano mass conservation laws intermediate masses can be calculated, which have to be corrected for neutron emission. The neutron distribution in function of the fragment mass, as obtained by Hilton and Fraser are used to calculate pre-neutron kinetic energies and masses event by event. rcr 240Pu such a neutron distribution is not available in the literature. Co w° -jsad that of 2 3 9 P L + n , multiplied by the ratio between the average num-

th per of nsutrons [v] emitted in both cases. Frorp the event by event analysis distributions of total kinetic energy ana the mass of the fragir.ents were composed as well as mass Distributions for different .alugs of the total kinetic energy.

-138-

4. RESULTS AND DISCUSSION

Fig. 1 shows the distribution of the total pre-neutron Kinetic energy fr»r

spontaneous and -.nriureri fusion.

The areas of the distributions are normalized to make the comparison easier.

A normal distribution is fitted through the experimental results- For the in­

duced fission the fit is a good one; but the distribution for spontaneous fission

shows a slight deviation of the gauss-shape at the high energy side-

In the latter case the total pre-neutron kinetic energy is by 1.1 i 0.2 ileV

lower than in the former : 176.85 ± 0.14 lleV and 177.95 + 0.04 MeV.

Numerical results are compared in Table 2, Indicated errors are statistical and

calculated by means of the law of error propagation. For the spontaneous fission

the distribution is also sligthly broader (figs. 1 and 2)

The mass distributions are compared in Fig. 3.

The peaks are narrower and the peak-to-valley ratio is higher for the spontaneous

fission.

The average heavy and ligt fragment masses are also slightly different : 100.76 ±

0.04, 139.24 ± 0.04 for 239Pu + nt, and 101.55 ± 0.14 and 13B.45 ± 0.14 for 240Pu

tn sp.f.

Our results are in good agreement with those of Hostovaya who carried out a simile

experiment with a double ionization chamber. The total kinetic energies are not

given in ref. £1), but Okolovich etal. (5) estimated that this value is 1.5 MeV

higher for (239Pu + n l than for spontaneous fission of 21+0Pu.

tn

Our results of the thermal fission agree reasonably well with those of Toraskar,

but for spontaneous fission there are disagreements. The most important different: between our results and those of Toraskar is that she ^ound the total kinetic ener for 21t0Pu spontaneous fission to be 3.7 ± 1.2 MeV higher than that for 239Pu+ п.. j

th whereas our results show a difference of 1.1 MeV with the opposite sign. Also the shape of the mass- and energy distributions for the spontaneous fission differ from our results : Toraskar detected shoulders in the mass distribution at (1 = ЭВ and И = 142, and a second maximum in the energy distribution near E , , =

tot 186 MeV. The comparison in Toraskars experiments is hampered by the use of a different set of detectors and a different fission source for both fissioning systems and hence systematic errors do not cancel in the comparison. Funthermore she used also a different calibration source in both cases, which can lead to a difference of 1.5 % in total kinetic energy (6).

-139-

the case of thermal fission the compound nucleus has an excitation energy 6.4 MeV gher than in the spontaneous fission in its grcund state. This difference in exci-tion energy leads to the same difference in <Q>, the average total energy released fission.

> is composed of the total Kinetic energy and the excitation energy of the frag-mts. In thermal fission the average number of neutrons emitted is 2.69, which is 7 neutrons more than in spontaneous fission {?). The energy released by Y~emission ; in both cases about 6 MeV [8). ie excitation energy released by neutron emission is about 21.1 MeV for 233Pu + п..

t i id 15.a HeV f o r 2 l + 0Pu. Thus the e x c i t a t i o n energy i s about 5.3 MeV h igher , and the

.net ic energy 1.1 MeV higher f o r the thermal neutron induced f i s s i o n . We f i n d a

i t e l <Q>-value of 207.2 MeV f o r 2 3 9Pu + п.. and 200.7 MeV f o r 240Pu spontaneous th

.ssion. Between both values the difference is about 6.5 MeV, nearly exactly the sme as the difference in excitation energy. j also studied the variation of the mass distribution with increasing total kinetic nergy. Fig 4 and Fig 5 show the mass distributions at values of the total kinetic ïergy ranging from 152 MeV to 192 MeV in steps of 5 MeV. At low values of the ki-

stic energy the yield is very low, the peaks are broad and the symmetric yield

slatively high .

ith increasing kinetic energy the valley becomes narrower, the structure less pro-

Dunced and the peaks shift ot the symmetric point 120. E.g. for thermal fission

t 162 P1eV <MH> the average heavy fragment mass, is 141,6 and at 197 MeV it is

36.2. Fine structure situated at masses 133, 137, 141, 147 is most pronounced at

72 MeV. They disappear at higher values of the kinetic energy. This structure is

Iso more pronounced in spontaneous fission.

. CONCLUSION

he most important result of our experiments is the difference in total kinetic

nergy of the fragments of both fissioning systems. A difference of 6.4 MeV in

xcitetion energy of the compound nucleus leads to a difference of 1.1 MeV in

inetic energy of the fragments. From this result one may conclude that there is

relatively strong damping during the first part of the descent from the saddle poinl

3 the scission point (9).

-140-

Table 1

Isotopic composition ot" the !Ju-1arееt

ISC'ODS ab-^dance

£ J°c,

7 3°<~ l , . ^

2^0 = , o , i , j ^ - ' j

Я *i Ï p u Q.653

2<t2o- , 0.36G

2 ^ A m 1.07

Cm " 0 .01

С f •-< 0 .01

Table 2

239 P u ^ ,. 2 l * ^ P b SD. t .

. <£*. t o t

> k m 177.у ; 0.C4 risV 17 5.Ö z C.14 MeV

<E*. > L

103.4 + 0 . 0 * MeV 102.4 ; 0 . 1J MeV

H 74. f t 0 . 0 * PIEV 74 .3 : 3.14 PIEV

100.73 ± 0.04 101.55 : 0 .14

< * v 139.24 ± 0.Q4 136.45 * С 1^

[* 3 pre-r.eL'tran -<ai_.55

-141-

Reierences

: - r o c s e a i n g s от t h e secor-c U.N. CGn-sr=Tjs en tf1? ~е&1&-л'.

ir a tomic snergy

Sar.9'.'a 'iS5B

[2 • J . 7 c r = c k a r . E. ^e l^o . - i iass : Fnys. Rev, С _£ ?;Э7 1, 26.

Phys. Rsv. С _4 : ' 9 7 D 1 3 И

3.; j . N . M e i l e r , F..: . ' . ' j s l^sr , H.:-.\ S c h ^ i t t : Phys. - lev. i^-: i l SS . i : сЭГ

•;л;, M.C. M i l t o n , J . S . Fras-зг •. Ann, Rev. o f N u c i . Sc. _1_S [1R5o] £ - j l

! 5 J V . N . Q k o l o v i c n , G.N. b 'm i rs r i k in 3ov, Phys. Jc~F J_B '313 [1S63)

(7'i 5NL. 325 s u p p l . '2 f e b r . S5

[6 3 H.F. Jamss : J o u r n . o f r u c l . en 23 [1953) 517

(? j 4 . 3 . S w i a t s c k i ; S. S j f i r - ina l r r P.-.yp. Rep. 4 '.19723 325

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и 167 MeV 100.0 140.0 5 172 MeV 1005 139.5 6 177 MeV 101.0 139J0

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Fiq.5 240Pu SPONTANEOUS FISSION.

- 1 4 7 -

TERNARY TO BINARY FISSION RATIO FOR NEUTRON INDUCED FISSION

IN «'Pu IN THE ENERGY REGION FROM 0.02 eV TO 50 eV

С WAGEMANS* S.C.K./C.E.N.. B-2400 Mol. Belgium

and

A.J. DERUYTTER C.B.N.M., EURATOM, 8-2440 Geel, Belgium

Abstract The measurements were performed at a 8.1 m flight-path of the C.B.N.M.-Linac at Geel. Binary and ternary fission fragments were consecutively counted with banks of sur­face - barrier detectors on both sides of a double-faced "9Pu sample. After correction for background and underlying cross-sections, the areas of corresponding resonances in ternary (T) and binary (B) fission and derived ; their ratio yields the T/B value for the resonance considered. Moreover the energy region through the first large resonance from 0.02 eV to 1 eV was subdivided into several zones for which T/B values were also calculated. The T/B ratio seems not to vary significantly in the energy region from 0.02 eV to 50 eV, except for the 15.5 eV resonance where we find about 10 % more ternary fission. Correlations of T/B with the resonance spin J and with other fission characteristics are discussed.

*N F WO , University of Ghent and S.C.K./C.E.N.

-1Д8-

INTRODÜCTIOM

Wnen a iLicls_= Missions - spci-ta eix.sly er ina-ced пу se'"e energetic partiele or j-sciatijn - it generally brsa\s .• i-to twe nes.-. -rag~er.t£ ar,- two or three neu­trons. This is the so-called Dinary fission.

;- n.v to Q.3 % of the cases these twj- nea-.y fragments are accompanied by a very

energetic light particle, mostly an a-particls. This is the ternary or LRA -is-

sion. The energy distribution •- these a-particles is compatible with a Gaussian

shape, with a peak at 15 MeV a;-j a ^e'i^.jT energy of about 30 ™eV -or the ^^"j

Missioning cQ~tpoLir.G r'-Jcla-5. : ,•

In the measurements which we are going to cescribe the zl+03u compound nucleus is

obtained by bombarding а гз9Ри nucleus iJ"' = 1/2 J with s-wave neutrons ££ = 0, IS +

s = 1/2). So compound states with J = D and 1 will be excited. In terms of

the classical channel theory of 8ohrz) and Wheeler^) these conpound 0 states cor­

respond either to the ground state or to the 0 quadruools vibration of the nucleus

at the saddle point, which are essentially symmetric states. This is not so for

the compound 1 state, which is considered to be formed oy the coupling of the

octupole vibrations К = G and K. - 1 which are both asymmetric states. These different properties of the 0 ano 1 states will be reflected in the correspon­ding fission exit channels, which are thus expected to be very different in na­ture. This implies that also the fission properties are expected to be very dif­ferent. Baseo on this idea several attempts have been made to classify the neutron resonan-ces into two groups corresponding to J = 0 resp. J = 1 by measuring the mass-asymmetry1*) , the total kinetic energy of the heavy fission fragments5), the average nurr-ber of neutrons emitted in fission6) 1( ) and the relative ternary fission yield^). We were especially interested in this last item since recently we were able to clas­sify the neutron resonances in гз5и neutron induced fission intc two groups corres­ponding to "low" and "high" ternary to binary fission ratios11). Moreover these T/B-values were correlated with the most reliable direct spin-determinations and with some other fission characteristics. Sir.ce 2ii5U with J ' = 7/2 forms compouno 3 and 4 states under Dompardment with s-wave neutrons, states whicn, according to the channel theory, are thought to have rather similar properties, we expect a priori to obserle an even stronger ef­fect in the Z 3 9 P L neutror. I-^cec fissic .

Untii now we have only thought in terms of the Bohr-wheeler picture of transition states on the top of a simple inverted oscillator potential barrier. Although their theory has a lot of merits, actually this picture is e little bit oversim­plified in view of the discovery of sub-barrier- ana isomeric tission and its ex­planation on the basis of a "double-humped" fission parrier12j'*)lüS. However

-149-

;cr-i-g to Bjdr-Kclm- 5 асе .-. - ". -,f the nuclei deexcite into the first well and only 0.01 % intD the second, whereas about 96 \ lead to normal fission. Moreover for neutron induced fission of 23<3Pu the energy available аооиэ the lowest fission threshold is about 1.6 MeV. In view of these considerations ;t is logical to expect that the channel theory of fission will still oe applicable in resonance neutron fission of 239Pu, although the subsequent interactions ta inf, place between the saddle- and the scission point should attenuate the chanrel effects taking place at the saddle point.

In the measurements which we will describe, we tried to classify the resonances according to their ternary to binary fission ratio T/B. Ir, the energy region from 1 eV to 50 eV we calculated the T/B values for the strongest resolved resonances and in the region from 20 meV to 1 eV we calculated T/B for 40 energy zones.

EXPERIMENTAL ARRANGEMENTS

The measurements were performed at a 8.1 m flightpath of the C8NM linac. By bombarding a mercury cooled uranium target with the 70 MeV electron Deam of the linac, fast neutrons were produced which were then slowed down by a polyethylene slab.

Figure 1 gives the lay-out of the detection and data collection system. The detection chamber is an evacuated cylindrical chamber with thin aluminium entrance and exit windows j its inner diameter is 50 cm. In the center of this chamber a double faced 239Pu layer (99.956 at.% ; 1 mg/cm2 thick) is mounted, viewed on each side by a bank of four large Si(Au) surfsea barrier detectors. These aetectors were calibrated daily based on the pulse-ri :!.;,ht of the natural plutonium ct-particles. Moreover, aluminium screens of different thicknesses can be inserted (ternary fission) or withdrawn (binary fissicn) from between the layers and the detectors. This detection technique allows rather good resolution of the time-of-flight spectra in the low-energy region, since only one back-to-back deposit of 239Pu is used. Moreover, in this way less scattering material is introduced into the neutron beam than with a multi-plate ionization chamber.

Pairs of detectors are connected in parallel and the signals from each pair are amplified by a charge-sensitive preamplifier ?nd a DDL main amplifier. The amplified signals are sent into a fast timing single channel analyser (T3CA). After mixing all the fast timing signals are fed into a 4096-channel time-of-flight analyser with an "accordeon" system. Fronn the analyser memory the data are transferred via an interface unit to an IBM 2311 disk for storage. The data handling is performed afterwards with an IBM 1800 system.

- 1 5 0 -

MEASURING PROCEDURE

With the apparatus described before three measurements of the r a t i o of the ternary

to b inary f i s s i o n cross-sect ions vs. neutron energy were performed.

Table 1 gives earns d e t a i l s of the d i f f e r e n t exDerimental cond i t i ons . The f i r s t

and the second measurement cover the energy region from 0.1 eV to 50 eV ; the

t h i r d covers the region from 10 meV to 15 eV. The t o t a l d i sc r im ina t i on l eve l

f o r ths ternary c t -par t i c l ss was f i xed at about 15 JleV f o r a i l the measurements.

Each measurement consis ts of several b ina ry , te rnary and background runs.

- In a b inary run we r e g i s t e r the t i m e - o f - f l i g h t spectrum of the f i s s i o n fragments

i n the analyser memory ; i n t h i s case there are no aluminium screens between the

detectors and the plutonium layers and the d i sc r im ina to rs are set to detect only

the f i s s i o n fragments.

- In a ternary run we r e g i s t e r the t . o . f . spectrum of the l i g h t te rnary f i s s i o n

fragments (LRA] i n the analyser memory. The ternary a - p a r t i c l e s are separated

from the heavy f i s s i o n fragments and from the na tu ra l a - p a r t i c l e s emit ted by the

plutonium isotopes i n the ta rge t by i n s e r t i n g a 20 um th i ck aluminium screen

between the detectors and the t a r g e t . By appropr ia te d i sc r im ina to r se t t i ngs the

de tec t ion leve ls were adjusted to 15 MeV.

- Figure 2 shows the ternary [upper pa r t ] and binary [ lower pa r t ] f i s s i o n t . o . f .

spectra from measurement I and f i g . 3 shows the same from measurement I I I .

- For both b inary and ternary runs, background runs were performed by p u t t i n g

appropr iate neutron f i l t e r s i n t o the beam. Moreover, f o r measurement I I I runs

were also performed w i t h a cadmium f i l t e r i n the beam to evaluate background

due to un-timed epicadmium neutrons i n the beam and room neutron background ( i n

the energy region below 0.1 eV). In a l l the measurements a thorough search f o r

the var ious possib le background sources has been done. A de ta i l ed desc r ip t i on o f

t h i s background study i s given in i ! ) . As a conclusion of a l l these background

measurements we found tha t the d i f f e r e n t background con t r i bu t i ons were extremely

sma l l , espec ia l l y i n measurement I I I where the r e p e t i t i o n frequency was only 100 Hz.

The same detec t ion system as described before was moved to the BR2 high f l u x reac to i

o f S . C K . / C . E . N . , Mol , where i t was i n s t a l l e d at a beam tube and connected to a

pu lse-he ight analyser . With t h i s apparatus several pu lse-he ight spectra of b inary

f i s s i o n fragments and o f te rnary a - p a r t i c l e s were performed to c o n t r o l the q u a l i t y

of these spectra and to v e r i f y the exact p o s i t i o n uf the detec t ion l e v e l s . Figure <•

shows a t y p i c a l ternary a pu lse-he ight spectra w i t h a detec t ion l e v e l of 15 MeV.

— 151-

TREATMENT OF DATA, RESULTS AND COMPARISON WITH OTHER T/B MEASUREMENTS

1. Energy region above 1 eV

The analysis of the data is rather straightforward. After correction for background

and underlying cross-sections, the areas of corresponding resonances in ternary CT]

and binary CB) fission are derived. Their ratio yields the T/B value for the

resonance considered.

Table 2 shows these T/B values for measurements I and II ; these results are

normalized to T/B = 100 for the 10.95 eV resonance. In order to obtain more

conclusive values we calculated the weighted mean of the T/B values from both

measurements. With these values we tried to classify the resonances in a "high"

£H), a "low" EL) and an "uncertain" tU) group, resp., based on the following

criteria :

H : T/B > Ю5 ; U : 106 > T/B > 103 ; L : 103 >* T/B

Brackets are used for the resonances far which the statistical error does not allow an unambigeous classification. We find that there is a significant difference between the 15.5 eV resonance EH] and most other resonances CD, especially the strong 7.B5 , 10.95 and 11.Э0 eV resonances. This higher a counting-rate cannot be caused by a-particles from the 239PuCn,a) 2 3 6u reaction since the highest energy a-line generated in this way is 11.46 MeV, which is well below the detection level in our experiment.

We performed some statistical tests on these data. We calculated the weighted mean Xw for the different measurements, taking into account all the data resp. L + (L) and H + EH]. These results are summarized in table 4, where we also calculated the hx-values of Birge :

Xi - X2 hx =

{•• 2 Coj2 + a22)

X] and X2 represent the weighted mean of the "low group" L + CU and the "high group" H + (H) and a\ and 02 the corresponding statistical errors. Taking into account that the probability that Xj and Xg are compatible with a unique value is smaller than 0.01 for hx > 1.83, we conclude from this table that there is a significant difference between the "high" and the "low" T/B values.

It is difficult to compare our results with those of llelkonian et al.5), who performed the only other T/B measurement in this energy region, since they did not

-152-

Dubl:^- f- г", •jr'sriJal values for the different resonance? nsza'-ss cf their rather poor .statistical accuracy. ;jevertneiess thay found that Г--5 .-.=ss significantly larger for two resonances with ." = 0, dhicn is in qualitative agreement with our results. 2. Energy region below I e" Th<2 third measurement i? analysed in a somewhat different vay. 3y cutting cadmium filters in tre bea~ -,e ;nec^.ej -he DacKgrounJ in the Energy region D9low 0.2 eV and found it nsgligiLls compared to the counting rate in that region. Then we divided The ternary and binary fission t.o.f. spectra in several intervals in the energy region frorr, 20 msV to 1 eV [thus including the strong 0.3 sV resonance] and calculated the ratios of the areas of the corresponding intervals. These results, which are normalized to the first two measurements, are represented graphically in fig. 5 and given numerically in table 3. We find that there is no significant difference between these T/3 values. Moreover, if we consider the weighted averages given in the fourth column of this table, we deduce that the D.2S5 eV resonance is very probably a "low" one and that also the thermal T/B value is predominantly low. Within the experimental errors our results agree with those of Panov et al.i6) [10 \ exp.err.) and Schroder17] [2 % exp.err.].

Finally we examined whether our low energy data are compatible with a uniaue distribution or not. Therefore we calculated x2 = 5.16 (with 7 degrees of freedom) with the corresponding probability P(x2 > X2

D) = 70 4. Furthermore we obtained for the Birge ratio :8)'9j R = 0 / 0 a y ai u e 0f 0.869 and a probable deviation of R from unity of 0.076. From these tests we deduce that the data considered are compatible with a unique distribution, although not very pronounced.

So we fitted a straight line through these data (fig. 5i. Although this fit is in agreement with the statistical laws, we were not completely satisfied since we felt that a weak structure might be present. So we tried to fit an interference curve through our d^ta, which is also represented in fig. 6. This curve follows better the experi^Rrtal points and tne fit results in a better R v a l u e than in the stiaight-line case.

Sur.h a possible interference effect is, however, not so easy to explain. In 1967 Mostovaya -°J rr-easured the r/3 ratio for 2 3 5U. She found a very pronounced inter­ference effect in the neighbourhood of the 2 eV resonance, which she explained by a different number of open fission channels in binary and in ternary fission.

-153-

This assumption ;з hnwpvsr nnt so evident. In ojr ;:азе the e- fe: t if ei f'Л '. there is - is much smaller and lass convincing. So ws consider t'is -?it snown in fig. 6 rather as a scientific guess.

DISCUSSION

In table 5 we г.отелг? our proposed clasai ricatian от' the resonances t?ased an trsir Г/Б value with the direct determination of the resonance spin J and .vir.h core other fission characteristics. This table clearly demonstrates that there is a complete agreement between our unambiguously classified resonances and the direct spin-determinations of Sauter and Bowman 2 2 ) , Asghar 23J, Trochon et al.2"1} and Simpson st al. 5 ) . Compared with the spinvalues of Fraser and Schwart?. '5 one of the five common resonances disagrees. However it must be stressed that none of ther-determined the spin of the irrportant 0.296 eV and 15-5 eV resonances. This has been done for the 0.296 eV resonance by Chrien et al.^63 via the detection nf high-energy capture утауз. They assigned J = 1f for this resonance, which agrees with our result. Moreover Farrell 2 7) and Becker "8) assignee both J11 = 0* For the 15.5 eV resonance based on the "interference method" tindirect determination).

When comparing our results with the average kinetic energy of the fission fragments measured by Plelkonian and Hehta b) we find a difference for the important 1'ï.'3 eV resonance. The same may be said for the fission symmetry measurements of Cw.'iav

et al. 'M in the 15.5 eV resonance. However our J = 1+ result for the O.V9fi eV

resonance agrees with Cowan's propor?1 for this resonance, which is based on tfv;

results of Regier et al. 2 9 b Here nowever it must be mentioned that Regier's

result that the asymmetric-to symmetric fission ratio for the thermal region is

about three times smaller than that for the 0.29S eV resonance, is nut reflscted

in our Г/В values, which are not significantly different in both regions.

Л rather difficult criterium for comparison is the fission neutron multiplicity v.

If we examine the various measurements we observe a rather clear biats dun to the rJs Lent ion method. (n) Weston st al.e) and I rochon et al.^i find no variation in \>, Thay both detectnu

the fission neutrons dircci.ly. (b) Weinstein et al.b), Ryaoov et al.7) and Phackleton p.t al.10) find e variation

of v" from resonance to resonance. They all detected the fission neutrons after moderation.

If we compare the absolute data of Weinstein and Ryabov shown in ta'iie b, wr чпе

that they are generally anticorrelated. Nevertheless this in not sn fnr thnir

- 1 5 4 -

spin assignments, which are almost in agreement. This i s e spec ia l ly the case for the 0.296 eV and 15.5 eV resonances, which are a lso in agreement with our r e s u l t s .

CONCLUSIONS

In the energy region from 20 meV tD 50 eV we observe only one resonance with a significantly higher T/B valut- : i.e. the 15.5 eV resonance. We assign J~ - С for resonances with a high Т/Б value and Jv = 1+ for resonances with a low T/B v/alue. This higher value for 0+ resonances cannot be due to an eventual loss of binary fission counts for one spin state - thus a 5-value which would be too small - since the difference between the Kinetic energies of the 0+ and the 1+

states is only about 0.7 % according to flelkonian and Hehta 5 ) .

As we have shown in the introduction, this higher ternary ot-yield for О* resonance: is in the sense expected according to Bohr 2) and Wheeler 3 ) , since the 0+ states are more symmetric than the 1+ states. More symmetric fission corresponds in gene to a lower total Kinetic energy of the fission fragments, thus to a higher excitat: energy of the fragments and a higher probability for ternary a-emission.

We can reach the same conclusions based on energetic considerations. From several analysis of experimental data we Know that the average fission width for 0+ states is much larger than that for 1 + states : < Pf > g+ >> < Tf > + . This implies that the number of open fission channels for 0+ states N(0+] is larger than IMC1+), thus that the 0* channel lies below the 1+ channel in the transition channel spectrum. From this we deduce that the remaining excitation energy via a D+ channel is larger than for fission via a 1+ channel. This implies a higher probability for ternary fission via a 0+ channel than via a 1+ channel.

ACKNOWLEDGEMENTS

The authors wish to thank Dr. M. Nève de Mévergnies für fruitful discussions. They are indebted to many colleagues from CBNPI, Geel for the preparation of the

samples and the operation of the linac. They especially acknowledge the skilful

assistance of Пг. R. Barthélémy, G. Le Dez and J. Van Gils during these experiment;

- 1 5 5 -

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6] R. C h r i e n , 0 . Wasson, S. D r i t s a , S. Sokharse and J . Garg , P r o c . o f t he 2no

Canf . on N u c l . Data f o r R e a c t o r s , H e l s i n k i 11970 ] , 377

73 J . F a r r e l l , Phys . R e v . , v o l . 165, 4 ( 1 9 6 8 ) , 1371

3) W. Becker , D o c t o r s t h e s i s , P h i l i p p s - U n i v . Marburg/Lahn [1973]

3) R. R e g i e r , W. Burgus , R. Tromp and B. Sorensen , Phys. Rev . , v o l . 119, 5 { 1 9 6 0 1 ,

2017

TABLE 1: Experimental conditions for the different measurements

Measurement Energy region Linac p a r a m e t e r s Overlap filter number

I 0 . 1 - 5 0 eV 24 ns , 600 Hz E . = 65 MeV, i = 45 ,uA el av / P = 3 kW 70 n s , 400 Hz E . = 65 MeV, i = 50 ,uA el av / P = 3. 25 kW

Cd

II 0. 1 - 50 eV 33 ns , 400 Hz E , = 67 MeV, i = 44 ,uA el av /

' P = 3 kW

Cd

III 0.01 - 15 eV 1. 2 ,us, 100 Hz E , 4 53 MeV, i = 45 ,uA

el av /

none 1. 2 ,us, 100 Hz E , 4 53 MeV, i = 45 ,uA

el av / P = 2 . 4 k W

TABLE 2: Results normalized to T/B = 100 for the 10.95 eV resonance

Resonance Measurement I Measurement II Weighted mean (Meas. I and II) energy

(eV) T /B t Stat, e r r . T /B i Stat. e r r . T / B Stat. e r r . Class .

7 .85 9 8 . 7 ] 2 .8 9 9 . 3 ! 3.1 99 2. 1 L 10.95 100 | 2.1 100 1 2 .4 100 1 .6 L 11.90 101.5 | 3.9 9B. 1 [ 4 , 5 100 3 L 14.30 ) 107.5 ; 4 . 5 106.2 [ 5 106.9 3 . 4 (H)a> 14.68 ) 103.7 ' 3.4 96.9 | 3 .8 100.7 2 . 6 L 15. 50 ) 112.4 ! 4 . 3 108.1 ; 5 110.6 3 . 3 H 15b) 106.9 ! 2 .3 102.2 1 2 .6 104.9 1.8 17.7 104.8 ! 4 9 9 . 5 ! 4 . 6 102.5 3 L 22.2 105.6 [ 3.7 101.4 ! 4 .2 103.8 2 . 8 U 26.2 106.4 J 5.6 106.8 ! 6.7 106.6 4 . 3 (H) 47 .8 9 9 . 5 J 7.Й 9 6 . 6 ! 9 9 8 . 3 5.9 (L) 50.1 104.4 J 7 .5 9 7 . 2 | 8.4 101.2 5 . 6 ,(ь)

Classification: H: T/B г 106 U: 106 > T/B > 103 L: 103 г Т/В

Brackets indicate that the statistical error is too large to be conclusive.

b)

an unambiguous classification is impossible due to the influence of the underlying tail of the 15. 5 eV resonance.

this stands for the group of resonances at 14. 30, 14. 68 and 15. 50 eV.

-159-

TABLE 3: Results from Measurement III normalized to the weighted mean of the 7.85, 10.95 and 11.90 eV resonance / as ob­tained from Measurements I and II (T/B = 99. 7 + 1. Z)

E ( e V ) т/в Stat . e r r . Weighted m e a n

0.29 6 102. 2 0 .65 7 .85 9 7 4 . 6 )

1 0 . 9 5 102 .2 3 .7 ) 9 9 . 7 + 2 .7 U - 9 0

я\ 9 7 6 . 7 ) 0 . 8 8 6 a ' 102 .4 2 . 9 0.465 102. 0 2. 2 0 .374 103.9 2 . 9 0. 345 9 9 . 9 2 . 2 0.319 100.9 1.8 ) 0.29 6 102. 2 1.6 ) 101. 4 + 1 0 .275 101 1.7 ) 0 .257 102.7 2 . 0 0.240 1 0 2 . 3 2 . 3 0 .225 1 0 5 . 5 2 . 6 0 .205 101 .8 2. 1 0. 182 106 .2 2. 5 0 .163 105.9 2 . 6 0. 146 104. 0 2 . 6 0. 132 101 .1 2 . 6 0. 120 103 .8 " 2 . 6 0. 110 102. 5 2 . 6 0, 101 9 8 . 7 2 . 6 0.09 25 101 .4 2 . 6 0 .08 53 105 .4 2 . 6 0.0790 103 .4 2 . 6 0.0733 102.9 2 . 6 0.0683 104 .0 2 . 6 0.0637 103 .7 2. 6 0 .0596 102 .8 2 . 7 0.0558 102.0 2. 7 0. 0524 9 8 . 7 2 . 9 0. 049 3 1 0 0 . 3 2 . 9 0.0465 9 7 . 6 3 . 0 0.0439 103. 1 3 . 1 0. 0404 9 8 . 9 2 . 3 0.0364 102.7 2 . 4 0.0329 104. 3 2 . 6 0.0299 9 9 . 1 2 . 7 ) 0 .0273 106 .1 3 .0 ) 0., 0250 1 0 0 . 3 3. 0 ) 102. 3 ± 1. 3 0. 0230 104 .2 3 . 3 ) 0 .0212 100. 5 3. 5 ) 0 .0197 105 .0 3 .8 )

the energies indicated below correspond to the middle of the energy-interval considered.

TABLE 4: Weighted average values and hx-values of Birge

Measurement number Data used X (weighted average) hx

I all data 102.81 + 1. 11

L + (L) 101. 03 i 1.29 )

H + (H) 109.20 4 2.72 ( 1.92

II all data 100.51 + 1. 26

L + (L) 98 .96 + 1.46 )

H + (H) 107. 08 +_ 3.13 | 1,66

weighted mean of I and II

all data

L + (L)

101.82 + 0.84

100.14 + 0.98 )

H + (H) 1 0 8 . 2 9 + 2 , 1 | 2. 49

III all data 102.32 + 0.40

Table 5: Comparison of our classification Of the resonances via their T /B values with other classification methods

Kinetic Fission Fission neutron Our classi­energy of symmetry ("v ) measurements fication via energy of symmetry ("v ) measurements fication via

E(eV) via neutron scatter ing vla у -ray detection

via interference method

fragm. a}

„f.5> « t . 4 » 2 "

T/B values E(eV)

rei. * ~ f . 1 2 > . I . » » r 24) rei . ref. ' , 1 5 ) ref. »t»> ref.

fragm. a}

„f.5> « t . 4 » 2 " ret .6» « f . 7 >

T/B values

о. г? ь i + .+ A(l+) M^) L(l+) 7.85 1+ •t н(Г) L H(l*) L

10.95 ! •

\ :+ ,+ н L H L.

11.90 14.30

! •

\ :+

;; ,+ н

н L H H (i-.)c)

14.68 0 i 1

i +

н L L

H J. ь , 15.50 17.7 гг. г * t !; Jï :+

i + t н

н н

A c )

A Л

L L

L(0+) H H

H(0+) ъ и

гб. г 0 + i о: ö i ; <н) A L L (И)

47.8 0 + i о: ö 0 + н A H и <L> 50.1 i + i * (Ь) L H fW

The notation L means lower average kinetic energy of ttus fission fragmenteand H higher average kinetic energy. The notation A means predominant asymmetric fission.

' Influenced by other resonances, ' The notation L means hete lower v v*lue and ti higher v value.

-162-

FIGURE CAPTIONS

Fig . 1: L a y - o u t of the de tec t ion and data col lec t ion s y s t e m 239 F i g . 2: Upper p a r t : The P u t e r n a r y a lpha t ime-o f - f l igh t s p e c t r u m

(Run I) L o w e r p a r t : C o r r e s p o n d i n g b ina ry f i s s ion t ime-o f - f l i gh t s p e c t r u m

239 F i g . 3: Upper p a r t : The P u t e r n a r y a lpha t ime-o f - f l igh t s p e c t r u m (Run III) L o w e r p a r t : C o r r e s p o n d i n g b i n a r y f i s s ion t ime-o f - f l i gh t

s p e c t r u m

F i g . 4: P u l s e - h e i g h t s p e c t r u m of t e r n a r y or - p a r t i c l e s ( d i s c r i m i n a t i o n l eve l 1 5 MeV)

F ig . 5: T / B - r a t i o s in the e n e r g y reg ion f rom 0. 02 eV - 1 eV (Run III)

F i g . 6: I n t e r f e r e n c e cu rve fit ted through the data below 1 eV.

1 63-

239 Pu foil

removable Al screens

detectors

TOF ANALYSER

4096 CH. MEMORY

INTERFACE

IBM 2311 DISK

IBM 1800

BIN

ARY

FISS

ION

CO

UNTS

01

о о U

I о о о

*** 4

vr-

*»»*

TER

NAR

Y Ft

SSIO

N C

OUN

TS

О

х > z z m

t~ z с ш гп

UI о

о о (Л

о

ел

о

"^

+ +*

»

*-*+

26

.2 e

V

+ *

* 22

.2 e

V

п **

+• +

+

17.7

eV

+ •*

+

+ 15

* eV

I

11.9

0 eV

-л*

10.95

eV

s-*

**•+

*>

+*

7.85

eV

to

"0

С

- 1 6 5 -

375

500 1000

CHANNEL NUMBER

1500 2000

10 000 •

1Л

3 о

й 5000

>-ос <

со

0 •*-

1000

CHANNEL NUMBER

Fig. 3.

•166-

13NNVH0/SlNnOO

E,eV

Fig . 5.

-168-

Д = 1 meV

f f = Га= 100 meV

Fig. 6.

ü-UltunAXOV xaöTXUIUTJS UM ТЛИ ATÜMIÜ EHERGY

G.A.Otroschenko, P.E.Vorotnikov

ON ÏEE EISSIOH ISOMER YIELD IN 255U -ь n REACTION

A major part of the experimental works, in which fission isomers were studied, was done using the reactions with charged particles.

Comparatively small number of the experiments was pub­lished in which, fission isomers were produced in the reactions with neutrons. At the same time the data concerning the yield of the neutron induced isomers, its dependence on the excitation energy, are of great interest especially as compared with data taken from the reactions with charged particles.

In 1970 Elwyn and Ferguson (1) published their experiment in which uranium and plutonium fission isomers were induced in the neutron capture reaction. At 2.2 MeV neutron energy the yield of 2^6U fission isomer was 3."\Q and that one for 40Pu fission isomer was 4.10 with respect to the prompt fission yield. It was noted by the authors, the yields were unexpectedly higher than the yields of the same isomers in the reactions with charged particles. At the same time the yields were much higher than,

242 241 for instance, the yield of Am fission isomer in Am + n reaction.

Later the Roumanian group published their work (2) on the yield of 2^ TJ fission isomer in the reaction "U + n. At 0.2 MeV neutron energy the value of 3 per cent for the rela­

tive yield of the isomer was obtained. Our measurements of the fission isomer yield in the re­

action 2 ^ U + n at 1 MeV neutron energy showed that the background

-170-

fisso/ons, produced Ъу scattered neutrons in the JJX} sample, play very significant role.

The measurements were done using the pulsed beam accele­rator of Van de G-raaff type with 6 nsec pulse duration at the repetition rate of 4 Mc, The T + p reaction was used as a neutron source. Fission events were detected in a gas chamber with Xe as a scintillator. The chamer was connected to the photomultiplier £?ЭУ -30. The pulses from the photomultiplier output were analysed Ъу a time analyser,

The background fissions were induced by the scattered neutron flux consisting of two components. The first component represents the neutrons experienced multiple scattering in the walls, floor and ceiling of the room. This part of the neutron flux is time independent and its value can be easily measured» In our experiment this part of the background fissions in a time channel was equal to 10 y with respect to the peak of the prompt fission, The second component of the scattered neutron flux re­presents the neutrons scattered by protons from the beam, stopped in the solid tritium target. A part of these neutrons is of so low energy, that their time of flight between the tritium target and ' U sample is of the same value as the life time of the fission isomer ^ U. The fissions induced Ъу these neutrons hide the isomer fissions. Moreover, the intensity of the second com­ponent is time dependent, as soon as the intensity of the scat­tered neutrons is simply proportional to the velocity they have •. after scattering. Thus the background fissions induced by the second component are time dependent and, hence, can imitate the isomeric fission. However, in general, the isomeric fission has an exponential dependence on time, whereas the background compo­nent with a good accuxacy has a power dependence on time. As soon

as in this experiment the background, due to the first component, was sufficiently low, i+ was possible to f inde out an interval in the time spectrum, where the second component background v/as domi­nating. This part of the time spectrum was used to determine the parameters of the time dependence for the second component back­ground. Now, it was possxble to roaJce reasonable background corx ec-tioas in all channels of the time spectrum, which were analysed.

The time spectrum, obtained in the experiment, contained 5.10 of fission events. With 100 nsec supposed to be the isomer life time the fission isomer yield was (0.4 - 2.ö).10"5 with respect to the prompt fission yield.. Hence, the upper limit for

235 -Б the isomer yield in the reaction v U + n equals to 3.10 ' at 1 MeV neutron energy. The yield data from ref. (1) and (2) con­tain large errors because the background fissions induced by the scattered neutrons were not estimated with sufficient accuracy.

R e f e r e n c e s :

(1) A.J.Elwyn, A.G.T.Ferguson, Nucl. Phys. A 148, 337 (1970) (2) I.Boca, M.oezon, I.Vilcov, IT.Vtlcov, preprint I M CBD-42-1970

-172-

ESTIMATION OF RESONANCE PARAMETERS OF CLASS II L E V E L S USING THE MAXIMUM LIKELIHOOD METHOD

R. W e r z , G. Rohr , J. P . Theobald, and H. Weigmann Cen t r a l Bureau for N u c l e a r M e a s u r e m e n t s

EURATOM, Geel , Belg ium

ABSTRACT

Doorway m e c h a n i s m s often man i f e s t t h e m s e l v e s in such a m a n n e r that b road n u c l e a r s t a t e s of in gene ra l low dens i ty a r e coupled to n a r r o w and dense ones th rough r e s i d u a l i n t e r a c t i o n . A c l e a r and typ ica l example of such a s i tua t ion i s given by the f i s s ion p r o c e s s through a double humped f i ss ion b a r r i e r . The c l a s s I s t a t e s ( C T I - S )

or u sua l compound n u c l e a r s t a t e s play the ro le of the n a r r o w and dense s t a t e s , while the c l a s s II s t a t e s (C-II-S) buil t upon a shape i s o m e r i c ground s ta te s tand for the broad l e v e l s . It h a s been shown in the f r a m e of the picket fence m o d e l , tha t the f i ss ion widths Г , of C-I -S coupled to a C-II-S follow a L o r e n t z i a n c u r v e . In a m o r e r e a l i s t i c mode l they f luctuate acco rd ing to a P o r t e r -Thomas d i s t r i bu t ion (PTD) a round a L o r e n t z i a n . In the p r e s e n t paper it i s a s s u m e d that in the m o r e g e n e r a l case the L o r e n t z i a n d e t e r m i n e s the m e a n v a l u e s of the P T D a s a func­tion of exci ta t ion ene rgy . Under th is a s sumpt ion ca lcu la t ions have been p e r f o r m e d to e s t i m a t e C-II -S p a r a m e t e r s f rom Г r d a t a . The qual i ty of t h e s e p a r a m e t e r s is d i s c u s s e d .

INTRODUCTION

The mix ing of exci ted s t a t e s of a spontaneously f issioning shape

i s o m e r e , the so ca l led c l a s s - I I - s t a t e s (C-II-S) into compound

n u c l e a r l e v e l s o r c l a s s - I - s t a t e s (C-I-S) has been de sc r ibed 3) Z)

on the b a s i s of the p icke t fence mode l ' . In ref. ' the f o r m a l i s m

developped by C. Mahaux and H. Weidenmüllex ' has 'been used.

The s a m e shal l be done in the p r e s e n t pape r , but the f r ame of the

p icke t fence mode l shal l be left a s far a s a c losed m a t h e m a t i c a l

fo rmula t ion of t h i s l eve l mixing a l lows to do. The a im is to obtain

a handy p r o c e d u r e to deduce the C-II-S p a r a m e t e r s r e s o n a n c e e n e r g y E > f iss ion width Г* and spread ing width Г 1

f rom the a v e r a g e spacing d and the f iss ion -widths Г t of the p, C - I - S ' s .

H*

In the f i r s t c h a p t e r the equat ions desc r ib ing the fine s t r u c t u r e of a C-II -S a r e out l ined, in p a r t i c u l a r the n e c e s s a r y r e s t r i c t i o n s a r e d i s c u s s e d and c o m p a r e d to those of the p icket fence model and in the second chap te r a m a x i m u m l ikel ihood method i s p r e ­sented , which y ie lds С-П-S p a r a m e t e r s under the a s s u m p t i o n s of the p r e c e d i n g c h a p t e r .

1. THE P I C K E T F E N C E MODEL

We a r e deal ing with M C - I - S ' s

I 0 > , m = 1, 2, . . . . M 1 m one C-II-S

10 > i о

and two continua

i } x L, > v > that of the incoming n e u t r o n s t a t e s

and ,r\ -j I x > f- , tha t of the outgoing f i ss ion f r a g m e n t s , L E

-174 -

The O - I - S ' s a r e coupled to the f i ss ion s t a t e s only th rough the

C-I I -S ac t ing a s a doorway

(1) < 0 | V j ó > < 0 } V | Y ^ > Ф- 0* while s m ' ' о о • ' Л Е

(2) < 0 I H j x ( ? > =*0, m = 1, 2 . . . . M

V i s the r e s i d u a l i n t e r a c t i o n of the tota l Hami l ton ian H=H +V. о

We a s s u m e f i r s t that the coupling of the s t a t e s j 0 > to the

s t a te | ф > is s t r o n g e r than the coupling of |0 > to the f r a g -i (f) m e n t cont inuum -' [ Хтр > |-

CASE 1:

! < * m ! V l 0 o > | 2 > > l < 0 o l V l 4 } > i 2 (3)

Now we can diagonal ize H in the sys t em (ref. )

| | 0 n > } = |0o>, | * 1 > f . . . \ФЫ>

and have as eigenfunctions M

\ib > - £ О Ф +Q d (4) 1 J r n _ . n m m no о

0 m e a s u r e s the p ropab i l i t y to find the C-II-S conf igura t ion

in the s t a te \lp > . The m a t r i x e l e m e n t s

d e s c r i b e the coupl ing of the s t a t e s j \£- > to the f r agmen t

cont inuum.

We get f rom (4) and (5)

v =<ф | V | x ^ f ) > = 2 П' <Ф jVK ( £? n f n 1 I \ E J^ n m m ' I X E / m=o

o r Q 2

v =Q <Ф V К ' > = - ; 1 (7) n n o о ' ' л E 2тт v '

Г i s t h e d e c a y w i d t h of t h e С - П - S . F r o m the o r t h o g o n a l i t y

of П f o l l o w s t h e s u m r u l e M _

2 TT E v = Г ! (7а) n v ' n=o 5)

C . M a h a u x h a s s h o w n u n d e r t h e fo l lowing a s s u m p t i o n s

M V 2 M V 2 ( E - E ) - i I V 2 \ _, " ï T m ч о m ' m_ ' L , E - E + i I , , _ „ \2 r 2 m = l о m m = l (E - E ) + 1 v o m

•if (8a)

V Z (E - E ' l - i i r m o m d E , = m l ' l T < V 2 >

w i t h

d " - ( E o - E ' ) 2 + I Z d

+ " V 2 (E - E ' ) m o b) f -& ~ =— dE' = 0 (8b) J (E - E') + I

- со О

a n d V = < 0 I V l 0 > , m = l . . . M, m m ( ' о

a n d I a n e n e r g y i n t e r v a l , t h a t

i < 2тг 2 d_ Г Ч ^ ) < 0 П [ У | 0 О > 1 +2 1) ( 9 )

^ n V , ,2 2 "Г 2 ( 2 П ) (E„"EJ + 7 < ¥ M J V | 0 > | +21)

T h e q u a n t i t y — p | < 0 | V | 0 > l i s c a l l e d Г % t h e s p r e a d i n g

w i d t h of t h e C - I I - S . I t d e s c r i b e s the c o u p l i n g s t r e n g t h of t h e

C - I - S < = > С - П - S l e v e l m i x i n g . If w e t a k e I « Г , w e 2

o b t a i n e x p e c t a t i o n v a l u e s fox v

- 1 7 6 -

< v 2 > , = -$- , I ^ - ^ - = (10) ( 2 Т Г ) (E - E ) 2 + I X 7 L " n o 4

U s u a l l y t h e s t r o n g e r r e s t r i c t i o n s of t h e p i c k e t - f e n c e m o d e l a r e

a p p l i e d : E , , - E = d fo r a l l m -ф О m + 1 m

2 2 2 V = < V > = V w h i c h l e a d to t h e s a m e e q u a t i o n s , m m

T h e t r u e m a t r i x e l e m e n t s v d e f i n e t h e C - I - S f i s s i o n w i d t h s n

r n f = 2 " V n ( 1 1 >

T h e y f l u c t u a t e u n d e r t he a s s u m p t i o n s (8) a r o u n d a L o r e n t z i a n

c u r v e .

I t h a s b e e n s h o w n by t w o of t h e a u t h o r s t h a t in s u b t h r e s h o l d

e n h a n c e d f i s s i o n the

C A S E 2 :

! < 0 j V | * o > l 2 « | < 0 O ' V )x®> I 2 (12)

i s m o s t p r o b a b l y r e a l i z e d i n n a t u r e . In t h i s c a s e t h e s i t u a t i o n

i s m o r e c o m p l e x f r o m r e a c t i o n t h e o r e t i c a l p o i n t of v i e w .

A t a n y r a t e i s t h e c o l l i s i o n f u n c t i o n m e r o m o r p h i c a n d c a n

be w r i t t e n

M ( R e s i d u e ) S ( E ) = 1 - i S F _ v? П U 3 )

n=o E - f С п

w i t h c o m p l e x p o l e s ^ = E + i r • T h e s e p o l e s a r e s o l u t i o n s , t n n n of t h e e q u a t i o n

i r t ( E - E + - ~ <ф I V | 0 > , о 2 m ' о

d e t (

\<ф | V 10 > (E - E ) 6 ( n ' l o m m n

•= 0 (14)

(for s i m p l i c i t y we n e g l e c t h e r e t h e c o u p l i n g to t h e c o n t i n u u m

{ , X t n ) > }

-177-

m , n = 1, Z, . . . M and can be d e t e r m i n e d by pe r tu rba t i on theory under the a s s u m p t i o n | < 0 m | V | 0 Q J << p 1 for al l m ^ 0

f = E + ° i ' о ( 1 5 ) m m . t v J ' E - E + Ч~-m о 2

V 2

= E _ + Ш

(E-Eo)+ i f -

The widths Г = Г , a r e given by m mf

У* m

with

rmf = 2 I m f m = Г (16) (E - E ) 2

+ ^ -m o 4

M M M V 2 Г* r t = S r = r + E Г r = Г + E Ш

n о . mf о ~' , ~ _t 2 m = l m = l ( E }2 X _

m о 2

Equ. (16) looks s i m i l a r to a L o r e n t z i a n d is t r ibu t ion for the widths

of the fine s t r u c t u r e peaks , a p a r t f rom the fact that the quant i t ies 2 V a r e subject to s t a t i s t i c a l d i s t r ibu t ions which a r e a s s u m e d to be m

u n c o r r e l a t e d with the e n e r g i e s E . & m

We t h e r e f o r e adopt the s t a t emen t that, in o r d e r to a r r i v e at a phy­s ica l i n t e r p r e t a t i o n of expe r imen ta l fine s t r u c t u r e widths Г in

r c m t e r m s of doorway s ta te p a r a m e t e r s , it i s m o s t r e a s onab l e to fit the

Г -d i s t r i bu t i on by a L o r e n t z i a n ene rgy dependence. This s t a t e ­

m e n t i s suppo r t ed by the obse rva t ion that the doorway s ta te in the t 2 /, (f) i

c a s e Г » V i s e s s e n t i a l l y decaying into the continuum \\ \ > > .

-178-

Genera l ly , any decaying s ta te i s a s s u m e d to have a dens i ty d i s t r i ­bution a s a function of e n e r g y d e s c r i b e d by a L o r e n t z i a n with a ha l f -width connected to the l i fe t ime by H e i s e n b e r g s u n c e r t a i n t y r e ­la t ion . F o r a doorway decaying into the cont inuum the half width is r ' , i. e. the s a m e a s that of the p s e u d o - L o r e n t z i a n in equ. (16).

In fitting e x p e r i m e n t a l fine s t r u c t u r e widths by a L o r e n t z i a n , one

h a s to r e p l a c e the V in equ. (16) by a cons tan t which p lays the ro l e of an o v e r a l l p ropor t iona l i t y fac to r . Th i s m a y bes t be done

2 Ъу defining an a v e r a g e V by an equation equivalent to equ. (8 ):

(17) 1 m

2 t v rT

m =

2 T T < V 2 > m = r 1 1 m (E - E )24 m o' 4

= d = r 1

Thus 2 d Г -Г ' m 2TT /, T TT t • r f z (18)

Again, we ca l l Г the " s p r e a d i n g width". It is to be noted that

the p icke t fence mode l yields the s a m e equ. (17), but p r e s e n t l y . 2 l

(17) is m e r e l y a definition of < V > and Г .

In concluding th i s chap te r we pos tu la t e that in both c a s e s the expec ta t ion v a l u e s of the fine s t r u c t u r e widths follow a L o r e n t ­z i an e n e r g y dependence (equ. 10 and 18). As is shown in fig. 1, the individual Г , f luctuate v e h e m e n t l y a round the L o r e n t z i a n , a s expected f rom e .g . equ. (16).

T h e r e r e m a i n s a s e r i ous lack of knowledge of the d i s t r i bu t ion dens i t y for the Г t & r°und the L o r e n t z i a n . The sum r u l e s (17)

and (7a) ca l l for D i r a c ' s Д function, if t h e r e i s only one C-I -S

within the r a n g e of a C-II -S and a d i s t r i bu t ion s y m m e t r i c with r e s p e c t to s m a l l e r and l a r g e r Г r v a l u e s , when t h e r e a r e two

u, t C- I -S within th is r ange . However , when t h e r e a r e many (~ 10) C - I - S ' s coupled to one C-II-S the d i s t r ibu t ion dens i ty a round the

-179-

L o r e n t z i a n should at l e a s t for smal l Г .- va lues IT . < p . ) иД u f ц f

a p p r o x i m a t e a P o r t e r - T h o m a s d is t r ibut ion known from s imi l a r p r o b l e m s :

1 Р ( Г f ) = Г (14)

lit . I -.z. ; Г f

"u1

2. ESTIMATION OF FISSION WIDTH Г* AND RESONANCE ENERGY E о

In th i s chap t e r we r e s t r i c t o u r s e l v e s without l o s s of genera l i ty

to c a s e 2 ( r 1 <S ГТ). As out l ined in the p rev ious chapter we a r e r e g a r d i n g the M p a r t i a l f i ss ion-widths Г a s s t a t i s t i c a l v a l u e s . The p r o b a b i -r m l i ty that

x £ Г £ x +dx (m = l , 2 , . . . , M ) m m m m

is given by

d P = f(x. . . . x . J d x . . . . dx (20)

1 M 1 m

w h e r e £(x, . . . x „ ) is the unknown probabi l i ty densi ty function.

The statist ical v a r i a b l e s x a r e r e s t r i c t e d to non-negat ive m

va lues x •?•

m >> 0.

F u r t h e r m o r e , following equ. (16) and (17) we have the sum rule

m E Г = Г \ (21) 1 m

w h e r e Г 1 i s the sp read ing width. This condition e n s u r e s that the v a r i a b l e s x m a y n e v e r be independent and that f fx^ . . x ^ ) h a s non -van i sh ing va lue only for those set s of x. which fulfil

I the sum condi t ion x , + x- + . . . +x = Г : 1 «A2 M

f(x, . . . x J = 0 if Z x Ï Tl ( 2 2 ) Vx^ = ° if \ х т ^ Г '

-180-

From the probability density f(x, . . . x^J we can deduce the M

marginal probability densities a> m

g i ( x i ) = / • • • J £ ( x i • ' • хм> d x i • • - *Ч-1 d x i+ i • • - d x M • о о

which define the probability to find the value of Г in the interval between x and x +dx, i r respect ive of the values of the remaining m m _ Г - As explained in the previous chapter we suppose that x., the expectation (mean) values of p. .are given by a Lorentzian form:

x. l

- , Ы,) - ƒ .igi(Xi)dx. - £ Г'Н (23) (Г'/2) +(E.-E )

1 О

E. is the energy related to the partial fission width Г. . We ex­plained that there -were good reasons for believing that the m a r ­ginal distributions g.(x.) for not too large values of x. axe not very different from a Por te r -Thomas distribution. Under a large value of x. we understand a value at least several t imes l a rger than the expectation value x. . It is clear that the rea l marginal distributions g.(x.), due to the sum rule (21) and (22) are always vanishing for values x. l a rger than Г >

g.(x.) = 0 if x. > 14 ,

and differ necessar i ly from the Por te r -Thomas distribution for la rger values. In order to estimate numerically the parameters Г and E from the given M couples of values Г and E we would have to define ь r m m a probability density function f(x. . . . x ) which fulfils the sum condition (22), the Lorentzian conditions (23) for the expectation values of f . i and for which the marginal functions g.(x.) a re not too different from Por te r -Thomas distributions.

We have tr ied to invent a statist ical model for the Г values in m

order to define a function f(x, . . . x ) giving satisfaction to the above outlined conditions. Unfortunately, this is not so easy and last not least , the function f(x.. . . x ) has to be sufficiently simple

- 1 8 1 -

for p e r m i t t i n g a m a t h e m a t i c a l and n u m e r i c a l t r e a t m e n t . Having a t p r e s e n t no be t t e r model , we p r e s e n t in th i s paper a very-poor app roach for f(x.. . . x ), neglect ing at f i r s t the sum con­dition (22). The advantage of this approach is the ea se with •which it can be handled .

P o r t e r - T h o m a s approach

Without a b e t t e r knowledge, we a s s u m e the following P o r t e r -T h o m a s d i s t r ibu t ions for the m a r g i n a l dens i ty functions g.(x.):

1 I х * * l x* 1 g.(x.) =.r—- exp( - £) = e x p ( - ( ^ -Щ^-J (24)

KZITX.X. I VZrrx. I l 1 i l l

This i s a viola t ion of the sum condition. F u r t h e r m o r e , we a s s u m e that the M v a l u e s J" a r e s t a t i s t i ca l ly independent . A l s o th i s a s s u m p t i o n i s s u r e l y not c o r r e c t . But due to these s impl i f i ca t ions it r e s u l t s immed ia t e ly that with x. = Г-

M M L exp{--f") (25) f ( r x . . • т м ) = ^ h { ]

with M

R = E 1

Ъ 1 ( ^ - _ in 4 - )

X. X. 1 1

Defining d

a = • — ZTT

rV

i fz^ Г.

Ъ. = ( Г Т / 2 ) + (E. - E )• 1 1 О

equ. (23) r e s u l t s in — a x i = b ~

2

l

(26)

(2?)

(28)

w h e r e x. depends now f rom the t h r e e unknown p a r a m e t e r s а, Г

and E . I n s e r t i n g (27) into (26) we obtain

t

Ы Г- b. b . R = т ( - i - i - - In —X- ) (29)

1 a a

In t h i s fo rmula R is a function of the M couples of v a l u e s V" . and E. and the th ree unknown p a r a m e t e r s а, Г ' , and E -

1 О

The m o s t obvious way for obtaining an e s t i m a t i o n of the unknown

p a r a m e t e r s i s the well known method of " m a x i m u m l i k e l i h o o d " . Those p a r a m e t e r s а, Г1 and E a r e the m o s t p l aus ib l e for which the function f{x, . . . x 4 , ) r e a c h e s i ts m a x i m u m : 1 M

M l R f ( Tj . . . Г - , а, Г , E o ) = TT "TZZIZr exp (- — ) = m a x i m u m (

1 2 TT Г-l

As only R i s depending f rom the p a r a m e t e r s and a s the fac tor M 1 T T •

1 i 2 TT Г.

i s pos i t ive we obtain t h e r e f o r e f rom (30)

M Г. b. b . R(a, r\ E ) = £ ( г l - I n — ) = m i n i m u m (31)

о l a a

P a r t i a l d i f ferent ia t ion of R with r e s p e c t to а, Г , E r e s u l t s in

о It is easy to show tha t (32) l e ads to the following s y s t e m of t h r e e , non l inea r i equat ions

M Г-Г ~ - = M (33) 1 x i

M M I Г = I x (34) 1 1 M M _ T E. Г. = Г Е. x. (3 5)

-183-

Equ- (33) has a very evident signification. As Г / x. is the i 1

value of the partial fission width in units of the expectation

(mean) value, the relative value of j \ , equ. (33) states that

the mean of the relative values Г ./x. equals 1. This seems 1 1

to be a very reasonable result. Explicitly written with the

help of (28 ) we obtain from (33)

M Г. b Z . 1 i = M 1 a

M a = M \ r i bi " <36>

By equ. (36) we get rid of the parameter a = df Г /2тт .

(As our function f(x . . . x .), equ. (25), was violating the

sum rule we could not use equ. (21) for fixing the parameter

Г and therefore fixing also the ла1ие of a).

The variable R is a function of the three parameters а, Г . E .

Inserting in equ. (26) the formula (36), which explains a as a

function of the two parameters Г and E , the variable R о

changes to a new variable Q which depends only from the two

last variables M Г. b. b.

Q (Г*. Е ) = E (—4—l In -1-) = minimum (37) О ч & SL

1 м

Let us now see some practical results of equ. (37): 242 In the system Pu+n there is a C-II-S at E = 475 eV coupled

П t to 4 C-I-S's. In fig. 2 we see the Q values as a function of Г

t and E . The minimum of Q is positioned at Г = 0 (point "a")

о in an almost horizontal "ravine". The deepest points of this

ravine are connected by a dashed line. As the Q-value along

this ravine is only very slightly raising, the maximum likeli-

- П 4 -

hood method ind ica t e s in this c a s e that the couple of unknown v a l u e s Г and E should be si tuated in o r n e a r the r av ine

° t which g ives b e t t e r defini t ion for E than for Г . In fact , s о the e s t i m a t i o n of 3 unknown p a r a m e t e r s f rom a r andom s a m p l e of s i z e 4 is a c a s e of v e r y poor s t a t i s t i c s . The hatched a r e a in fig. 2 def ines the r eg ion for which the sp read ing -width Г = 2тт а / ^ Г (see equ. (27)) l i e s in the i n t e rva l given by E Г. i 5%. As this r eg ion i s c r o s s e d by the r a v i n e , t h e r e is some r e a s o n that the bes t v a l u e s of Г and E a r e to be found in this pa r t of the r av ine (point " 6", Г = 1 5 eV). A th i rd point " b " h a s been chosen a r b i -

t t r a r e l y in the r a v i n e with а Г -va lue of 7. 5 eV.

Each po in t in the p lane of Г and E of fig. 2 c o r r e s p o n d s to a spec i a l L o r e n t z i a n f o r m . The expec ta t ion va lue of г • was equal to x. . F u r t h e r m o r e the chosen P o r t e r - T h o m a s

1 . - 2 d i s t r i bu t i ons a r e giving the va lues of Г- a v a r i a n c e of 2 x. . The va lue

| / M (Г- - x ) D = /( Г. * * ) / (M-3)

V 1 2 x. l

can be r e g a r d e d a s a m e a s u r e for the goodness of a fit defined

by the va lues of Г and E . The number of M-3 h a s been chosen о

somewha t a r b r i t a r i l y b e c a u s e th i s i s the n u m b e r of the d e g r e e of f r eedom in the p r o b l e m . It is expected that at r andom the v a l u e s of D should be in the neighbourhood of 1. In fig, 3 the r e l a t e d D-va lues a r e p r e s e n t e d . It i s seen tha t the p a t t e r n of D - v a l u e s is a l m o s t the s a m e as that of the Q-va lue s . Again we have the r av ine . T h i s ind ica tes that in the p r e s e n t c a s e , the e s t i m a t i o n of Г and E is not so m u c h inf luenced by the

о ' cho ice of s t a t i s t i c a l a p p r o a c h but by the n a t u r e of the b o r e n t z i a n f o r m with the pos s ib i l i t y of having a pole if Г = 0 and the p o s i ­t ion of the four p a r t i a l f i s s ion widths r e l a t i ve to the L o r e n t z i a n .

-185 -

F ig , 4 i nd i ca t e s the posi t ion of the four r . va lues and the L o r e n t z i a n c o r r e s p o n d i n g to the t h r e e points "a" , " b ' \ and " c " of fig. 2 and 3 . F o r m , r c " s e e m s to be the m o s t p laus ib le .

The next fig. 5 shows the Q-va lues for the 6 C-I-S coupled to a 242 C-I I -S of the Pu+n s y s t e m a t E = 762 eV. Again, we have

a r av ine connect ing the m i n i m u m (point "a") with the point " c " . T h e r e i s a l so a s m a l l s e c o n d a r y r av ine around the point " b " . The D - v a l u e s of the fig. 6 show a s i m i l a r pa t t e rn . The fig. 7 r e p r e s e n t s the L o r e n t z i a n f o r m s of the point "а" , "Ъ", and " c " , It b e c o m e s c l e a r that the s econda ry r av ine around " b " is due to the fact tha t in t h i s c a s e , the peak of the L o r e n t z i a n can be s i tua ted to the left of the c e n t r a l l eve l .

237 The C-I I -S at 40 eV of the s y s t e m Np+n is coupled with 13 C - I - S . Th i s e leva ted n u m b e r should r e s u l t in a l e s s i m ­p r e c i s e e s t i m a t i o n of the unknown p a r a m e t e r s . In fact, the Q - v a l u e s of fig. '8 ind ica te i n s t ead of a r av ine a well defined "hol low" a round the m i n i m u m point " a " which for tunately l i e s on the b o r d e r of the 5% sum condit ion a r e a . The D-value p a t t e r n of fig. 9 h a s a s i m i l a r p a t t e r n with a hollow around the m i n i m u m point " b " which is shifted somewhat f rom point " a " . In th i s ca se i t s e e m s that not only the mos t p lausible v a l u e s of Г and E a r e be t t e r defined, but that the i r p o s i ­t ion m a y be influenced by the mode l chosen for the s t a t i s t i ca l a p p r o a c h . The l a s t fig. 10 shows the Lo ren t z i an foT the two poin ts " a " and " b " .

The s t a t i s t i c a l app roach chosen for the e s t ima t ion of the decay width Г a i*d r e s o n a n c e ene rgy E is a v e r y rough s impl i f ica­t ion of the p r o b l e m . It v io la tes s e v e r a l condit ions a s the sum of the p a r t i a l widths and t h e i r s t a t i s t i ca l in te rdependence . It i s only just i f ied by the ac tua l l ack of knowledge for a m o r e r e a l i s t i c p robab i l i ty dens i ty function f(x. . . -Xi/P' N e v e r t h e l e s s , the r e s u l t s obta ined a r e not so wrong as could be expected.

- 1 8 6 -

At a n y r a t e a s l ong a s the n u m b e r of c o u p l i n g C - I - S i s no t

c o n s i d e r a b l e g r e a t e r t h a n the n u m b e r of u n k n o w n p a r a m e t e r s ,

a n e s t i m a t i o n of p ' a n d E i s p e r t u r b e d b y a p o o r s t a t i s t i c .

A s t h e n u m b e r of c o u p l i n g s t a t e s i n c r e a s e s , t h e e s t i m a t i o n of

t h e p a r a m e t e r s i s m o r e p r e c i s e , but d e p e n d e n t on t h e m o d e l

f o r t h e s t a t i s t i c a l a p p r o a c h .

A c k n o w l e d g m e n t

T h e a u t h o r s e x p r e s s t h e i r g r a t i t u d e to D r . J . E . L Y N N for

h i s c l a r i f y i n g c o m m e n t s t o t h i s s u b j e c t , w h i c h a r e p a r t l y 7)

c o m m u n i c a t e d in a H a r w e l l r e p o r t

R E F E R E N C E S

1) J . E . L y n n , H a r w e l l R e p o r t , A E R E - R 5891 (1968)

2) H. W e i g m a n n , Z e i t s c h r . f. P h y s . 2 1 4 , 7 (1968)

3) C . M a h a u x and H. A. W e i d e n m ü l l e r , N u c l . P h y s . A 9 1 .

241 (1967)

4) C. M a h a u x and H. A. W e i d e n m ü l l e r , S h e l l M o d e l l A p p r o a c h

to N u c l e a r R e a c t i o n s , N o r t h - H o l l a n d P u b l . , A m s t e r d a m (1969) .

5) C. M a h a u x , I n t e r n a t i o n a l C o u r s e o n N u c l e a r T h e o r y ,

P a p e r SMR 6 / 2 2 , T r i e s t , I t a l y , (1969)

6) H. W e i g m a n n a n d J. P . T h e o b a l d , N u c l . P h y s . A 1 8 7 , 3 0 5

(1972)

7) J . E . L y n n , H a r w e l l Pcepor t A E R E - R 7279 (1972)

0.1

aoi

E 0W ) = 762eV

E0fn ) = 475eV

r'=16eV

r ' = U m e V

t»V)

350 Fig.1

«Ю «50 500 550 eoo 650 700 750 800 850 900 950'

-133-

r t 15 eV

Fig. 2 Q-values

Fig.3 D -values r t . 15 eV

550 eV

Lorentzian forms energy

- 1 9 0 -

! 6eV

Fig. 5 Q-values

6eV

Fig.6 D-values

100

meV

80

60-

•o

40

20-

Fig. 7

700

i ! '

; • : !

: Hl ; 'II

1

i,C

i

! <

'• i '•

243 p u

i

1 :

Hf J •• > - ' ©

1.\

r6f 1 . , -.._ 0 ( - 1 1 " " " i ° 750 800

Lorentzian forms

850 eV energy

- 1 9 2 -

Fig.8 Q - values 1-1 tOeV

Fig. 9

- 1 9 3 -

00 со

®

° 5-й> В

г

V'

см

S41PIM

-194-

SYSTEMATICS OF TOTAL, RADIATIVE WIDTHS OF NEUTRON

RESONANCES

H, Weigmann and G. R o h r

Cen t r a l Bureau for N u c l e a r M e a s u r e m e n t s

EURATOM, Gee l , Belgium

ABSTRACT

An a t t e m p t i s m a d e to fit e x p e r i m e n t a l r ad i a t i ve widths o{ n e u t r o n

r e s o n a n c e s of nuc le i in the m a s s n u m b e r r ange 40 ^ A s 247 by

a s e m i e m p i r i c a l e x p r e s s i o n . This e x p r e s s i o n con ta ins b e s i d e s of

the u s u a l s t a t i s t i c a l mode l t e r m a second t e r m which t a k e s into

accoun t v a l e n c y nuc leon con t r i bu t i ons . Shell effects have been taken

into account through a s imp le r e p r e s e n t a t i o n of t he i r inf luence on

compound n u c l e a r l eve l d e n s i t i e s . Throughout the a n a l y s i s it h a s

been t r i e d to l im i t the n u m b e r of f ree p a r a m e t e r s and to r e l a t e

the p a r a m e t r i z a t i o n as c lose ly as poss ib l e to phys i ca l p r i n c i p l e s .

C o m p a r i s o n is made to e a r l i e r s tudies of s i m i l a r type .

-195-

I . INTRODUCTION

The knowledge of n e u t r o n r a d i a t i v e c a p t u r e c r o s s sec t ions of

m a n y i so topes o v e r wide r a n g e s of neu t ron e n e r g i e s i s of g r ea t

i m p o r t a n c e for the des ign of nuc l ea r r e a c t o r s . If t h e s e c r o s s

s e c t i o n s a r e not d i r e c t l y m e a s u r a b l e , a s i t i s the c a s e e . g . for

f i s s i on p r o d u c t s , t h e o r e t i c a l e s t i m a t e s a r e n e c e s s a r y . This is

p a r t i c u l a r l y t rue for the c a p t u r e c r o s s sec t ions of t r ansp lu ton ium

e l e m e n t s whjch a r e i m p o r t a n t for the n u c l e a r fuel cycle and the

w a s t e m a n a g e m e n t . The r e l i a b i l i t y of such e s t i m a t e s depends

s t rong ly on our knowledge of a v e r a g e r ad i a t ive widths of c o m ­

pound n u c l e a r l e v e l s and t h e i r dependence on exci ta t ion ene rgy

and o the r n u c l e a r p a r a m e t e r s .

M o r e o v e r , the knowledge of r e s o n a n c e p a r a m e t e r s t h e m s e l v e s

and p a r t i c u l a r l y of r a d i a t i v e widths of r e s o n a n c e s i s d i r e c t l y

needed for the d e t e r m i n a t i o n of self shie lding fac to rs and

Dopple r coeff ic ients in r e a c t o r ca l cu la t ions .

B e c a u s e of the l imi t ed ava i lab i l i ty of r e l i ab l e exper imen ta l

r a d i a t i v e widths - again , for r ad ioac t ive f i ss ion p roduc t s and

t r a n s p l u t o n i u m e l e m e n t s e x p e r i m e n t a l da ta a r e h a r d l y avai lable -

the developrnent of t h e o r e t i c a l e x p r e s s i o n s for the calculat ion of

r a d i a t i v e widths b e c o m e s v e r y i m p o r t a n t .

Ano the r i n t e r e s t i n g field for appl ica t ions of t heo re t i ca l l y d e t e r ­

m i n e d neu t ron cap tu re c r o s s sec t ions and t he r eby of rad ia t ive

wid ths is the study of heavy e lement syn thes i s in s t a r s .

Because of these r e a s o n s we have a t t empted to se t up a s e m i -

e m p i r i c a l r e l a t i on for the ca lcu la t ion of r ad ia t ive widths which

i s fitted to e x p e r i m e n t a l l y known da ta .

S i m i l a r inves t iga t ions have been done by Levin and Hughes ', 2) 3)

C a m e r o n , and Stolovy and Harvey , and m o r e r ecen t l y by 4) 5)

Malecky et a l . , and Zakha rova et a l , . Both, amount and qual i ty of e x p e r i m e n t a l data have i n c r e a s e d cons ide rab ly s ince

-196-

the f i r s t t h r e e of t he se s tud ies had been m a d e -which in i t se l f

jus t i f i e s a r e i n v e s t i g a t i o n of the p r o b l e m . F u r t h e r m o r e , our

a p p r o a c h differs f rom al l of the p r e v i o u s ones mentioned, above

in two a s p e c t s : l ) B e s i d e s of the u s u a l s t a t i s t i c a l m o d e l e x ­

p r e s s i o n for the r a d i a t i v e width we add a second t e r m which i s

to t a k e into account va l ency nucleon c o n t r i b u t i o n s . 2) Throughout

the a n a l y s i s we t r y to r e l a t e the p a r a m e t r i z a t i o n a s c l o s e l y a s

p o s s i b l e to phys i ca l c o n s i d e r a t i o n s .

In s e c t i o n II we sho r t l y d i s c u s s the a v a i l a b l e e x p e r i m e n t a l

da ta , in sec t ion III the s t a t i s t i c a l m o d e l e x p r e s s i o n for r a d i a ­

t ive widths i s d i s c u s s e d in s o m e de ta i l , s ec t ion IV dea l s with

v a l e n c y nuc leon c o n t r i b u t i o n s and in s ec t i on V we give the r e ­

s u l t s of the ca l cu l a t i ons and c o m p a r e them to the e x p e r i m e n t a l

da t a a s well a s to e a r l i e r s y s t e m a t i c s t u d i e s .

II. EXPERIMENTAL, DATA

Tab le I l i s t s , b e s i d e s of o the r e x p e r i m e n t a l da t a which wil l be

d i s c u s s e d in the following s ec t i ons , m e a s u r e d m e a n r a d i a t i v e

widths for s - and p -wave n e u t r o n r e s o n a n c e s (co lumns 8 and 9,

r e s p e c t i v e l y ) . In column 10 we give r e f e r e n c e s p e r t i n e n t to the

e x p e r i m e n t a l da ta in the t a b l e , including l e v e l spac ings and

s t r eng th func t ions .

In c a s e s , w h e r e m o r e than one e x p e r i m e n t a l va lue for the a v e r a g e

r a d i a t i v e width a r e ava i l ab le and t h e s e v a l u e s differ s ignif icant ly ,

we have u s u a l l y s e l ec t ed the value due to the m o r e r e c e n t a n d / o r

m o r e comple t e ( l a rge r n u m b e r of r e s o n a n c e s ana lysed) m e a s u r e ­

m e n t . In some c a s e s , when a se lec t ion on th i s b a s i s w a s not

p o s s i b l e , we have used a weighted m e a n .

Some spec ia l c a s e s should be expl ic i t ly ment ioned : 58)

1) We did not inc lude e x p e r i m e n t a l r a d i a t i v e wid ths f rom ref.

for e v e n - e v e n Z r t a r g e t nuc le i because the p a r i t y a s s i g n m e n t

of the r e s o n a n c e s is unknown and the r a d i a t i v e widths show

- unexpec ted ly l a r g e f luctuat ions , even if one c o n s i d e r s only

r e s o n a n c e s •which a r e c e r t a i n l y s -wave.

-197-

2} We did not include data on radiative widths of Pb and Bi isotopes,

because only few resonances have been measured and strong

fluctuations from resonance to resonance are expected for the

radiat ive widths which in these nuclei are a sum of only a very

small number of part ial widths.

3) Strong correlat ions between total radiative widths and reduced 44) neutron 'widths have been observed for several isotopes in

the region of the peak of the s-wave strength function around

A = 50, Because of this fact we define an average radiative

width for these isotopes only if the number of individual r a ­

diative widths that have been determined is not too small {about 5).

On the other hand, the information from, the observed corre la­

tions in all of these isotopes is used to determine the valence

nucleon contribution to total radiative widths in this mass

region (see section 4). •<

III. STATISTICAL MODEL TERM

The statist ical model expression for the total radiative width

reads :

r y {stat. ) = g A 2 / 3 D{B) ƒ ^ ^ p (П

he re В is the excitation energy of the compound nuclear resonance, i. e. for slow neutron capture essentially the neutron binding energy, D{B) is the average spacing of levels of the same spin and parity as the capturing resonance, D(E) is the spacing of levels at excitation energy E to which dipole transit ions are possible, and § is a constant to be determined from comparison to experimental data.

a) Average level spacing The average level spacing D(E) or alternatively the level density p(E) = l/D(E) is usually assumed to be well represented by a F e r m i gas type expression

n ( E , J ) = 2 J + 1 ± 5 / 4

Za Ui

-198-

Here ?.", = E + ц - Ti i s an effective exc i t a t ion e n e r g y {see below),

a i s the leve l dens i ty p a r a m e t e r and o" i s tbe sp in cut off fac tor

for which, the a p p r o x i a m t e r e l a t i on ho lds :

a2 „ 0 . 0 6 A 7 / 6 (3)

I n s e r t i n g (2) into (1), the spin dependence of D(B) and D { E )

a p p r o x i m a t e l y c a n c e l s so that we a r e left with

Г (s ta t . ) = ? А " / л ( В д ) э / % 2/3, , ,*. 5/4 -2VaB7(B-El Гг 3 2 f a E e

CE*) 5 / 4 • d E

Equat ion (2) for the l eve l dens i ty is not va l id for s m a l l exc i ta t ion

e n e r g i e s ( ~ 1 MeV), We t h e r e f o r e u se , following G i l b e r t and 7) C a m e r o n , a compos i t e leve l dens i ty e x p r e s s i o n :

(E) =

\ **•' Z T T F

e ( : J 1 ' ( E * ) 5 / 4

( P2 = с e T

for E * > 1.5 MeV

for E < 1.5 MeV (5)

H e r e , the th i lde denotes that *p g ives only the e n e r g y dependence

of the l e v e l dens i ty whi ls t ene rgy - independen t f a c t o r s have been ± omi t t ed . The cons tan t s T and с a r e chosen such tha t at E = 1 . 5 MeV

d i n oi d lnp - , In n. = In p., and —-r= = —г-i;— f rom which one obta ins

^ 1 2 dE dE

Y-k I 5 , . - , Г — p 5 . . _ 1. 5-6 -n t i cxr ir " 7Т7ТГ a n d In с = 2 y i . 5 a - ~ l r i l . 5-——— T r l . 5MeV 6MeV ' 4 T

With th i s г-epresentat ion for the l eve l dens i ty we have

Г ( s t a t . ) = * A 2 / 3 ( B * ) 5 / 4 e / (B- E ) 3 ? ( E ) d E (6)

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b) Shell c o r r e c t i o n s

The p r o b l e m of i n c o r p o r a t i n g the effect of nuc l ea r shel l s t r u c t u r e

into a d e s c r i p t i o n of the compound n u c l e a r l eve l dens i ty has been 8) deal t with ex t ens ive ly by Kahn and Rosenzweig .

The i r r e s u l t i s tha t if one a p p r o x i m a t e s the t r u e she l l s t r u c t u r e by a p e r i o d i c s ingle p a r t i c l e ene rgy l eve l s cheme , the gene ra l form of equ. (2) for the l eve l d e n s i t y i s ma in ta ined with an effective exc i ta t ion e n e r g y

E * = E + i - n (7)

w h e r e u i s a shell c o r r e c t i o n and i s analytically e x p r e s s i b l e in t e r m s of the p e r i o d i c s ingle p a r t i c l e l eve l s c h e m e and n is a c o r r e c t i o n for p a i r i n g . M o r e r e c e n t l y , Wi l l i ams et a l . ' have used n u m e r i c a l m e t h o d s to g e n e r a t e nuc l ea r l eve l dens i t i e s from a N i l s s o n s ingle p a r t i c l e leve l s c h e m e . They, too, a r r i v e at the conc lus ion tha t equat ions (2) toge the r with (7) m a y be used to d e s c r i b e nuc l ea r l eve l d e n s i t i e s , but that the abso lu te value of the shel l c o r r e c t i o n 5 wil l t hen depend s t rong ly on the range of exc i t a ­t ion e n e r g i e s one i s i n t e r e s t e d in. E x p e r i m e n t a l ver i f ica t ion of equat ion (2) for the e n e r g y dependence of the nuc lea r level dens i ty h a s been obta ined by Vonach and НШе

F o r the p r e s e n t p u r p o s e we want to have a s imp le analyt ica l

e x p r e s s i o n for the l eve l dens i ty . The re fo re we use toge ther

with equa t ions (2) and (5) an e x p r e s s i o n for the shel l c o r r e c t i o n 8) Д s i m i l a r to the one given by Kahn and Rosenzweig , with an

o v e r a l l n o r m a l i z a t i o n fac tor to be fi t ted to the expe r imen ta l data . The r e l e v a n t e x p r e s s i o n i s equat ion (3. 16) in the paper of Kahn

8) and Rosenzwe ig . In approx ima t ing the shel l mode l level scheme

by a q u a s i p e r i o d i c s ingle p a r t i c l e level s cheme , we put (using

the s a m e symbo l s a s Kahn and Rosenzweig) 6 = 2 ( rk(g , ) - r u ( l ) ) . A A A A

i. e. r e p l a c i n g the n u c l e a r shel lsby bands of un i formly spaced l e v e l s (g is the number of l e v e l s in a band), with the d i s tance

A of two ne ighbour ing bands being equal to t he i r wid ths ; this is roughly what, i s c h a r a c t e r i s t i c for usua l shel l model level s c h e m e s ,

- 2 0 0 -

With this model and neglecting t e r m s of order — against 1 we obtain

A X = \ \ (gX ~ V

4 ел 32 (8)

X = 1, 2 stands for protons and neutrons, respectively, and n is л

the number of nucleons in the last (partly filled) shell. Thus, if the number of nucleons N in a given nucleus lies between the two

, X magic numbers N. and Nu , then

/•- X h'\ Nv W N . (9)

For 6 we write A

б = d • fr(« X X о г<ы„ 41 MeV

л i / 3 (10)

The quantities d have been taken from the shell model level . 102)

scheme (for deformation zero) given by S. G. Nilsson The numerical values a re given in table III together with the relevant magic numbers which have as well been used in equ. (9).

Table I I I :Parameters used in the calculation of the shell correct ion

type of particles N x К dx 20 28 0. 8

protons 28 40 0. 6 and 40 50 0. 5 neutrons 50 82 1.0

protons only 82 114 0. 6

neutrons only 82 126 1.1 126 164 0. 5

- 2 0 1 -

Finally, the shell correct ion as used in the present analysis i s , with the exception of nuclei in the regions of strong deformation, given by

Д = С Д ( Л 1 + Д 2 ) (П>

with the normalizat ion constant с to be fitted to the experimental data. Fo r strongly deformed nuclei, i. e. if

N s 86 and Z & 78 ) or Z > 88 and N <; 134 l Л = ° ^ 2 * is assumed,

c) Pair ing correct ion

The pairing energy correction to the effective binding energy is calculated according to Nemirovsky and Adamchuk :

n / ' P - i T 7 3 t " - ' . w ( i t T ' z V H i 4 аз) P P 9A / J л А

% •«„ -7^73-1" - °- " l l s f " i L 1+44- 5 7 r 9A ' A

•wi th

^ £ [ B ( Z , . N ) - B ( Z - l . N ) ]

(14)

c n = | [ B n ( Z , N ) - B n ( Z , N - l ) ]

where В and В a re proton and neutron binding energies, respectively, p n The philosophy underlying the practice to subtract the pairing energy from the binding energy in order to obtain the effective binding energy, i. e. the assumption that no levels exist below the pairing energy gap, is , of course, not fully justified (there are collective levels). We take this fact into account empirically by multiplying the pairing energy as given by equation (13) by a factor с < 1 which is to be fitted to the experimental data. Thus, finally,

- 2 0 2 -

1"! ~

c (Л + V ) f o r e v e n - e v e n n u c l e i П *p n

f o r e v e n - o d d n u c l e i

f o r o d d - e v e n n u c l e i

f o r o d d - o d d n u c l e i

c Л П p с n

(15)

IV. VALENCY NUCLEON CONTRIBUTION In r e c e n t y e a r s , e v i d e n c e h a s b e c o m e a v a i l a b l e fo r s t r o n g

n o n s t a t i s t i c a l e f f e c t s in n e u t r o n c a p t u r e b y n u c l e i i n c e r t a i n

r e g i o n s of t h e p e r i o d i c t a b l e . S u c h n o n s t a t i s t i c a l e f f e c t s h a v e r * T, v , 104 , 105) . , « . ^ f i r s t b e e n o b s e r v e d m p - w a v e n e u t r o n c a p t u r e b y n u c l e i a r o u n d A = 100 a n d l a t e r 44) .

in s - w a v e n e u t r o n c a p t u r e

by n u c l e i a r o u n d A = 50. T h e i n t e r p r e t a t i o n ' of t h e s e

o b s e r v a t i o n s i s b a s e d on t h e s o - c a l l e d v a l e n c y n u c l e o n m o d e l

w h i c h p r e d i c t s s u c h e f f e c t s fo r n u c l e i c l o s e to m a x i m a in t h e

r e l e v a n t n e u t r o n s t r e n g t h f u n c t i o n w h e n e v e r E l t r a n s i t i o n s to

u n o c c u p i e d l o w - l y i n g s i n g l e p a r t i c l e o r b i t a l s a r e p o s s i b l e .

A p a r t i c u l a r f e a t u r e of t h e n o n s t a t i s t i c a l e f f e c t s i s t h a t c o r r e ­

l a t i o n s of p a r t i a l o r e v e n t o t a l r a d i a t i v e w i d t h s a n d r e d u c e d

n e u t r o n w i d t h s a r e o b s e r v e d . T h u s w e u s e t h e a n s a t z :

Г ( v . n . ) = s A g Г Y J n

(16)

o r , m a v e r a g i n g o v e r m a n y r e s o n a n c e s

2 / 3 < Г (v. n . ) > = s Au/J g ' D S.

v o b s 1 (17)

h e r e , Г ( v . n . ) d e n o t e s t he v a l e n c v n u c l e o n c o n t r i b u t i o n to t h e Y

t o t a l r a d i a t i v e w i d t h , S, i s t h e s t r e n g t h f u n c t i o n , D , i s t h e i obs

o b s e r v e d s - w a v e l e v e l s p a c i n g .

g ' = (4 I 4- 2) E g J b J

"• (2J+1) (18)

i s a sp in s t a t i s t i c a l f a c t o r , w h e r e t h e s u m s a r e o v e r a l l c o m ­

p o u n d s p i n s J w h i c h m a y be p r o d u c e d in t h e i n t e r a c t i o n of

-203-

n e u t r o n s of o rb i t a l angu la r m o m e n t u m 1 with a nuc leus of spin I;

( 1 0

g j = j 2 for J = 1/2

( 3 * 1

denotes the n u m b e r of decay channe l s for dipole e m i s s i o n of a compound s t a t e of spin J.

The fac to r s i s to be e x t r a c t e d f rom expe r imen ta l data for each g roup of nuc le i showing n o n s t a t i s t i c a l ef fects , s e p a r a t e l y :

a) s -wave r e s o n a n c e s in n u c l e i a round A = 50 Strong c o r r e l a t i o n s be tween tota l r a d i a t i v e widths and reduced

44) n e u t r o n widths have been o b s e r v e d by St iegl i tz et al , for • * . , , • 52лг 51, 53, 54„

s -wave r e s o n a n c e s in the compound nuc le i V, Cr and Ni . In o r d e r to d e t e r m i n e the fac tor s f rom these data we did p roceed in the following way: We have se lec ted 2 o r 3 r e s o n a n c e s with l a r g e s t T and Г - v a l u e s for each of the above i so topes . We

Y n

then have , in a p r e l i m i n a r y r u n of the p rese : i t p r o g r a m , e s t ima ted

the s t a t i s t i c a l m o d e l cont r ibut ion to the total r ad i a t ive widths of

t h e s e i so topes and put г ( v - n - ) -T ( е х р ) - Г (s ta t ) . Y Y Y

We then have used equ. (16) to d e t e r m i n e s a s s = s = 3 .9 • 10 for s - w a v e s , A £ 63 (19)

The u p p e r l i m i t of the m a s s r ange whe re th i s va lency nucleon

con t r ibu t ion to the r a d i a t i v e widths i s a s s u m e d to exis t , is

chosen a c c o r d i n g to the obse rva t i on that for h e a v i e r nuclei the

s ingle neu t ron p - s t a t e s which ac t as final s t a tes for the va lency

nucleon t r a n s i t i o n s , a r e e s s e n t i a l l y f i l led.

b) p - w a v e r e s o n a n c e s in nuc le i a round A = 100

Valency nucleon effects have been obse rved •'04, lUbJjn p _ w a v e

r e s o n a n c e s of s e v e r a l nuclei in this m a s s r ange . Total rad ia t ive 28 ^

widths a r e known for p -wave r e s o n a n c e s in the compound 99

nuc leus Mo. H e r e , the s t a t i s t i ca l mode l contr ibut ion m a y De

a s s u m e d to be given by the r ad i a t ive widths of s -wave r e s o n a n c e s

in the s a m e isotope, thus Г (v. n. ) = Г (exp. , p - w a v e ) - Г (exp. , s -Y 1 1 Q. Г ? S "

w a v e ) . F o r the compound nuc le i v ' A 3Sn p a r t i a l r ad i a t i ve

-204 -

75) wid ths a r e known for those t r a n s i t i o n s which show va lency

nuc leon c h a r a c t e r . Thus , in th i s c a s e Г (v. n. ) m a y s i m p l y be Y

t aken a s the sum o v e r t h e s e (only 2) p a r t i a l r a d i a t i v e w i d t h s . F r o m these Г (v. n. ) - v a l u e s and the c o r r e s p o n d i n g r e d u c e d

n e u t r o n wid ths we aga in h a v e d e t e r m i n e d s a c c o r d i n g to equ . (16)

to be -4 s = s = 3. 82 • 10 for p - w a v e s , 88 <: A < 125 (20)

The u p p e r l i m i t of the m a s s r a n g e i s chosen a c c o r d i n g to s i m i l a r

a r g u m e n t s a s for equ. (18), the l ower l im i t is to a c e r t a i n d e g r e e

a r b i t r a r y . However , the v a l e n c y nuc leon con t r ibu t ion due to equ. (2 0)

t u r n s out to be of some i m p o r t a n c e only for nuc le i in the peak r eg ion

of the p - w a v e s t r e n g t h function.

c) s -wave r e s o n a n c e s in nuc le i with 196 < A < 204

A r a t h e r di f ferent type of n o n s t a t i s t i c a l effects h a s been o b s e r v e d

for n e u t r o n c a p t u r e in nuc le i a round m a s s 200, i . e . the s o - c a l l e d

" a n o m a l o u s b u m p " (for a de ta i led d e s c r i p t i o n s ee ref. ).

In c o n t r a r y to the c a s e s of v a l e n c y nucleon effects d i s c u s s e d above ,

a r a t h e r l a r g e n u m b e r of p a r t i a l r ad i a t ive wid ths is r e s p o n s i b l e

for the effect of the anomalous bump .

In the p r e s e n t a n a l y s i s it h a s tu rned out that a p u r e l y s t a t i s t i c a l e x p r e s s i o n p r e d i c t s much too s m a l l r ad i a t i ve wid ths jus t in the r ange of nuc le i w h e r e the anoma lous bump is m a i n l y o b s e r v e d . Thus , we a s s u m e a n o n s t a t i s t i c a l cont r ibu t ion a l so to the to ta l r a d i a t i v e widths of t h e s e nuc le i which we again w r i t e in the form of equ. (17), al though it is ques t ionable w e t h e r it i s just i f ied to a s s u m e a p ropo r t i ona l i t y with the s t r eng th function a l so in th i s c a s e . The p ropo r t i ona l i t y fac tor s = s , is d e t e r m i n e d along with the o v e r a l l fit of the p r e s e n t model to the e x p e r i m e n t a l da ta .

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V. RESULTS AND DISCUSSION

Our model conta ins 4 f ree p a r a m e t e r s : с , с , E; and s , where the l a s t one conce rns only the l imi ted m a s s number range 196 ^ А Й 204. In o r d e r to adjust t hese p a r a m e t e r s to the exper imenta l data we p roceed in the following way: p a i r s of va lues с с a r e

А Л chosen and for each pa i r a l e a s t square fit of the calculated radia­t ive widths to the exper imen ta l data of table I, columns 8, 9 is m a d e which yie lds the p a r a m e t e r s § and s». The va lues of с t and с a r e va r i ed in s teps of 0. 01 and 0. 05, r e s p e c t i v e l y , and the bes t fit is se lec ted . The set of p a r a m e t e r s co r re spond ing to the bes t fit, i s

c. = 0 .07 E = 3.72 • 1 0 " 3

Д

Cn = 0 .75 s = 4 . 9 - 1 0 " 2

(21) ^ 4 q . 1 n ~ 2

F o r th i s set of p a r a m e t e r s the data and r e s u l t s given in tables I and II have been obtained. Table II l i s t s ca lcu la ted radia t ive widths a l so for some nucle i whe re no cor responding exper imenta l v a l u e s a r e avai lable , but where the n e c e s s a r y p a r a m e t e r s for the ca lcu la t ions , l ike level spacing.s and eventually strength func­t ions , a r e known. The way by which the r e s u l t s of table II have been obtained is de sc r ibed below and this i s at the same t ime the p resc r ip t ion for the calculat ion of rad ia t ive widths which we propose : F i r s t , from the m e a s u r e d neutron binding energ ies l is ted in table I, column 2, and equ. (7) - (15) with

с = 0. 07 с = 0.7 5 (22) Л Л

one ca lcu la te s the effective binding ene rg ie s which a r e given in table I, column 4. F r o m these data and the exper imenta l level spacings (table I, column 3) the level spacing p a r a m e t e r s a a r e calculated accord ing to equ. (2), (3). The va lues obtained for a a r e given in table I, column 5. This table contains fur ther the s - and p-wave s t rength functions where these, a r e n e c e s s a r y to ca lcula te Г (v. n. )(columns^, 7) the exper imenta l s - and p-wave

Y

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radiative widths (columns 8, 9) and references (column 10).

With the aid of these data and the parameter values

§ = 3. 72 • 10"3

(s = 3 . 9 ' 10" s-waves, A £ 63 f -4 vs = 3.82- 10 p-waves, 88 <r A <; 125 (23) S = ( 2 -2 ( s 3 = 4.9.10

(0 otherwise

, s =4. 9*10 s-waves, 196 ^ A <204

the. theoretical s- and p-wave radiative widths

Г (theor. ) = Г (stat. ) + г (v. п. ) (24) Y Y Y

•v J

are calculated according to equ. (6) and (17)

The present results are compared to the experimental data in

table II. In this table, column 2 gives p (stat. ), columns 4 and 6

give Г (theor. ) for s- and p-wave resonances, respectively and

columns 3 and 5 give the corresponding experimental values.

The root mean square values of the percent deviations of the

theoretical radiation widths of table II from the corresponding

experimental values is 2 5%. This is not much better than cOrres-4 5) ponding figures obtained in ref. ' . However, an improvement

with the present analysis lies in the fact, that this figure is ob­

tained from comparison of calculated and experimental radiative

widths including data from the region of mass numbers around

A - 50 to 60. (and also around A =200) which had been excluded 4 s)

in ref. ' , This improvement is, of course, due to the addition

of the valency nucleon term. We believe that a further advantage

of the present analysis lies in the fact that we have essentially

avoided purely empirical relationships but that instead all formulae

used in the calculations have a physically sound basis. This fact

should increase the reliability of the present approach when it is

extrapolated to regions where little experimental information is

available.

" it should be noted, however, that equ. (17) gives the valency nucleon contribution to the average width. For individual resonances, equ. (16) should give a better estimate.

-207-

The p r e s c r i p t i o n for ca lcula t ion of r ad i a t ive widths as it is de sc r ibed above n e e d s e x p e r i m e n t a l da ta on l e v e l spac ings . In o r d e r to be able to c a l c u l a t e r ad i a t i ve wid ths a l s o for nuc le i w h e r e no such data a r e ava i l ab le , we have t r i e d to set up a r e l a t ion which a l lows to ca lcula te the l e v e l spac ing p a r a m e t e r . Tabula t ions of l eve l spac ing p a r a ­m e t e r s found in the l i t e r a t u r e should not be used because they u sua l l y a r e ba sed on o the r a s s u m p t i o n s concern ing the effective binding e n e r g y than the one adopted in the p r e s e n t a n a l y s i s .

Our r e l a t ion for the ca lcu la t ion of the l eve l spacing p a r a m e t e r 8) aga in is based on the one given by Kahn and Rosenzweig for

p e r i o d i c s ingle p a r t i c l e l eve l s c h e m e s . ' It r e a d s

X a ( theo r . ) = c a ( a 1 + a 2 ) ; a = - — 8л

v% (25)

H e r e , the quan t i t i e s g , d a r e again taken from equ. (9), (Ю) A A.

t o g e t h e r with the p a r a m e t e r s of table III.

F o r the r e g i o n s of s t rong ly de fo rmed nucle i a s defined by equ. (12), Ji_ w h e r e equ. (9) and (10) a r e not va l id , the quant i t i es

d i r e c t l y f rom the Ni l s s o n - m o d e l leve l s c h e m e (table IV):

Tab le IV: Quant i t i e s

a r e r e a d

The coefficient c, is aga in obtained f rom a l e a s t squa re fit of a

equat ion (2 5) to the e x p e r i m e n t a l level spacing p a r a m e t e r s of table I, column 5, for nucle i with Z, N > 28, where the data on e l e m e n t s Hg through Bi have been excluded because equ. (2 5) does not give a sat isfying fit to t he se i so topes . The value obtained is

с = 1.93 a and the root mean s q u a r e deviat ion of ca lcula ted and expe r imen ta l

a - v a l u e s is J 1. 7 %

- 2 0 8 -

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265.

] 1 U ! I: Inyut <)а!л lucd for f,. «( nucl-ar Tidlatlie *»idtt. — 2 1 4 ~

> . Ï 1 iVw в' с

C - " l ы [ S i * ' 0.44OE 3 5 7 .163 0 . Ч 1 Е Щ O.l ' .OE 0 * Ч .34 1 0.6 l o t O l 0.22OF OS 7 . 7 * 6 0 . 4 7 8 f O l 0 .16 Of 0 * * . Ч | П 0 .55JF 0 1 0 .1 Я П Е o* 4 . 9 7 1 0.5*-7F Г Ч D^h^C^ e* *..'.!•• 0.516E O L 0 , 6 0 " F 0 ' 7 , Э7Н 0 .555F 0 1 O . I P D E 0 ? 4 . 1 4 9 0 , * - . 4 t r j l 0.45OE r,S 6 . 7 1 4 0.4P9E Sï 'J.5ÏOE 0 » . 7 . 7 ° 3 0 . Ы 7 Е Sï G . j i o e os 5 . - 4 J 0.66EF o t L -3 T Qt л 4 7 . 4 4 ^ Q.574F 0 1 o . ; i " i t 0 5 Й.2Й4 0.4ft?h o\ 0.250E 0 5 6 . Ы 1 £ . « . * P 0 1 O. lPOf 0 5 Г.911 0 . 5 ! j e O l 0 . 1 9 0 c 0* . 7 . ^ J 4 0.659E (11 0 .2? iT : 0 4 7 . г*03 0 - fO?s

t . S U F Э 1

с . г и Е Г 5 6 . в 1 * 0 - fO?s t . S U F 0 1

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ТаЫе II (cont inued)

M o - 93 0. 284 0 .224 0 .284 M o - 95 0. 171 0 .149 0. 171 M o - 96 0. 202 0. 17 0. 202 0. 207 M o - 97 0. 136 0 .113 0 .136 M o - 98 0, 167 0. 16 0. 167 0. 170 M o - 99 0 .0802 0 .088 0 .0802 0 .0889 Mo-101 0. 0597 0. 071 0. 0597 0. 0646 T c - 1 0 0 0. 137 0. 13 0. 137 R u - 1 0 0 0. 229 0. 152 0 .229 Ru-102 0. 168 0 .179 0. 168 R u - 1 0 3 0. 109 0. 109 R u - 1 0 5 0. 0967 0 .0967 R h - 1 0 4 0. 165 0. 154 0 .165 0. 165 Ag-108 0. 172 0. 14 0. 172 0. 172 Ag-110 0. 141 0. 132 0.141 0. 141 Cd-112 0. 186 0 .12 0. 186 Cd-113 0. 109 0 .109 Cd-114 0. 163 0 .11 0 .163 Cd-115 0. 0821 0 .095 0. 0821 In-116 0. 154 0. 154 0. 154 Sn-117 0. 0970 0. 0970 Sn-118 0. 133 0 .095 0 .133 Sn-119 0. 0988 0. 0988

.Sn-121 0. 0647 0. 0647 Sn-123 0. 0676 0. 0676 Sn-125 0. 0515 0. 0515 Sb-122 0. 120 0 .10 0. 120 Sb-124 0. 111 0 .10 0. 111 T e - 1 2 3 0. 104 0 .104 T e - 1 2 4 0. 169 0. 105 0. 169 T e - 1 2 5 0. 0828 0. 0828 T e - 1 2 6 0. 151 0 .145 0. 151 0 .151 T e - 1 2 7 0. 0685 0. 0685 0 . 0 6 8 5 T e - 1 2 9 0. 0614 0. 0614 0 .0614 Te -131 0. 052 0 .052 0. 052 I -128 0. 130 0. 130 0 .130 Cs -134 0. 140 0. 12 0. 140 0. 140 Ba - l 3 5 0. 0968 0. 070 0 .0968 0. 0968 Ba-136 0. 166 0. I 15 0. 166 0. 166 La -140 0, 0523 0 .0523 0 .0523 P r - 1 4 2 0 .0874 0 .085 0 .0874 0 .0874 Nd-143 0. 0595 0 .0595 0. 0595 Nd -144 0.0911 0 .073 0.0911 0.0911 Nd-145 0 . 0 6 4 5 0. 078 0. 0645 0. 0645 Nd -146 0. 07 58 0. 050 0. 07 58 0. 0758 Nd -1-17 0 .0374 0. 055 0. 0374 0 .0374 Pm -1 4 8 0. 0653 0. 066 0. 06 53 0, 0653 Sin -1-1 8 0 .0897 0. 073 0. 0897 0. 0897 Sm -151 0 .0328 0 .0328 0. 0328 Sm-J 53 - 0 .0491 0 .065 0. 0491 0.0491 S m - 1 5 5 0 .0576 0 .079 0 .0576 0. 0576

Tab ic IT (continued) -217-

E u - 1 52 0. 0621 0 .090 0 .0621 0.0621 Eu-154 0 .0718 0 .095 0.0718 0. 0718 Gd-153 0. 0544 0 .054 0.0544 0.0 544 Gd-155 0 .0542 0 . 0 6 5 0. 0542 0. 0542 Gd-156 0 . 0 9 4 3 0.107 0 .0943 0. 0943 Gd-157 0 . 0 7 2 5 0 .080 0. 0725 0. 0725 G d - 1 5 8 0 .0981 0 . 1 0 3 0. 0981 0. 0981 Gd-159 0 .056 0 .089 0. 056 0. 056 Gd-161 0 . 0 5 3 5 0 .098 0 .0535 0. 0535 T b - 1 6 0 0 .0787 0 .087 0. 0787 0.07S7 Dy-162 0 .114 .0.114 0 .114 0. 114 D y - 1 6 3 0 .0823 0 .155 0. 0823 0. 0823 Dy-164 0 .116 0 .109 0. 116 0. 116 D y - 1 6 5 0 .0639 P. 055 0, 0639 0. 0639 Ho-166 0. 0756 0. 073 0. 0756 0. 0756 E r - 1 6 2 0 .0652 0. 06 52 0. 0652 E r - 1 6 5 0 .0702 0. 0702 0,0702 E r - 1 6 7 0 . 0 7 9 5 0. 088 0. 0795 0. 0795 E r - 1 6 8 0 .0983 0. 090 0. 0983 0.0983 E r - 1 6 9 0 .0731 0.081 0. 0731 0. 0731 T m - 1 7 0 0.0929- 0. 090 0. 0929 0. 0929 Yb-171 0 .0872 0. 0872 0. 0872 Yb-172 0 .106 s 0 .077 0. 106 0. 106 Yb-173 0. 0855 ; 0 .072 0. 0855 0. 0855 Yb-174 0 . 0 9 1 5 i 0. 074 0. 0915 0. 0915 Yb-175 0. 076 , 0. 080 0. 076 0. 076 Yb-177 0 .0704 0 .082 0. 0704 0. 0704 L u - 1 7 6 0 .0923 : 0 .060 0. 0923 0. 0923 Hf-175 0. 0804 '• 0. 0804 0. 0804 Hf-177 0 .0728 ; 0. 0728 0. 0728 Hf-178 0 .0822 ! 0 .0655 0. 0822 0.0822 Hf-179 0 .0646 1 0. 0646 0. 0646 Hf-180 0. 101 \ 0. 101 0. 101 Hf-181 0. 0587 ! 0. 0587 0. 0587 T a - 1 8 2 0 .0773 j0. 053 0. 0773 0. 0773 W -183 0. 0687 10. 072 0. 0687 0. 0687 W -184 0. 0832 •0. 082 0. 0832 0. 0832 W - 1 8 5 0 .0578 •,0.072 0. 0578 0. 0578 W -187 0. 0445 .0. 047 0. 0445 0 .0445 R e - 1 8 6 0. 077 |0. 0528 0. 077 0. 077 R e - 1 8 8 0. 0655 lo. 054 0. 0655 0.0655 O s - 1 9 0 0. 0871 '0. 090 0. 0871 0.0871 P t - 1 9 3 0. 0874 '0. 062 0. 0874 0. 0874 P t - 1 9 5 0. 0843 0 ,069 0. 0843 0.0843 P t - 1 9 6 0. 09 52 0. 11 0. I l l 0.0952 Ли-198 0. 118 0. 128 0. 155 0. 118 Hg-199 0. 0985 0. 13 0. 148 0.0985 Mg-200 0. 160 • 0 .28 0 .315 0.160 Hg-202 0. 133 0. 37 0.271 0. 133 P b - 2 0 5 0. 185 • 0. 185 0. 185 P b - 2 0 8 0 .484 0 .484 0. 484 Bi -210 0. 102 0. 102 0. 102

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MALYSIS OF NEUTRON KESONAMCES IN lk4d

H. Ceulemans SCK-CEN, Mol, Belgium

1. Introduction

The study of the neutron resonances of the Neodymium isotopes presents several interesting aspects. First of all the Nd isotopes are situated in the mass region 142 - ISO which is at the first maximum of the split 4S

о size resonance in the s-wave neutron strength function <Гп >/<D>. Further­more, the isotope 1If2Nd has a closed neutron shell and the average level spacing <D> for all the Nd isotopes will be influenced by this shell closure.

Therefore, large values of Гп , the reduced width, are to be expected. This has been confirmed by previous analyses by a group from Dubna |1| and by H. Tellier from Saclay |2|. The sum of the reduced neutron widths ЕГ о between 0 and 840 eV, which is the interval covered in ref. |l|, is n respectively .724 eV^ and .741 eV|. Considering an error of about 0.01 in each of these two results the agreement between them is good. In ref. \2\ ,

however, for a slightly different energy interval, the author came to a different conclusion and reported important variations in the strength function for different energy ranges. Some of these effects, however, may be due to the analysis which becomes rather complicated at higher, energies. To determine such effects and verify the behaviour of the strength function was one of the purposes of this analysis.

2. Data analysis

The neutron transmission data were obtained at the Nevis Synchrocyclotron Laboratory of the Columbia University and analysed at our laboratory. For a reliable determination of resonance parameters from transmission data it is important to use a very wide range of sample thicknesses. Both natural and isotopically enriched (or depleted) samples were available. In this way thicknesses in 143Nd of 8.78 E-3 at/b, 2.41 E-3 at/b,

-220-

5.98 E-4 at/b and 2.92 E-4 at/b were used. A shape analysis of the trans­mission spectra was performed for each sample thickness separately, although it would be preferable to do this analysis for all samples in a single analysis. The analysis starts with a reasonable guess of the resonance parameters, calculates the Doppler-broadened cross-sections by using the complex probability integral and convolutes the calculated transmissions with a Gaussian resolution function by the Gauss-Hermite integration method. The calculated transmission is subtracted from the experimental value and these differences are used to calculate corrections for the level parameters by a method of steepest descent (only first derivatives are used). The least-squares solution of this problem of n equations with m unknowns is obtained by using Householder transformations which reduce the nxm matrix to an upper triangular form with only m non­zero rows. This method avoids uncontrolled loss of precision as can be the case when the usual method of multiplying the coefficient matrix by its transpose is used. In the case of a single thickness the least-squares minimum can be very broad and a scan has to be made for different values of Г e.g., to obtain the corresponding value of Г . For each Sample thickness a line is thus obtained in the Г -Г plane and the

n t intersection or the region between these lines gives the resonance parameters, including the spin, if Г is sufficiently large (at least

n 500 meV). In view of the large neutron widths of the Nd isotopes Doppler and resolution broadening are not prohibitive up to several keV neutron energy. The influence of the resolution width was verified and was found to be very small. For high transmission (T) values, however, as is more often the case at higher energies, attention should be paid to proper determination of the T=l level, because a 1% change in this level is amplified to 3% and more change in the neutron width.

3. Results

The results obtained so far are presented in table 1. This table gives also the data obtained in refs. |l| and |2|. The spin values obtained by Stolovy |3.j are also presented. At low energies the agreement between all authors is relatively good, with a better precision for the more recent values. At higher energies however, systematic differences become visible.

-221-

This can best be seen by summing the reduced widths and calculating S =sr o/ET because in this way the statistical fluctuations on the о n L determination of the individual resonance parameters are expected to cancel. The limits for summation ET are chosen at 840 eV, to include all the results of ref. |l|, at 1680 for ease of comparison with the first interval and at 2128 eV to include all of our data. The results are shown in table 2, for both spin states combined. When comparing the figures in different energy intervals it should be remembered that the fluctuations due to width and spacing distributions are about 40% of the nominal value, due to the small number of resonances involved. The tendency, however, is the same for all experiments, with enhanced lower values for our results at higher energies. Our result for the strength function 0.5fs <3~)+S (4~)1 is (3.42±0.7)xlO_lfeV~^

L о о J

-222-

REFERENCES \

\\\ E-N. Karzhavina, Nguyen Nguyen Phong, A.B. Popov, A.I. Taskaev,

Jadernaia Fisika, T.8 Vol. 4 0968) 639.

|2| H. Tellier, Note CEA-N-1459, 1971.

|3| A. Stolovy et al., Phys. Rev. C5 (1972) 2030.

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-223-

b l e 1 : P a r a m e t e r s of Neut ron Resonances i n 1 ц % о

.ergy (eV) P r e s e n t R e s u l t s R e s u l t s of Ref. 1 R e s u l t s of Ref. 2 Ref. 3

2 * Г п (meV)

r t (meV)

J

(meV)

Г Y

(üteV)

2 * Г п (meV)

r t (meV)

J

5 5 . 2 8 41 .6± 2 U0± 10 40± 4 80±20 41 .2* 1 U5± 15 4 27 .26 320+ 23 515+ 50 3 360± 60 94±14 330± 20 550± 50 3

.35 .39 46± 2 155+ 20 62± 10 70±23 56± 5 115± 10 3

.58 .56 1082± 30 1050+ 80 4 1200±120 83±13 I040± 50 1100±100 4 179.36 530± 35 750± 50 3 640±100 6I± 9 575± 25 800± 40 3 186.50 1480+ 40 1480± 80 4 I700±100 89±13 1500*100 15501100 4

Ï26.2 n o t seen n o t seen 0 .2840.1

106.08 740± 30 850+ 50 4 710±140 67+10 770± 80 960±100 4

324.15 770± 30 1050±100 3 430±120 810± 40 1170±100 3

337.0 700+ 30 770± 40 4 520± 80 770± 30 785 4

350.25 670± 30 1000±120 3 600±140 790± 30 1020+100 3

iO l . 30 1050+ 35 1160±100 4 • 1040±200 1080± 50 1200±100 4

107.98 450± 45 600±100 - 460± 80 500± 30 660± 60 3

W6.15 I760± 60 1940+150 - 1800±160 1960± 50 1860+100 4

507 n o t seen 20± 2 no t seen 3

523.1 200± 20 168± 32 245± lO- 340± 20 (4)

555.2 96± 10 70± 14 i n t 5 250± 50 4

576.2 142± 28 5 .4±0 .5 (3)

657.2 390+ 40 580±100 70+10 420+ 15 470± 30 4

707.8 270± 30 374± 80 340+ 15 425+ 40 (3)

777.0 1200± 60 1200±100 4 1160+160 76±11 1320± 40 1580+100 4

803.2 8+ 2 15.8±1.5 (4)

818 .4 6 .8+1 .4 10.5±1.0 (4)

840 .2 660+ 40 850±100 960±140 810± 30 870± 40 (4)

852.6 25 .8+1 .3

971.5 59.2± 3

9 8 4 . ! 400± 60 600±100 500± 25 900±100

007 .2 510± 40 630±100 ass igned t io l t t 5Nd

027.9 180+ 20 250± 10

081.9 90± 15 •100± 10 600+100

124.5 . 490± 40 500± 25 990+100

165.0 31± 2

-224-

Energy (eV) Present Results Results of Ref. 1 Results of Ref. 2 Ref. 3 2gr n (meV)

Ft (meV)

J 2 ^ (meV)

Г Y (meV) 2*Гп (meV)

rt CmeV)

J

1210.6 1030+ 70 1430+ 70 1433.1 765± 50 980+ 50 1463.5 140+ 15 175± 10 1462.7 660± 60 754± 30 1511.1 290+ 30 255+ 10 1557.5 390+ 30 660+ 20 1583.5 1490+100 1920+100 1653.0 600+ 60 945± 30 1667.4 2650±250 3390±100 1724 520+ 50 790± 40 1760.3 1000+100 1270± 60 1849.6 770+ 50 2000+100 1910 910±150 1510+ 80 1963 no t measured 120± 20 2004' 1160+100 1855± 80 2088 340+ 40 460± 25 2128 6700±600 8400±400

Table 2 : Sum of Strength Function S (3 ) and S (4 ) for ^^Hd in different energy regions

Energy interval

[•v]

S (3*")+S (4") [eV'^xlO-'1] Energy interval

[•v] Present results Results of ref. 1 Results of ref. 2

0 - 840

840 - 1680

0 - 2)28

8.13

6.20

6.85

8.62 8.82

6.87

7.92

-226-

NEED OF NUCLEAR LEVEL SCHEMES FOR CALCULATED

CROSS SECTIONS OF FISSION PRODUCT NUCLEI

H. Gruppelaar.

Reactor Centrum Nederland, Petten, the Netherlands

Abstract

For many fission product nuclei, no measurements of fast neutron cross

sections are available; for other fission product nuclei only a few

measured points are known. Therefore, calculated cross sections are

needed to provide a set of data with adjustable parameters. Adjustments

to cross section data can be applied by using experimental data of

differential measurements from accelerators or by using results of

integral experiments like the reactivity worths measured in the Dutch

STEK reactor.

In the energy range between 0.1 MeV and 3 MeV, which is important:for

fast breeder reactors, a good knowledge of excitation energies, spins

and parities of levels in the target nucleus is necessary for the cal­

culation of both the neutron inelastic scattering cross section and

the neutron absorption cross section. In the present note the need of

level scheme information and the desirability of a compilation and/or

evaluation of these data for practical calculations of fission product

neutron cross sections will be discussed.

1. Introduction

In fast breeder reactor calculations cross sections of about 150 fission

product nuclei in the mass range 81 < A <_ 164 are important. The required

accuracy for the capture cross section at energies from about 100 eV to

10 MeV is generally stated to be +^ 10% [l,2[. Since for the majority of these

nuclei no cross section measurements have been performed in the entire

energy range of interest, one often has to rely on evaluations primarily

based on calculations with phenomenological nuclear models. In some cases

•J.J. i -

cross section measurements will hardly be possible, since for many isotopes not enough target material is available, or because targets are highly radioactive. To overcome these difficulties, effective cross section measurements in different well-defined fast reactor spectra might be of great help. Experiments of this kind are being performed at Petten in the STEK facility J8|, where the reactivity of a large number of individual isotopes, listed in table I, is measured in five different neutron spectra. To evaluate the results of these integral measurements, the application of a statistical adjustment technique on calculated effective cross sections is foreseen |8|. The cross sections depend on a limited number of parameters which influence the cross section in a wide energy range and a large number of parameters which show a more local effect, such as resonance parameters, and ex­citation energies, spins and parities of the target nucleus. Uncertainties in these parameters need to be known before adjustment calculations can be applied. In the present note some remarks will be made about the influence of uncertainties in the level scheme of the target nucleus, particularly on the capture cross section of fission product isotopes as a result of competitive inelastic neutron scattering.

2. Present situation

Only for about one third of the isotopes listed in table I, one or more measured cross section points at energies above 0.1 MeV are available.

In the energy range from 1 keV up to ]0 MeV evaluations of capture cross sections of many fission products, based on the statistical model, have been published by Benzi et al. |3,4| and Cook et al. |5| , who used the same cross sections in the high-energy range. Calculations of fast neutron capture cross sections for inclusion in the ENDF/B-III nuclear data library have been reported by Schenter and Schmittroth |б|. All authors estimate a maximum error of about +50!£ in the calculated cross sections.

Information on level schemes is currently being published in the

Nuclear Data Sheets. Unfortunately, for about 50 of the 60 nuclei listed

in table I the most recent evaluation is more than five years old. For

nuclei in the mass range 91 <_ A <_ 139 recent level schemes have been com­

piled without evaluation |7|. In general, the number of unambiguous spin-

parity assignments is rather low and often uncertainties in the level scheme

arise already at energies below 1 MeV

-228-

3. Effects of Unknown Inelastic Scattering

To study the influence of unknown inelastic scattering on a and a , ny nn

Hauser—Feshbach calculations have been performed, using the codes FISPRO |9| and SASS1 j10], which were kindly supplied to us by Prof. V. Benzi. The same parameters as used in J3,4J were utilised and only the level scheme of the target nucleus was varied. For a number of nuclei (95Mo, 103Rh, 107Pd, 109Ag, 1 3 3Cs), with recently evaluated level schemes, cross section calculations have been performed. The results of these calculations were compared with earlier evaluations of Benzi et al. |3,4|. In general deviations from 10% to 30% in the energy range from 0.1 to 3 MeV were found both in a and a ,. Since for most of

ny nn the nuclei investigated the present level schemes still do contain many ambiguities, uncertainties of the same order of magnitude might be expected even in the most up to date calculations. As an example, consider the important unstable fission product nucleus 107Pd for which a recent level scheme evaluation is available j II|. In table II is shown that for most excited states two J values are possible; the most probable one is given as the "first" possibility. The difference between the level scheme used in the 1970 cross section calculation [4| and the present one (both drawn in fig. 1) is the inclusion of five additional levels. As a result a decreases and о , increases an amount of at most

ny nn 30%, which can be seen from fig. 1. At neutron energies above 1.5 MeV the Weisskopf-Ewing model, which is also adopted in the FISPRO code, was used. In between 0.9 MeV and about 1.5 MeV a smooth curve is drawn in order to match the Hauser-Feshbach and continuum calculations. In the above mentioned example the change in cross section was mainly caused by an increased number of levels and did not depend very much on the values of J , which was found from a calculation in which the second spin possibility, listed in table II, was preferred. Apparently this is due to

it + the high value of the spin of the ground state (J = 5/2 ) , which weakens the influence of the angular momentum and parity selection rules. If the spin of the ground state is low and the level density not too high (e.g. for even-even nuclei), the spins and parities of individual excited states may be very important. This can be demonstrated clearly for 103Rh, where the level scheme is well known f 121 up to 0.65 MeV: JW = .1/2", 7/2+, 9У2+, 3/2", 5/2~, 5/2+ 7/2+ for E = 0 , 0.040, 0.093, 0.295,

0.358, 0.537, 0.650 MeV, respectively. If the spin of the excited state were 3/2 instead of 7/2, the capture cross section would decrease drasti­cally with a maximum change of 40%.in the region between 0.05 and 1 MeV, due to angular momentum selection rules. Less pronounced effects can be shown for a change in parity of some particular levels.

For a number of nuclei (e.g. 93Zr, 1 2 9 I , 151Sm) the level scheme is rather unknown, so that Hauser-Feshbach calculations cannot be performed in the energy region above 100 keV.

4. Conclusions and Pinal Remarks

Effects in a and cr . due to missing levels in the target nucleus or due to unknown J values can be large, with maximum of about 30-50% at energies between 0.1 and 3 MeV, which is larger than required in |l,2|. In general the spin and parity of the first excited state is well known, so that for many even-even nuclei uncertainties in the cross section do not occur below 0.5 MeV.

It can be concluded that level.'scheme information on fission product nuclei for excitation energies up to 3 MeV is important for accurate cross section evaluations. This might give additional stimulus to nuclear spectroscopists and level scheme evaluators. A convenient type of evaluation is that of Nuclear Data Sheets. It would be very useful if in case of ambiguities the most

7Г probable J values were clearly indicated (e.g. like in table II). Some final remarks will be made on the effects of level scheme uncertainties on fast reactor parameters. For a fast breeder reactor the most important part of the neutron spectrum with respect to capture is below 0.2 MeV. In the worst case (50% change in о for E = 0.2 to 1.4 MeV), the change

ny n in the absorption reaction rate for an average fission product in a typical fast breeder reactor is not more than 4% (in case of 107Pd, fig. 1, the level scheme uncertainty produces a 1% reactivety uncertainty). The influence of level scheme uncertainties to the breeding ratio was not investigated. From a paper submitted to this symposium |l3| it appears that the contribution of fission products to the breeding ratio cannot be neglected in this energy range. Errors of less than 15S | 131 are required in о and o t in the energy range where level scheme uncertainties might influence the nn

Effects in the inelastic scattering to individual levels can be much larger.

-230-

cross sections. This has been calculated for a mixture of all fission product nuclides. For individual fission product isotopes it seems that the commonly assumed goal |l»2| of а Л0% inaccuracy in the capture cross section is somewhat overestimated for present reactor calculations above 0.2 MeV.

In the last reactor core which is foreseen in the STEK project, the reactivity will be more sensitive to the MeV range, the change in reactivi­ty for 107Pd in the above mentioned example still is not more than 2.5%. In this reactor core, but also in some of the other STEK cores, inelastic scattering contributes significantly to the reactivity worth. Thus uncertainties in the level scheme will effect the calculated reac­tivity worth as a result of uncertainties both in a and a ,. Therefore

ny nn' a good knowledge of the level scheme of a number of fission product iso­topes is important for the evaluation of results from STEK.

- 2 3 1 -

BEFERENCES

| 1 | G r e e b l e r , P . , H u t c h i n s , B .A. , Cowan, C . L . , Second I n t . Conf. on

N u c l e a r Da ta f o r R e a c t o r s ( P r o c . Conf. H e l s i n k i , 1970) , Vol . 2 ,

IAEA, Vienna (1970) 17.

| 2 | Renda 72 , IAEA, Vienna ( 1 9 7 2 ) , Rep. INDC(SEC)-27/L.

U i B e n z i , V . , D ' O r a z i , R. , R e f f o , G. , V a c c a r i , M., P a s t Neut ron Radia­

t i v e Cap tu re Cross S e c t i o n s of S t a b l e Nuc l e i w i t h 29 < A < 7 9 ,

Rep. CNEN-RT/FI(72)6 (1972) .

J4 | B e n z i , V . , P a n i n i , G .C . , R e f f o , G. , V a c c a r i , M., D i s c r e t e and

Continuum I n e l a s t i c S c a t t e r i n g Cross Sec t ions fo r Neut rons up t o 10

MeV ( 1 9 7 0 ) , d a t a a v a i l a b l e v i a CCDN Neutron Data Compi la t ion C e n t r e .

| s | Cook, J . L . , F i s s i o n P roduc t Cross S e c t i o n s , Rep. AAEC/TM-549 (1970) ,

and Rose , E .K . , The AAEC F i s s i o n P roduc t Cross S e c t i o n L i b r a r i e s

FISPROD.P0INTXSL and FISPR0D.GR0UPXSL, Rep. AAEC/TM-587 (1971) .

| б | S c h e n t e r , R . E . , S c h m i t t r o t h , F . A . , Cross S e c t i o n E v a l u a t i o n s of 27

F i s s i o n P r o d u c t I s o t o p e s fo r ENDF/B-III , Rep. HEDL-TME-71-143 (1971) .

171 B a s s , W.T., Horen, D . J . ' , Ewbank, W.B. , C u r r e n t Nuc lea r Level Schemes:

A - 91 t o 117, Rep. 0RNL-4627 ( 1 9 7 0 ) , and Horen, D . J . , Cur ren t Nuclear

Leve l Schemes: A * 118 t o 139, Rep. ORNL-4730 (1971) .

j 8 | B u s t r a a n , M. e t a l . , STEK, The Fas t -Thermal Coupled F a c i l i t y of RCN

a t P e t t e n , Rep. RCN-122 (1970) .

| 9 | Benz i , V . , P a n i n i , G . C . , Ref fo , G. , FISPRO I I : A F o r t r a n IV Code for

F a s t Neu t ron R a d i a t i v e Capture C a l c u l a t i o n s , Rep. CNEN-RT/FI(69)44

( 1 9 6 9 ) .

[10 | Benz i , V, , F a b b r i , F . , Z u f f i , L . , SASSI - A F o r t r a n Programme for the

C a l c u l a t i o n of Neut ron S c a t t e r i n g from a S p h e r i c a l O p t i c a l P o t e n t i a l ,

Rep. CNEN-RT/FI(71) 6 ( 1 9 7 1 ) .

( П j B e r t r a n d , F . E . , Horen, D . J . , Nuc l . Data B£ (1972) I .

(12( Avignone, F . T . , F r e y , G.D. , Phys . Rev. C4_ (1971) 912.

j 1 3 | Usachev, L . N . , Manokhin, V .N. , IAEA Symposium on A p p l i c a t i o n s of

N u c l e a r Data i n Sc i ence and Technology ( P a r i s , 1973) , paper

IAEA/SM-170/91.

-232-

SLIDES PRESENTED AT THE SYMPOSIUM

During the oral presentation, slides of tables II, III and figs. 1-5 have been showed. The footnotes to table III and the captions to figs. 2~5 follow below.

Footnotes to table III

Table of isotopes, measured at STEK. a) Underlined isotopes do have a reactivity effect of more than 1% of all

fission products in a typical fast breeder reactor. b) Number of measured point cross sections with maximum energy in MeV" in

parentheses, mentioned in a recent evaluation by Benzi et al. |3|, m = many points.

c) Number of unambiguous sp in -pa r i t y assignments of exci ted s t a t e s , counted

from the f i r s t - e x c i t e d s t a t e up to the f i r s t "gap" in the known l eve l

scheme. These data are taken from the most recent evaluat ions (Nuclear

Data Sheets) or compilations J 7 | . No recent reviews ex i s t for i so topes

l i s t e d i n the table with mass number A > 139.

Caption to f i g . 2

Calculated capture and inelastic scattering cross sections for 107Pd for the two level schemes, given in table II. In this figure (on double loga­rithmic scale) a larger part of the cross sections as a function of neu­tron energy is given than in fig. 3.

Caption to fig. 3

Calculated capture and inelastic scattering cross section for 109Ag, plotted with the same conventions as used in fig. 1.

Caption to fig,., 4

Capture cross section of 103Rh. The solid curve has been calculated by Benzi et al. |з[. Experimental points are from Diven et al., Phys. Rev. 120 (1960) 556 (EXP.l), Cox, Phys. Rev. 133B (1964) 378 (EXP.2), and Macklin and Gibbons, Phys. Rev. }5У_ (1967) 1007 (EXP.3). The lower part of the level scheme of 103Rh, which is rather well known 112J is given at the bottom of the figure. The dashed curves represent (unrealistic) cases where the spin and parity of the first-excited state of 103Rh has been changed into J 3/2 and J = 3/2 , respectively, in order to show the influence "of angular momentum and spin conservation rules to the cross section.

-233-

Caption to fig. 5

Calculated capture cross section of 93Zr. The solid curve is taken from the evaluation of Benzi at al. |Л|- Since the level scheme of' 93Zr is very uncertain, the calculation is mainly based on a continuous level-density function of the target nucleus. The dashed curves represent Hauser-Feshbach calculations with different values of J for the first-excited state. The adopted cross section curve is based on a much higher number of levels than which has been reported at present.

-234-

TABLE I

ISOTOPES MEASURED AT STEK a)

9 0 Z r

9 1 Z r

9 S Mo 1 0 0 M o

1 0 7 p d

1 0 8 p d

1 3 2 X e 1 3 4 e

^ ^ d ! « N d

^ 9 S m 9 0 Z r

9 1 Z r

9 S Mo 1 0 0 M o

1 0 7 p d

1 0 8 p d

1 3 2 X e 1 3 4 e

^ ^ d ! « N d 1 5 0 S m

9 2 Z r 9 3 Z r

9*Zr

Э Э Т с

l O l R u

102Ru

1 1 0 P d

1 3 3 C s

1 3 5 C s

l ^ N d

^ % d

l ^ N d

^ I S m 9 2 Z r 9 3 Z r

9*Zr

Э Э Т с

l O l R u

102Ru

1 1 0 P d

1 3 3 C s

1 3 5 C s

l ^ N d

^ % d

l ^ N d

1 5 2 S m

9 2 Z r 9 3 Z r

9*Zr

Э Э Т с

l O l R u

102Ru

1 1 0 P d

1 3 3 C s

1 3 5 C s

l ^ N d

^ % d

l ^ N d 15 t*Sm 9 6 Z r

1 0 4u 1 2 8 T e ^ 7 ^ ^ % d 1 5 1 E u

9 2 M o

*4o 10 i» P d

1 3 0 T e

127-j; " Э ь а 1 ^ 0 C e

1 5 0 N d 1 5 3 E U 9 2 M o

*4o 10 i» P d

1 3 0 T e

127-j; " Э ь а 1 ^ 0 C e

1 5 0 N d

1 5 6 G d

9 5 M o 10 5 P d 1 2 9 J ^ 2 C e l ^ S m 1 5 7 G d

9 7 M o 10 6 P d " l X e l i t l p r l ^ S m 159xb

a) Underlined isotopes are fission products with a reactivity effect of more than 1% of the total fission product mixture in a typical fast reactor.

-235-

TABLE II

LEVEL SCHEME OF 107Pd

1970 a i 1972 b)

E x (MeV) J * E x (MeV) J ï ï

0 . 0 5 / 2 + 0.0 ( 5 / 2 ) +

0 .115 l / 2 + 0.1157 l / 2 +

0 .210 11 /2" • 0.214 ( 1 1 / 2 ) "

0.3028 ( 5 / 2 , 3 / 2 ) +

0.307 7 / 2 + 0.3122 ( 7 / 2 , 9 / 2 ) +

* 0.3482 c>

0.366 ( 7 / 2 , 9 / 2 ) +

0 .390 3 / 2 + ' . 0.3819

0 .3924°)

( 3 / 2 t 5 / 2 ) +

0:412 l / 2 +

0.470 3 / 2 + 0.4712 ( 3 / 2 , 5 / 2 ) +

0 .570 5 / 2 + 0.5677 ( 5 / 2 , 3 / 2 ) +

0 .670 7 / 2 + . 0.6701 ( 5 / 2 , 3 / 2 ) +

0 .685 (7 /2~) d>

0 .700 l / 2 + 0.69S U2+

0 .770 3 / 2 + 0.759 ( 3 / 2 , 5 / 2 ) +

0.781

0.806 c : >

( 1 / 2 , 3 / 2 ) "

0 .890 ! / 2 + 0.889 l / 2 +

Level scheme used in the 1970 cross section calculation [4].

Level scheme from [ll] . If more than two J values are possible, the first possibility in general is more likely.

Not used in the cross section calculation shown in fig. 1.

Not adopted in [ll] .

-23'J-

TABLE III

ISOTOPES, MEASURED IN STEK

1 • . a ) i s o t o p e p o i n t

X - s e c t i o n s

— • c ) e x c i t a t i o n .

e n e r g i e s i s o t o p e

p o i n t X-secfcions

. c ) e x c i t a t i o n

e n e r g i e s

9 0 Z r 20 ( 0 . 0 5 ) 13 2 X e 0 4 ( 1 . 8 0 )

£izx 27 ( 0 . 0 6 ) 3 < 1 . 8 7 ) 1 3 4 X e 0 3 (1 .73 )

9 2 Z r I ( 0 . 0 3 ) 4 ( 1 . 8 5 ) 13 6 X e 0 3 ( 1 . 8 9 )

5 3 Z r 0 13 3 C s 47 ( 0 . 2 0 ) 7 ( 0 . 6 4 )

9 4 Z r 17 ( 0 . 2 0 ) 4 < 1 . 6 7 ) 1 3 5 C s 0

9 6 Z r 3 ( 0 . 2 0 ) 2 ( 1 . 8 9 ) 1 3 7 C s 1 ( 0 . 4 6 )

92Mo 0 2 ( 2 . 2 8 ) 13 9 L a m ( 3 . 0 0 ) 1 ( 0 . 1 7 )

9^Мо 0 2 ( 1 . 5 7 ) 14 0 C e 1 ( 0 . 0 2 ) 9 5 ц 0 14 ( 0 . 0 5 ) 3 ( 0 . 7 9 ) l «*2 C e 1 ( 0 . 0 2 ) 97Но 24 ( 0 . 0 6 ) 1 ( 0 . 6 6 ) 1 4 1 p r m ( 4 . 0 0 )

98Ho m ( 3 . 0 0 ) 1 ( 0 . 5 4 ) l ^ K d 0

10 Оно m ( 6 . 0 0 ) 1 ^ 3 Ш 0 9 Э Т с 4 ( 0 . 5 1 ) l ^ N d 0

1 01 Ru 0 3 ( 0 . 3 1 ) l^SHd 0 1 0 2 R u 2 ( 0 . 2 0 ) 3 [ 1 . П ) 14 6yd 0

lO^Ru 3 ( 3 . 0 0 ) 2 ( 0 . 9 0 ) 1 4 8 K d 14 ( 0 . 3 0 ) 10 3 R h m ( 4 . 0 0 ) 6 ( 0 . 6 5 ) 15 0 N d 14 ( 0 . 2 0 ) 1 0 4 p d 0 2 ( 1 . 3 2 ) l " P m 1 0 5 p d 0 4 ( 0 . 3 5 ) l " S m 1 ( 0 . 0 2 ) 106pd 0 . 6 < 1 . 5 6 ) i ^ s S m 2 ( 0 . 0 3 ) 1 0 7 p d • 1 < , 0 . 1 2 ) 14 9 S m 1 ( 0 . 0 3 ) 10 8pd 4 ( 0 . 2 0 ) 2 ( ; 0 - 9 3 ) 15°Sm 2 ( 0 . 0 2 ) U O p d 4 ( 4 . 0 0 ) 3 < ; 0 . 9 2 ) ISlSm lO^Ag 38 ( 0 . 6 0 ) 1 1 0 . 0 9 ) 152S m 5 ( 3 . 0 0 ) 11 iCd 0 5 < , 0 . 6 2 ) 154 S m 27 ( 6 . 0 0 ) 1 2 8 ï e 51 ( 0 . 1 0 ) 4 [ 1 . 8 1 ) ISlEu 32 (3 .00 )

13 0xe 47 ( 0 . 1 0 ) 4 ( r 1 . 8 2 ) 15 3 E u 20 ( 0 . 4 0 ) 1 2 7 j m ( 6 . 0 0 ) 4 CO.42) i 5 6Gd 0

1 2 9 Ï 1 1 0 . 0 3 ) lS7Gd 0

l " X e 0 2 0 . 16) 1 5 9 T b 65 ( 0 . 2 0 )

-237-

Fig. 1_ Calculated capture and inelastic scattering cross section for 107Pd for two different level schemes, labeled with "J970" and "1972" (see table II). Continuum calculations.have been performed for excitation energies above 1.5 MeV. In between 0.9 MeV and about 1.5 MeV a smooth curve is drawn in orde г to match the Hauser-Feshbach and continuum calculations.

-238 -

i ) Г Ш | I * I T l I I I 1 • Л . . .10

(b)

1.0 .

ai : 1970

001

Gnn'l (b)

nn'

Q01 0.1 10

Fig. 2

- 2 3 9 -

0.2 0Л 06 OS 10 1.2 U 1.6 E(MeV)

*ig- 3

-240-

(b) к

ОА - 1

0.3 V 1 \ \ \

103Rh(n ty)10^Rh

о=ЕХР 1 А = ЕХР 2 Ш = ЕХР 3

= CAUC. CORRECT LEVEL SCHEME

zCALC WITH DIFFERENT 1* OF FIRST-EXCITED STATE

\ \ Л1)=3/2"

0.2 \ \

^ ( 1 ) = ^ \ ^

0.1 0.2 0.3 ОЛ 0.5 0.6 '0.7 0.8 EfMeV) ,

Fig. 4

• 2 4 1 -

т l 1 - г

93 Zr

^ч^Ш

/ У

У -у У

У У

\\?л\Я% у Н.Е CALCULATIONS

+ «-

,1(1)=5/2+

ADOPTED CROSS SECTION

:NZI ET AL.

5/2+ (3/2+) (%>^h7/f)

J I L

Q2 0Л 0.6 Q8 1.0 1.2 W 1.6 E(MeV) „

-242-

SPINS OF i H ' H S c d , 1 5 7 Gd, 1 6 1 ' 1 6 3 D y NEUTRON RESONANCES;

E.N. Ka rzhav ina , Kim Sek. Su, A.B. Popov.

J o i n t I n s t i t u t e f o r Nuc lea r Resea rch , Dubna, USSR.

A b s t r a c t

Spins of neutron resonances of odd Cd, Gd, Dy isotopes were measured at

the neutron spectrometer of the Laboratory of Neutron Physics (JINR,

Dubna) using the gamma-ray multiplicity method. The check is undertaken

of the experimentally obtained spin effect with theoretical estimations made

for these and some other nuclei in terms of the statistical model of the

nuclear-level density and probability of electromagnetic transitions

according to Weisskopf. The strength functions and average level spacings

are obtained to be for 157Gd:S0 = (2. 1±0.7) x !0_1+ and D = 13-3+1.5 eV

for I = 1, S0 = (2.3+0.6) x I0_tf and D = 9.5±0.9 eV for 1 = 2 , respectively.

-243-

Введение

Информация о спинах нейтронных резонансов , помимо чисто компилятивного значения , представляет определенный физиче­ский интерес для уточнения наших представлений о спиновой зависимости плотности уровнен, силовых функций или о других эффектах, проявляющихся в индивидуальных и усредненных характеристиках резонансов . Подробная информация о спинах может о к а з а т ь с я полезной и при выявлении некоторых особен­ностей нзанмоденсгния нейтронов с ядрами, например таких, как проявление промежуточной структуры, поскольку промежу­точное состояние должно приводить к усилению резонансов с определенным спином.

В настоящее время имеются обширные данные о таких пара­метрах нейтронных резонансов , как резонансная энергия Ь'и , нейтронная ширина \'\ . » вместе с чем весьма ограничены све ­дения о спинах. 'Это объясняется гем . ч го не существует про­стого и надежного способа определения спинов. Определение спинов прямым методом с использованием поляризованного пучка нейтронов и поляризованной мишени до сих норме получило широкого применения из-за . трудностей создания интенсивных пучков поляризованных нейтронов в 'резонансной области н осу­ществления достаточной поляризации ядер мишени. Оценка спинов путем комбинации р е з у л ь т а т о в измерений полного и пар­циальных сечений также является не простой задачей /особенно измерение резонансного р а с с е я н и я / и о к а з ы в а е т с я эффективной только для мишеней с низкими значениями спинов. В последние годы получили развитие методы определения спинов, с помощью которых исследуются характеристики у -спектров от радиаци­онного з а х в а т а нейтронов: вариации отношении интенсивностей низкоэнергетических переходов или среднего числа у - к в а н т о в в каскаде .

-244-

Авторы использовали последний метод для определения спи­нов резонансов некоторых ядер / J-2*3/ . Результаты этих работ показывают, что способ определения спинов по множественности у ^квантов также не является универсальным, и для некоторых

изотопов найти спины не удается. Поэтому нам представлялось полезным выяснить для выбранных в эксперименте ядер возмож­ность оценки спинового эффекта с помощью расчетов.

Расчетные оценки эффекта и сравнение с экспериментом

Напомним методику эксперимента.Образец,в котором проис­ходит резонансный захват нейтронов, окружен несколькими кристаллами / у нас четырьмя/ №J, детектирующими' у -лучи, которые возникают при захвате нелтронов. В электронной схеме детектора имеется два канала: одиночного счета и двойных совпадений, в которых пороги регистрации можно устанавливать независимо. Для каждого резонанса можно получить отношение площади в режиме одиночного счета 5-^ к площади в режиме совпадений Sc, /? = SV /Sc , которое будет пропорционально сле­дующему отношению:

где i->y и v - среднее число у -квантов в каскаде, энергия которых выше выбранных порогов регистрации в соответствую­щих каналах. Возможность определения спинов индивидуальных резонансов заключается в том, что совокупность отношений R распадается на две группы в зависимости от спина захват­

ного состояния, поскольку i'v и v могут иметь заметную за­висимость от спина нейтронного резонанса J =1+1/2/1 - спин мишени/. Удобно определить величину спинового эффекта сле­дующим образом:

К Я >

1-1/2

<R 1+ i/l

Для расчетных оценок К мы воспользовались программой ра­счета спектра у -квантов, возникающих при захвате нейтро­нов, которая разработана Т. фон Эгиди ^4> . В этой программе на основе статистических предположений плотность уровней со­ставного ядра от границы известного спектра нижних состояний до энергии возбуждения описывается формулой

-245 -

(J+ l/2)2

параметры которой £0> Т определяются реальной плотностью нейтронных резонансов и плотностью известных нижних состоя­ний. В программе учитываются переходы на известные нижние состояния, а вероятности электромагнитных переходов Л" ' Л К , Л ] , А тт) берутся по оценкам Ванскопфа с поправками на некоторые факторы ослабления, которые принимаются разными для разных мультипольностеи излучения; учитывается также разное ослабление 5 аблнзн энергии связи или вблизи основного состояния. Используя расчетную форму у -спектра для двух возможных спинов захватного состояния, мы получили оценки спинового эффекта К в зависимости от порогов детектирования у -квантов. При этом порог, эквивалентный каналу совпадений,

выбирался в пределах 0,1 - 0 ,5 Мэв, а одиночному каналу - в пределах 1,5 - 3,5 Мэа. Некоторые расчетные оценки спинового эффекта А' с чприведены в табл. 1. Их можно сопоставить с экспериментальными значениями К э к с п - полученными нами для приведенных в таблице ядер в предыдущих работах ; ' " ' 'и в настоящем сообщении. Значения К расч и & эксп соответству­ют одинаковым порогам регистрации у -квантов. В расчетах проверялась устойчивость результатов к вариациям исходных параметров. Наибольшую неопределенность вносят факторы ослабления вероятностей электромагнитных переходов. Тем не менее для ряда ядер К р а С ч слабо зависит от изменений пара­метров, используемых в расчете. Для тех ядер, для которых наблюдался разброс значений К р а с ч , в таблице приведены гра­ницы оценок Красч- Сравнение экспериментальных и расчетных значений К обнаруживает удовлетворительное качественное согласие. Из экспериментов следует, что для надежной спиновой идентификации достаточно, чтобы спиновый эффект К > 1.10.Из табл. 1 видно, что для всех ядер, для которых /^расч > !•№ > в

эксперименте, действительно, наблюдается не меньший эффект. Для ,65Ио и l71Yb отсутствие заметного спинового эффекта в расчетах также подтверждается экспериментально. Неудовлет­ворительно согласие расчетных оценок К- с эксперименталь­ными для 1бЧ)у и '63 Dy -Однако трудно было ожидать, что грубые модельные расчеты у -спектров будут всегда давать хорошее согласие с экспериментом. Вопрос как раз и состоял в том, можно ли с помощью таких модельных расчетов предуга­дать наличие достаточных спиновых эффектов у. выбираемых для исследований мишеней и выяснить, насколько однозначно

Е - Е . отт

р(E,J, тт) = тт

тт

21 + 1

•2а

-246-

можно предсказать знак спинового эффекта, т .е . что fi,_j/2^HJ/r Как нам кажется, результаты расчетов показывают., что такие оценки спинового эффекта весьма полезны для предварительного отбора образцов, пригодных для исследовании спинов нейтрон­ных резонансов по методу множественности у -квантов, для выяснения знака спинового эффекта и выбора порогов регистра­ции квантов в каналах одиночного счета н совпадений.

Результаты

Измерения образцов из естественного кадмия, ij7Cd и ес­тественного диспрозия проведены на нейтронном спектрометре Лаборатории нейтронной физики ОИЯИ с разрешением ~ 16 нсек/м. Методика измерений и обработка эксперименталь­

ных данных была такой же, как в / J .V, Для оценки достовер­ности определяемых значений спинов резонансов мы использо­вали метод, предложенный в А / , где вероятности значений спина I \ I/2 или 1-1/2 вычисляются следующим образом:

2 t

VI e 2" ƒ If- " , _ ° - ^ , J = / + 1/2

{R . -^а)^ (ft f - b )

2 о* н. 2о 2

ir <• w а Ь

h e

( R i - ь)2

2

Wt = , J =1-1/2. ( Rj-a)2 ( R i-b)

IF e e 20' +Wb e 2°2i

Здесь a, b • средние R для двух возможных значений спина; ° i - дисперсия R. ,в которую входит, кроме о { э к С П , еще

дисперсия, обусловленная портер-томасовскими флюктуаииями, <* РТ » т - е -

„2 2 2 Qi = а ' Э К С П + С Т Р Т

lf„ , II" h - априорные вероятности иметь резонансу спин / + 1/2 или / -1/2 .которые разумно положить

-247-

Wb - sb = 4 " [/ -(21 f / ;"'l -

Из условий экстремума функции правдоподобия для всей сово­купности наблюдаемых резонансов можно найти параметры и , Л а РТ. а следовательно, и вероятности W)" и JÏ * .

Результаты идентификации спинов резонансов исследованных образцов приведены в табл. 2, 3 , 4 . В измерениях с образцами кадмия и диспрозия использовались пороги в канале совпадений 0,3 Мэв, в одиночном канале - 2,5 Мэв. Образец 157С<1 имел обогащение -* 95°fo, измерения с ним проводились при нескольких порогах в одиночном канале / 2 , 0 - 3 , 0 Мэв/ и пороге 0,1 Мэв в канале совпадений. На основании проведенных расчетных оценок спинового эффекта можно было ожидать, что использова­ние амплитудных окон в каналах совпадений в пределах 0,1 -2 ,0 Мэв будет приводить к заметному увеличению спинового эффекта. Однако применение таких окон в измерениях с 157<><i и 1)у не привело к ожидаемому эффекту. Это расхождение мож­но объяснить тем, что при использовании дифференциального окна в реальном детекторе в этом окне на самом деле регист­рируется значительная доля жестких квантов за счет комптон-эффекта в кристаллах, в то время как при получении расчетных оценок К подразумевалось полное поглощение квантов.

Используя параметры нейтронных резонансов П7 Cd из нашей работы /<>/ и спины, полученные в настоящей работе, мы нашли, что силовые функции 157Gd для двух возможных значе­ний спина имеют следующие значения:

S0 = / 2 , 1 + 0 , 7 / . Ю - 4 для ƒ = / ,

и S9 = / 2 , 3 ± 0 , 6 / . Ю " 4 для / - 2 .

Средние расстояния между резонансами составляют f)J=i = L3,3+1,5 и / J / » 2 = 9,5+0,9 эв, что позволяет дать следующую оценку спинового фактора, входящего в формулу плотности уровней, даваемую статистической моделью ядра; а = Л,5 ^t>() .

С целью увеличения числа определяемых спинов для резо­нансов кадмия и диспрозия мы планируем продолжить измерения на образцах разделенных изотопов.

- 2 4 8 -

Авторы выражают признательность В.И.Фурману ïi В Л ' . Н И -коленко за полезные обсуждения и интерес к работ*.- и И.И.Ше-лонцеву за помощь в проведении расчетов на ЭВМ.

Литература

1. Э.Н.Каржавина, Ким Сек С\, А.Б.Попов. ОИЯИ, РЗ-6092, Дубна, 1971.

2. Э.Н.Каржавина, Ким Сек Су, А.Б.Попов. ОИЯИ, РЗ-6237, Дубна, 1972.

3. E.N.Karzhavina, Kim Sek Su, A.B.Popov, The determination of spins of neutron resonances by the gamma ray multiplicity method. Conference on nuclear structure study with neutrons, Budapest, 1972.

4. T. von Egidy. Statistical calculation of neutron capture radiation. Proceedings of the internatiional simposium on neutron capture gamma ray spectroscopy. Studsvik Aug. 1969, IAEA, Vienna, 1969, p. 541.

5. A.Stohvy et a/., Phys.Rev., 5C, 2030, 1972. 6. Э.Н.Каржавина, Нгуен Фонг, А.Б.Попов. ОИЯИ, РЗ-3882,

Дубна, 1968.

Рукопись поступила в издательский отдел 14 февраля 1973 года.

-249-

Таблнца I

ЕЛ Ядро

мишень Спин К»йсп |ЧМ£Ь ft» f ы I . u*pd &/2 1,29 1,14-1,19 9,55 12 2,2 2 . lu Cd 1/2 1,27 1.12-1,17 9,05 9 2,2

3 . " * < * 1/2 1,27 1,12-1,16 9,05 8 2,2

4 . WS»« 7/г 1,23 1,24 8,14 14 2,3

5 . **S»« 7/г 1,18 1ДЗ 8,01 У Х^-

ó* х**ы 3/2 1 .П 1 ,П 7,94 14 i , o

7 . ш Dy 5/2 1,21) 1,04-1,13 8,19 6 1.0 8. 9 .

5/2 7/2

1,20

1,00

1,00-1,14

1,01

7,64

6,33

14

17 0,48

10. myb 1/2 1,00 1,03 7,98 21 2,1

I I . ,nYb 5/2 1,13 1,09 7,50 7 1,6

12» »©0» 3/2 1,1? 1 .И 7,75 14 1,8

О ц - энергия связи нейтрона; J/ - число известных нижних состояний, включенных в

расчёт; Р - - верхняя граница диснрвтного спектре.

-250-

Табляца 2 Спнны резоазвсов * СА % С&

а = U?6, % =2.скг} 6 ^ = 0 . 1 5 2

ъъ Изотоп Ri JT Спнв вероят­ность 2

18.3 113 1.505 0.038 I 100 27.5 III 1.555 0.006 I 100 56.1 И З 2.222 0Л74 0 90 63.7 из 1.603 0.015 I 99 84.8 из 1.653 0.007 I 99 86.0 I II 1 .9П 0.021 0 65 99.4 III 1.480 0.010 I 100 102.5 I II 1.247 0.029 I 100

'108.5 из 1.596 0.013 I 99 .138.0 I I I 1.4У9 0,014 I 100 142.9 из 1.904 Ü.052 0 >9 158.8 XI3 i .623 0.022 I 99 163. У ш 1.655 0.010 I 99 192.5 из 2.088 0.022 0 98 2I5 . I из 1.589 0.017 I 100 225.1 I I I 1.702 0.011 I 96 231.8 I I I 1.670 0.011 I 98 260.8 из 1.689 0,020 I 97 269.2 из 1.863 0.030 I 57 275.3 III I.6I5 0.025 I 99 29I.X из 1.955 0.075 0 73 3II .4 III 1.985 0.065 0 83 331.7 I II I . I89 0.077 l 100 354.9 III 1.548 0.023 I 100 390.1 I II 2.334 0.018 0 100 414.0 из 1.702 0.021 1 96 430.8 из 1.650 0.033 I 98

-251-

Таблица 3 Спины рвэовансов *Gr(£

а. = 1.978 > 4 = глэг С= o.rai

Е0эв & ^даь. 7 Бероя га

16.1? 2 . I2 I 0.012 i 65 16.77 1.962 0.003 2 99 20.5 Ï . 9 I I 0.004 2 I0Q 21.6 1.944 0.016 2 99

23.2 2.225 0.023 1 97 25.3 2.034 0.010 2 89 40.06 2.170 0.032 I 86 44 ,1 1.973 0.007 2 98 48.7 I .90I 0.005 2 100

58.1 1.972 0.006 2 98 66.4 2.271 0.ÜI5 I 99 81.2 2.195 0.011 I 95 82.0 2.056 0.016 2 80

87.0 2.035 0.014 2 88 96.5 2Л52 0.015 1 83

100.0 2.179 0.013 I 92 104.8 2.214 0.012 I 97 107.3 I . 96 I 0.022 2 98 110.0 1.927 0.009 2 100 I I 5 . 2 I .95I 0.024 2 99 120.7 I . 99 I 0.026 2 96 135.1 1.827 0.032 2 100 137.9 2.008 0.010 2 95 138.8 ( I ) 143.7 1.989 0.011 2 97 148.3 2.179 0.025 I 90 156.4 1.939 0.018 2 99 164.8 2.179 0.023 I 91 171.3 2.314 0.016 т 4 100 178.6 1.975 0.023 2 98 182.9 2.164 0.026 I 86 190.6 2.444 0.028 1 100 194.4 1.969 0.016 2 98

-252-

^02.8 2.091 0.038 (г) 59 207.7 1.948 Ü.013 2 99 217.2 2.045 0.062 2 79 22I . I 1.890 0.069 2 98 228.3 I . 7 I I 0.О43 2 100 239.2 2.172 0.015 I 95 246.4 \Л) 2t>u,2 2.1га 0.054 I ы 26Ü.I Ш 2бъ.а- uwr Q,VJ6I г У1 268.2 1.964 0.U78 г 93 281.8 2.105 0.028 (i) 52 ^87.6 2.099 0.037 (г) 53 290.8 2.198 0.Ü34 i 93 293,7 2.180 0.060 i 81 300.9 2.306 0.046 i 99 306.4 (г) 319.0 U) 321 (2) 339 (2)

-253-

Таодлца 4 Саяны резонавсов ' * Ду а » г. 153, I « г. 587, фу- - оазо

Е0 эв Изотоп (Ц ( J J ^ 3 Вороятяость

7.72 161 I.99I 0.015 3 100 10.4 161 2.908 0.013 2 100 10.99 161 2.277 0.020 3 94 12.66 161 2.890 0.221 г 96 14.2 161 2.164 0.008 3 100 16.2 163,161 2.327 0.007 3 82 16.6 161 2.162 0.008 3 100 18.4 161 2.125 0.009 3 100 19.6 163 2.434 0.027 2 77 20.3 161 2.747 0.017 2 100 23.3 (3) 29.0 161 2.204 0.023 3 99 29.8 161 2.034 0.038 3 100 34.9 161.163 2.200 0.050 3 99 35.7 161.163 2.485 0.013 2 93 37.7 161 2.078 0.011 3 ICÖ 38.4 161 2.120 0.010 5 100 43.2 161 2*006 0.011 3 100 45.0 161 2.167 0.013 3 100 50.2 163 2.227 0.025 3 98 50.8 161 2.098 0.023 3 100 51.7 161 2.281 0.006 3 94 55.0 161 2.484 0.011 2 93 55.8 163 2.510 0.050 г 94 58.9 163.X6I 2.625 0.011 2 100 61.3 161 2.209 0.022 3 99 63.6 161 1.962 0.050 3 100 65.9 163.161 2.502 0.019 2 95

-254 -

SPINS OF 1ц75т AND l l + 9Sm NEUTRON RESONANCES.

E.N. K a r z h a v i n a , Kim Sek Su, A.B. Popov.

J o i n t I n s t i t u t e f o r N u c l e a r R e s e a r c h , L a b o r a t o r y of Neu t ron P h y s i c s ,

Dubna, USSR.

Abstract Spins of ltf7Sm and ltv9Sm neutron resonances were measured in the region up to 400 eV by the method of y-quantum multiplicity using the neutron spectrometer of the Laboratory of Neutron Physics. Spins of 50 resonances of 147Sm and 70 resonances of llt9Sm were determined. It is shown that the strength functions of Sm and l °Sm are independent of the spin, and the level density dependence on the spin agrees well with theoretical predictions.

-255-

1. В предыдущей работе авторов описана методика (аналогичная предложенной в ' 2 ' ) определения спинов нейтронных реаонансов по мно­жественности у -квантов, испускаемых при захвате нейтронов. В данном сообщении приводятся полученные с помощью этой методики оезультаты

т - 149 о исследования спинов резокансов лш и ьт , На установке из 4-х кристаллов JVa/ , описанной в /у, проведены измерения выхода У -лучей в зависимости от времени пролета нейтронов в режиме совпадений и в режиме одиночного счета. Измерения выполнены на 250-метровой пролет­ной базе в бустерном режиме работы реактора, что обеспечивало разре­шение = 16 нсек /м . Образцы Sm и Sm представляли собой окись самария с обогащением по основному изотопу = 95%.

Обработка полученных спектров проводилась на осциллографе со све ­товым карандашом на ЭВМ БЭСМ-4 ?*', В результате обработки были получены площади резонансов S^ -в режиме одиночного счета и S е

в режиме совпадений, а также их отношения R -—— . Порог в канале с

одиночного счета составлял в 3 Мэв, а в канале совпадений -

0,33 Мэв. Анализ отношений площадей позволил провести спиновую иденти­

фикацию почти всех разрешенных резонансов Sm B области до 250 эв 149

и Sm в области до 140 эв. Кроме того из анализа графиков совме­

щенных спектров можно было указать спины плохо разрешенных резонан­

сов, расположенных в области больших энергий. Результаты спиновой

-256-

идентнфикации резонансов Sm и Sm приведены в таблицах 1 и 2.

В этих таблицах показаны также данные других авторов. В столбцах таб­

лиц, где приведены наши результаты, в скобках указаны спины, которые

мы приписываем плохо разрешенным резонансам из анализа совмещенных

спектров (рис. 1-4).

На рис. 5 приведены полученные значения R° для разрешенных р е -147 149

зонансов Sm и Sm •

2, Из таблиц 1 и 2 видно, что наша идентификация спинов в боль­

шинстве случаев согласуется с результатами других авторов. Полученные

подробные сведения о спинах нейтронных резонансов Sm и Sm поз­

воляют с использованием наших данных о параметрах резонансов этих / 7 / изотопов проанализировать спиновые эффекты в плотности уровней

и силовых функциях.

На рис. 6,7 представлена зависимость числа наблюдавшихся уровней

с определенным спином от энергии нейтронов. Для Sm наблюдается ли­

нейная зависимость N (Е) Для обоих спиновых состояний как в области

до 250 эв (где спиновая идентификация достаточно надежна) , так и в

более высокой области до 400 эв (где возможны ошибки в определении

спинов). Из рис. 6 видно, что для 147Sm среднее расстояние между р е -

зонансами с / = 3 D? = 15,0 + 1,5 эв, а с / » 4 D4 = 12,8 +.1,2эв.

Как было отмечено в ' , в условиях нашего разрешения для Sm в

области выше 130 эв наблюдается заметный пропуск уровней, что можно

также видеть на рис. 7. Оценка средних расстояний между уровнями для 140

двух спиновых состояний Sm по линейным участкам графиков рис.6,7 приводит к следующим значениям: л = 5,2+.0,5 эв , D = 4 , 1 + 0 , 3 эв .

3 4 ~~

-257-

Таблица 1

Спины резонансов Sm

Спин резонанса Е0 эв Данная

работа / 4 / / 5 / Е0 эв Данная работа

З Л 3 3 225,3 3 18,3 4 4 4 228,6 (3) 27 ,1 3 3 3 240,6 4 29,7 3 3 3 247,7 4 32,1 4 (4) 4 256,5 (4) 39,7 4 (4) 4 263,5 СЗ) 40,6 3 3 3 265,8 (4) 49 ,3 4 (4) 271,0 3 57 ,9 3 (4) 274,4 3 64 ,9 4 (4) 283,3 4 76,0 4 289,4 (4) 79,8 4 4 290,5 83,4 3 3 3 308 (3) 99,5 4 312 (4)

102,6 3 3 321 (3) 106,8 4 330 (3) 108,4 (4) 332 (4) 123,4 3 3 3 340 (*) 140,0 4 3 350 СЗ) 143,3 4 359 (4) 151,3 3 3 362 (3) 160,8 4 379 (3) 163,6 4 4 382 (3) 171,7 4 4 391 (4) 179,7 3 398 (4)

183,7 3 3 399 (3)

190,8 . 3 406 (3) 193,5 4 412 (4) 198,0 (3) 205,8 4 221,6 3

-258-

Таблица 2 Спины резоавнсов

Ео Данная работа / б / / 5 / Ео

Данная работа / 5 / ^ Данная J,-, ао работа / J /

4,98 4 4 4 83,9 4 185,4 3 3 6,48 3 3 4 87,7 3 188 (4) 8,93 4 3 90,6 4 4 192,9 4

12,0 3 3 3 92,1 3 195,0 14,9 4 3 4 95,6 4 197,4 3 15,8 3 3 3 96,3 3 201,1 17,1 4 4 4 98,1 4 203,7 3 23,2 4 4 4 99,5 4 210,9 4 24,6 (4) 101,6 3 214,7 3 25,2 3 3 104,7 4 4 218,2 4 26 ,1 4 3 4 107,0 3 225,6 4 27,9 3 3 109,0 ü 4 228,2 (4} 29,9 3 3 111,2 3 230,1 3 30,7 4 4 4 115,1 4 (3) 234,0 (4) 33,9 4 4 4 117,0 3 238,4 40 ,1 3 3 119,4 3 240,1 (3) 41,3 3 3 121,7 (4) 244,3 (4) 44,3 4 4 125,2 4 (3) 248,7 3 45 ,1 4 4 130,3 4 3 254,7 3 49,5 3 134,1 4 (3) 258,9 (4) Ь0,5 (3) (4> 138,6 (4) 51,6 4 4 141,0 (3) 57,4 4 4 144,2 4 59,7 4 4 145,7 (4) 60,9 3 3 146,9 4 62 ,1 4 4 149,5 (4) 64 ,7 3 4 154,7 4 68 ,3 4 4 157,5 3 70,8 3 3 158,7 (3) 72,2 (3) 168,3 3 (3) 73 ,1 4 4 173,5 (3) 74,6 4 (4) 174,7 75,3 3 3 177,8 4 (3) 76,9 4 179,9 3

- 2 5 9 -

1000 A гооо.

1000

гооа\

теоо

гооо

з<оо зет

Рис. 1. Самарий-147, Сплошная кривая - спектр в режиме совпадений, 'точки - спектр в режиме одиночного счета. Показаны участки спектров, нормированные по резонансу 57,8 эв.

2000

ГК «> * ГЧ

й' ее en ' • -J? O) 8 * t4" Й-" >л о >» en ' • -J? in 8 * у (0 o О)

"*co n °» " p o O v c , < N < N 4 CM 14 o N V, 1, . O • о м - f*> c\j ^ *** U 4 . v» ^ i t 2 1,

. * Jfcil 'A ' l>5 C*> ( Э t>J C*) •» W A A V ЛЛ ft 2 i А. ЩЛ\ JW/VJV к#у\ h Л, к л, л /V 50

2000

550

2000^

го

А 550

I ы о

1050

toso f300

Рис. 2. Самарий-147. Сплошная кривая - спектр в режиме совпадений, точки - спектр в режиме опиночного счета. Показаны участки спектров, нормированное по резонансу 79,8 зв.

- 2 6 1 -

20OO

toso

гоао \

1600

tsoo

ï 9"

гооо

2000

А А/ч 1ЮО 2S0O

гооо

геоо зооо

гооо

3S0O

iOOO

Рис, 3 . Самарнй-149. Сплошная кривая - спектр в режиме совпадений, точки - спектр в режиме одиночного счета. Показаны участки спектров, нормированные по резонансу 33,9.

2000-

2000

I to О-to I

iOSO

Рис. 4. Самарнй-]48. Сплошная кривая - спектр в режиме совпалений, точки - спектр в режиме одиночного счета. Показаны участки спектров, нормированные по резонансу П9,4.

-263-

R' 1*3 _ 147_ .- Sm *- Sm

1.3

1,2

f.1

f

T - . * * * * « * •

' 4 • * T * I

* * » • • . * • * # t

0,9

0,8

' -* • ц - r"*^- .-*•-> •*.- ï - г - - - -v.-. - -- * *

0.7

. ,_.! _ - !_ . _ . J _ 1 100 eoo £-»^g

Рис. 5. Значения R° для разрешённых реэонансов t4JSm и , 4 ? Зт . ^Для большинства точек ошибки меньше их размера).

100 200 300 400 Е-эд

Рис. 6. Зависимость числа реэонансов с разными спиновыми состояниями от энергии нейтронов для t41Sm .

-264-

Полученные значения Dj для разных спинов дают такое отношение D р

—i = —I = 0,85 ±_0,И и 0,79 i 0,10

147 с 749 4

для S"1 л 5/я , соответственно. Эти данные интересно сопоста­

вить с общепринятой теоретической зависимостью плотности уровней от / я / спина при постоянной энергии возбуждения ядра ' °'

(J + Y02 р(1) = const(2J + I) exp [ ] . (1)

2az

Сравнение (D,/D ) э к с п с теоретическим отношением, даваемым фор­

мулой (1) , позволяет получить оценку спинового фактора о , входяшего 147 ~2.5 149 —6,5

в эту формулу: для Sm а = 7 + м , для Sm о - 12 + м ,

т . е . для обоих изотопов a i .4,5, что согласуется с оценками величины

а в этой области атомных весов, даваемых разными авторами (напри-

м е р , / 8 / ) . Оценивая силовые функции для разных спиновых состояний как.

5° = sJ. и используя данные из ' ' ' для 147 Sm > мы получили J Д £

(рис. 8-10), что по интервалу до 260 эв S° = 4,4 +_ 1,6 (число резоная-

сов "» = IS) и s4° = 4,2 + 1,5 ( т = 20) ( S° везде в единицах К Г 4 ) .

Оценка S° по интервалу до 400 эв дает S° = 3,9 + 1,2 и S° = 3,8+1,1

( т3= 25, т4 = 32). S o i47 г*

..^...j .......w,_ „.»-... f показывают, что у й т не наблюдается

никакой зависимости силовой функции от спина резонансов. Не имеется

существенного различия в силовых функциях для разных спинов и у Sm , Так, на интервале до 120 эв, где надежна спиновая идентификация и нет пропуска резонансов, S° ~ 6.3+.2,1 ( т =23) и S0 =7,7 +.2,2 ( т = 30) .

3 4

>

-265-

N

" s S m 40 y^~^x' 3 = 4

30 r*jJ~~r^ J-3 го jf Л ^

10

5*Г7 ..._ __L - > 100 200 £-=эб

Рис. 7. Зависимость числа реэонансов с разными спиновыми СОСТОЯНИЯМИ от энергии нейтронов для I49Sm .

Г Г, п 150 wSm

100 • J J =4

50 У L ..._ .. ,.!_.._ 1 _ i — _ _

100 200 $00 400 ЕвЭб

Рис. 8. Зависимость суммы приведенных нейтронных 'ширин реаонансов с разными спиновыми состояниями от энергии нейтронов,

£Ъ

-2u6-

^гп 150

u7Sm

I—гТ=з 100

50

' / i t i

100 zoo зоо 400 £=э6

Рис. 9. Зависимость суммы приведенных нейтронных ширин резоне с разными спиновыми состояниями от энергии нейтронов для м?

1ГГ п 150

ioo - Т^7 =

э-з 50

-чС5-С , -I ., -J _ . , „1. ,.1 -100 200 £ " « э б

Рис, 10. Зависимость суммы приведенных нейтронных ширин резо. с разными спиновыми состояниями от энергии нейтронов для 1 4 9

-267-

Для интервала до 250 эв получены такие значения: S° = 4,1 + .1 ,1

( w = 36) и S° = 5,8 +_ 1,4 ( т = 4 6 ) .

Если принять во внимание более достоверные оценки S° (для

Sm по интервалу до 260 эв, а для Sm по интервалу до 120 эв) ,

то полученные нами величины S° и S° не дают никаких оснований

предполагать сушествование спиновой зависимости в силовых функциях

для 1475л1 и 149 Sm • В этом отношении наши результаты для изотопов /а/

Sm противоречат выводам, сделанным в работе / 7 / В нашей работе обращалось внимание на флуктуацию в зависи­

мости нарастающей суммы 22#Г я ° от анергии нейтронов для изото­

па Sm , Вычисления S° по интервалу 0-40 эв {= 20 резонансов)

и по интервалу 40-100 эв ( «• 25 резонансов) приводили к значениям

S° = 2,8 +_ 1,0 и 11,7 +.3,6, соответственно. Результаты настоящей ра­

боты показывают, что эта флуктуация ни в коей мере не связана с груп­

пированием резонансов с определенным спином.

Изучение распределений приведенных нейтронных ширин резонансов

исследованных изотопов Sm приводит к заключению, что распределения

Г ° для резонансов с J = 3 и ƒ = 4 как для Sm t т а к и для

'*9 Sm находятся в удовлетворительном согласии с распределением Порте­

ра-Томаса.

Авторы выражают признательность В.Б. Злоказову за помощь в

обработке экспериментальных данных на ЭВМ.

-268-

Л и т е р а т у р а

1. Э.Н. Каржавина, Ким Сен Су, А.Б. Попов. Препринт ОИЯИ РЗ-6092, Дубна, 1971.

2. C.Coceva, F . C o r v i e t a l . N u c l . P h y s . A117, 586 ( 1 9 6 8 ) . 3. В.Б. Злокаэов, Л.С. Нефедьева. Сообщение ОИЯИ, 10-5966,

Дубна, 1971. 4. И. Вильгельми, Ю.П. Попов, М. Пшитула, Р.Ф. Руми, М. Стэмпинскн.

Сообщение ОИЯИ, РЗ-5553, Дубна, 1970. 5. B .Cauvin , A . L o t t i n , A.Michaudon e t . a l . S a c l a y ( 1 9 7 1 ) . 6. F . B e c v a r , R . C h r i e n r O.Wascon. BNL-15056 (1970) . 7. Э.Н. Каржавина, А.Б. Полов. Препринт ОИЯИ, РЗ-5655, Дубна, 1971. 8. А.В. Малышев. Плотность уровней и структура атомных ядер.

Атомиздат, Мосхва, 1969.

9. c . N e w s t e a d , J . D e l a r o c h e , B .Cauvin . I n t e r n a t i o n a l Confe rence on s t a t i s t i c a l p r o p e r b i e s of n u c l e i . Repor t 5 . 1 1 . August 2 3 - 2 7 , 1 9 7 1 . A lbany .

Рукопись поступила в издательский отдел 18 января 1972 года.

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JEUTRON RESONANCES OF IRIDIUM ISOTOPES.

J. Lason, H. M a l e c k i , L .B. P i k e l n e r , I .M. S a l a m a t i n , E . I . Sharapov.

J o i n t I n s t i t u t e fo r Nuc lea r Resea rch , Dubna, USSR.

A b s t r a c t

Measurements of radiation capture cross sections of separated iridium

isotopes 19iIr, 193Ir are performed by the time-of-flight method using

pulse reactor IBR with linac.

Energy of 106 resonances and values gf for the majority of them are

determined.

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Опреаеление параметров нейтронных резонансов иридия с исполь­зованием разделенных изотопов представляло интерес в связи с отсутст­вием подробных данных для этих ядер / * Л В нашем распоряжении име­лось 11,8 г изотопа 7г с обогащением 82% и 24,6 г изотопа h с обогащением 98%. С этими образцами были проведены измерения ра­диационного захвата нейтронов.

Измерения проводились на нейтронном пучке импульсного реактора 111 ИБР-30 в режиме рабоп.! с инжектором . Разрешение при пролетной

базе 500 м составляло 8 нсек/м, В качестве детектора радиационного

захвата нейтронов использовался секционированный жидкостный сцинтил-

ЛЯ1ШОНПЫП детектор ' 3 / объемом 210 литров, имеющий цилиндрический

канал вдоль оси пучка нейтронов. Чувствительный объем детектора

составляли 6 симметрично расположенных секций, каждая из которых

просматривалась двумя фотоумножителями ФЭУ-49. Электроника детекто­

ра позволяла отбирать импульсы от каждой секции, лежащие выше задан­

ного порога, а также регистрировать двойные и тройные совпадения меж­

ду любыми секциями. На рис. 1 приведены участки аппаратурных спектров tot ƒ 9JJ

/г и /г , полученных в режиме двойных совпадений.

- 2 7 1 -

пхагквте мл s;« m ,u, шг> *, i i l i . i l i t

1 * — . — < • — • — . 1 — - — _ — • *

«» ,m то «те то то и« ли

Рис. 1. Участки аппаратурных спектров 191'1г и 193 h , полученных в режиме двойных совпадений.

Плошась резонанса на экспериментальной кривой при вычтенном фоне описывается, выражением

2 N . = П (Е ) с - £ * - А , (1)

где П (Е ) -число нейтронов, падающих на образец за время измерения

на единичный интервал энергии ; e -эффективность регистрации акта

радиационного захвата нейтрона, Гу и Г -радиационная и полная ширш

резонанса ; А —площадь резонансного провала на кривой пропускания.

Произведение П(Е )с находилось путем определения величины А

из дополнительного измерения пропускания для нескольких резонансов

с Гп « Г , для которых отношение П, / Г близко к единице и практи

чески не зависит от величины Г п и Г у . Тогда из (1) следует, что

П (Е) ( = fit. / -f?- А .

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Энергетический ход IÏ (E ) определялся с помощью тонкого борного счет­

чика. Для контроля постоянства эффективности детектора для различных

резонансов проводились измерения радиационного захвата в режиме ре­

гистрации одиночных импульсов каждой секции с высоким порогом

(3 Мэв) и в режиме двойных и тройных совпадений между секциями с

низким порогом (0,5 и 0,2 Мэв соответственно). Отношения площаде;!

резонансов, полученных в разных режимах, оказались совпадающими

в пределах статистической точности - для большинства резонансов не

хуже 5%. Это позволило считать эффективность постоянной с указанном

точностью, а общая неопределенность произведения (I ( Е)е составляла

около 10%.

Толшины использованных обогащенных образцов h и ir coc­on Qfl p

тавляли 3,5- 10 и 8,7*10 и ядер изотопа/см' соответственно-Экспериментальные величины 2 N. / \\(E)t=~y£ -4 приведены для

обоих изотопов в таблицах 1 и 2 вместе с энергиями резонансов. В

случае, когда Гп « Г , можно получить из выражения (I) значение

g Г резонанса, не привлекая каких-либо дополнительных данных кроме

П. . Нами использовалось значение Г = 80 мэв, заимствованное-

из ' ' ' . Полученные таким образом величины g Г также приведены в

таблицах I и 2.

Найденные в эксперименте энергии резонансов позволили построить

графики нарастающего числа уровней, представленные1 на рис. 2, и олре-г, 191.

делить средние расстояния о между уровнями для изотопов "" \\ '1т , равные соответственно (3,4 ^ 0,2) эв и (7,5 +_ 0,5) эв.

Ошибки величины D включают неопределенность, связанную со / 4 / / РЯ/

статистикой числа уровней , и вероятность пропуска слабых уровней'0 ' .

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Таблица I

ПАРАМЕТРЫ РЕ30НАНС0В I9Ilr

В э$ л£ э& SLA э £ л(<1А] э8 %Гп глЛ А$ГПМЭЬ

I 2 3 4 5 6

19.23 0.05 0.079 0.009 1.2 0.24

20.22 Ü.Ü5 ü.uol 0.008 0.94 0.25

25.2 0.07 0.21 0.02 5.5 I . I 7

29.9 0.1 0.23 0.025 9.5 2.3

31.6 0.06 0.13 0.015 3.5 0.65

56.6 0.1 0.068 0.010 1.9 0.42

40.4 ил О.П 0.014 4 .0 1.0

41.5 0.12 0.052 0.005 1.0 0.2

44.6 0.12 0.078 0.010 0.6 0.17

45.7 0.13 0.058 0.ÜU7 1.3 0.48

51.0 0.12 0.27 0.03 27.0 5.7

52.8 0.13 . 0.09 0.01 4 .1 0.8

55.8 0.IA 0.031 • 0.0046 1.3 0.33

62.9 0.06 0.057 0.007 2.8 0.65

64.9 0.12 0.071 0-.0С.9 5.6 0.9

65.7 0.06 0.09 0.01 5.2 1,25

68.0 0.06 0.095 0 .0I I 5.3 1.35

76.6 0.07 0.063 0.1Л.85 5.7 0.9

78.8 0.08 0.13 0.014 10.0 2.0

80.6 0.08 0.08 0.01 5.6 I . I

81,9 0.16 0.025 0.004 1.5 0.33

87.4 0.09 0.08 0.01 6.0 1.6

97.6 0.11 0.125 0.015 I I . 0 3.0

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I 2 3 4 5 6 99.9 0.11 0.072 0.009 5.8 1.4

103.6 0.12 0.11 0.013 12.0 2.7 I » . 8 0.24 O.II 0.013 I I . 0 2.8 106 Л 0.12 0.015 0.0015 I . I 0.32 114.3 0.14 0.049 0.007 4.3 I . I I IC.7 0.14 0.053 0.007 3.9 1.0 127.0 0.32 0.028 0.007 2.7 0.96

128,1 0.16 0.040 0.006 3.8 1.0

129.9 0.16 0.066 0.008 7.5 1.7 134.2 0.17 0.08 0.01 10.0 2.5

137.6 0.18 0.051 0.0U83 5.8 1.6

142.9 0.38 0.10 0.016 8.0 3.6

147.7 0.2 0.13 0.02 >40

151.8 0.4 0.035 0.017 4.Ü 2.0

156.2 0.43 0.13 0.018 5>40

161.5 0.23 0 . П 0.018 > 4 0

163.6 0.23

165.2 0.47

166.4 0.24 169.3 0.24

171.0 0.25 178.7 0.26

186.3 0.28 194.7 0.3

b ' 9 . 9 0.31 206.0 0.33

208.6 U.34 210.7 0.34 214.1 0.35 217.6 0.36 223.0 0.7 225.2 0.4

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Т.аблицг 'i.

lïAPAMKTPiJ PS301EAIIC0B I 9 5 / r

E э& лЕ ЭЗ tfA3& • л(^д)ъ& }Гпмэ& л$Гп„эе

I 2 3 4 5 6 24.51 0.05 0.22 0.02 2.15 0.2

25 . 04 0.05 0.21 0.02 2.1 0.2

26.08 0.05 0.19 0.02 1.95 0.2

4 Ï . 6 0.09 0.122 0.016 1.3 0.18

43.2 0.12 0.60 0.06 ^ 4 0

52.6 0.04 0,143 0.016 2.65 0.27

54.0 0.04 0.29 0.03 8.0 0.9

69.3 0.2 0.48 0.05 > 40

71.6 0.07 0.053 0.007 1.1 0.15

77.8 0,08 0.356 0.04 2.3 3.9

80.8 0.15 0.09 0.01 2.6 0.2S-

89.1 0.09 0.10 0.013 3.0 0.4?-

98.3 0.2 0.10 0.018 3.2 0.65

109.9 0.25 0.246 0.035 13.0 2.4

116.2 0.14 0.102 0.015 3.9 0.7

123.7 0.15 0.022 0.007 0.8 - 0.26

127.6 -0 .16 0.020 0.007 0.8 0.26

143.5 0.2 0.133 0.018 7.1 2.65

149.9 0.4 0.155 0.027 9.0 2 .0

152.6 0.2 0.29 0.04 > 40

163.4 0.23 0.42 0.06 >40

174.3 0.5 0.12 0.022 8 2.2

Ï78 .9 0.27 0.146 0.023 10 1.9

185.7 0.28 0.30 0.046 >40

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l-t 2 3 4 5 6

201.5 0.65 0.033 0.01 1.95 0.5

206.0 0.65 0.086 Ü.OII 6.0 I . I

213.4 0.35 0.09 U.0I3 6.4 1.3

216.9 0.35 U. 065 0.009 4 .6 0.9

222 0.73 0.055 0.0065 4.9 0.9

223.4 0.37 0.16 0.026 20.0 4

229.0 0.38 0.16 0.035 20.0 4

267.0 0.5 0.025 O.OII 2.0 0.9

272.0 0.52 0.226 0.025 ,>40

279.0 0.54 0.232 0.026 ^ 4 0

288.0 0.57 0.17 0.02 > 4 0

29У.0 0.57 0.08 0.014 8 Ï . 6

309.0 0.6 0.21 0.03 > 4 0

315.0 1.2

322.0 0.64

326 1.3

531 0.67

336 0.68

346 2.2

350 0.73

357 0.75

363 0,77

372 0.79

378 1.6

380 0.82

388 1.7

391 0.86

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t

SO 100 150 200 2S0 300 3S0 EtpV)

Рис . 2. Графики нарастания числа уровней с энергией для изотопов иридия.

На графике рис. 2 для /9*'/г обращает на себя внимание э н е р г е ­

тический , участок 230-265 эв , не содержащий резонансов. Проведенные,

оценки показали, что на этом участке могут быть пропущены уровни с

величиной g Г)? , пе превышающей 0 ,7 м э в .

Найденные значения D для изотопов иридия позволили определить

величины параметра плотности одночастичных состояний а, вхолятего в

известную формулу Б е т е для плотности уровней ( с м . , н а п р и м е р , ^ б / ) . д л я

Ir н [г они оказались равными соответственно 23,1 М э в - 1 и

21,8 М э в " ' , что согласуется со значениями а для соседних ядер.

В заключение мы считаем своим приятным долгом поблагодарить

B .C . Золотарева и его сотрудников з а любезное предоставление изотопов,

а Т . С . Афанасьеву и Н.Т. Хотько - з а помощь в проведении измерении.

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Л и т е р а т у p a

1. N e u t r o n C r o s s S e c t i o n s , BNL-325, S u p p l . 2 , 1966-2. B.B. Голиков, Ж.А. Козлов и др. ОИЯИ, 3-5736, Дубна, 1971.

3 . X. Малэцки, Л.Б. Пикельнер, И.М. Саламатин, Э.М. Шарапов. АЭ, 32. вып. 1, 49 (1972).

4 . X. Малэцки, Л.Б. Пккелькэр, И.М . Саламатия, З .И. Шарапов. ЯФ, Ц , вып. 1, 111 (1970).

5. T . P u k e t a , J . A . H a r v e y . N u c l . I n s t r . and M e t h . , 33_, 107 (1965) .

6. U . F a c c i n i , E . S a e t t a - M e n i c h e l l a . E n e r g . N u c l . , 1 5 , 54 ( 1 9 6 8 ) .

Рукопись поступила в издательский отдел 22 июня 1972 года.

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CROSS SECTION MEASUREMENTS ON 2 3 6U BELOW 2 KeV

L. Mewissen*, F. Poortmans* , G. Rohr0, O.P. Theobald0, G.J. Vanpraef, h\ Weigmanri0, R. Werz0

1. INTRODUCTION

A study of the reactions between 236U and slow neutrons is of 'interest for various reasons.

The neutron cross sections and resonance parameters are requested by reactor de­signers1}, mainly for the calculation of isotope build-up in thermal reactors.

The only information published on 2 3 eU, to our knowledge, are the measurements of CARLSON et al 2), giving results on capture and self-indication, for neutron energies up to 415 eV. For 28 levels Г values have been determined and Г was

n Y found for 12 among them • Thus more resonance parameters have to be known, in order to study their statisti­cal properties such as s-wave strength function, mean level spacing and mean total capture width. The present paper reports on elastic scattering, capture and total cross section measurements, performed between 30 eV and 1800 eV.

From these experiments the neutron widths Г were deduced for 99 levels and the n

capture widths for 56 levels. 2. EXPERIMENTAL DETAILS

The measurements were performed with a time-of-flight spectrometer using the LINAC of C.B.N.M. as pulsed neutron source.

The experimental details for the three runs are given in Table I. The oxide samples were on loan from the U.S.A.E.C. Their isotopic composition was the following t *

1i 5,4 g uranium compound : 235U 0.2 4 2 3 6U 99.68 % 238U 0.12 %

2) 57.8 g uranium compound : 2 3 4 ) 0.12 % 2 3 5 U 9.2 % 2 3 6U 89.38 4 ' 2 3 BU 1.3 %

*S.C.K,/C.E.N. Moa °C.B.N.M. Geel **Rijksuniversltair Centrum Antwerpen [RUCA)

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The data collection and reduction was done Lsi;-.g rne C.B.N.M. data acquisition system3), which consists of different 4096 channel tine-cf-flight analysers, interfaced with an IBM 1300 computer.

Table I Experimental details

SCATTERING CAPTURE TRANSMISSION

Flight path length '-) 31 .'7 SO.5 31.17 T.O.F. resolution AE/E^F.W.H.N.J2.10"3 0.7-B.7 ns/m 1.5-5,1 ns/m Detector system 3He scintillators Мохоп-йае 3Не scintillator Sample thicknesstat/b) 2.15.10~ц [99%) 2.15.1С"1•99%) 7.6.10"3 [99%)

1.5 .10~3 (39 4) 1.5 ,10"3Ce3%) Sample diameter (mm) 83 83 14

2.1, Scattering experiments

The 30 m flight path, where these measurements were performed, has an angle of 9C

with respect to the normal to the moderator. As detector system we used six 3He nigh pressure gaseous scintillators (LND type 600, pressure 250 atmospheres). The counters were placed at an angle of 102°. The main advantages of these de­tectors are high efficiency and good timing properties.

The 236U scattering cross section was measured relative to Pb for which о = [11.26 ± О.Б) ЬагтЛ). n Black resonance filters [Mn, Co, Mo, Au) were used to determine the background and a Na sample was kept in the beam as a permanent filter. The raw scattering data were corrected for self-screening and for absorption of the scattered neutrons, using a Monte-Carlo program on the IBM 1800 computer.

2.2, Capture experiments

To obtain the spectrum of the incident neutrons, we have used a 10B slab and a Nal crystal, assuming that the 10B(n,a)7Li cross-section, varies as E~ in the energy range of interest. The absolute normalisation was done using capture in black resonances of Ag at 5.2, 16.3, 51.4 ana 70.9 eV. The capture arees vers analyzed with 3 computer program, described by Frohner and Haddad.5)

2.3, Transmission experiments

These measurements were made using a 1 err diameter beam and with a 3He gaseous scintillator as transmission detector. The total background was very small : 4 \

at 2 keV and 2.5 % at 100 eV.

The data were analyzed with a modified version of the Atta-Harvey area program6!.

3. LEVEL PARAMETERS

The resonanca parameters were deduced by combining the results from the area ana­lysis of the three experiments. The neutron width Г could be obtained for 99

n levels and the total capture width Г for 56 among them. The individual resonance parameters will be published elsewhere. 4. STATISTICAL PROPERTIES OF RESONANCE PARAMETERS

From the Г -values a weighted mean value of Y Г = [22.3 ± 0.5(stat.] ± 1.0[syst.f) meV. was obtained. Y

From 12 resonances below 415 eV, Carlson deduced : Г" = (23.9 ± 1.0] meV.

Figure 1 shows a plot of the observed number of levels versus energy. The mean level spacing below 1200 eV is : D =[17.3 ± 0.5)eV. A fractional uncertainty 2 — is given, where n is the number of levels. The value given by Carlson is : П + 2 2 D" =C15.4 _ * )eV. The figure also shows that below 1500 eV not many levels are missed-In figure 2 we have plotted the integral distribution of rVF5", below 1200 eV. The average reduced neutron width in this energy range is : T° =[2.03 ± 0.34)mev\ The figure shows also the calculated curves, assuming for Г° a chi-squared distri­bution with one and two degrees of freedom.

Finally we have plotted [fig.33 the sum of the reduced neutron widths for 99 reso­nances, from zero neutron energy up to 1800 eV, as a function of E. The slope of this function is the neutron strenght function for s-wave levels, being Г"!!/0. The fractional uncertainty on the parameters Г° and S is taken equal to 1.4//n~. The result for S was found to he (1.05 ± 0.15).10-1+. The value obtained by

+ 0 4 -t Carlson is : 5 =[1.02 n' ),1C 4. The quoted values are preliminary, because О - U.2 a correction for missed levels has not yet been applied. Moreover whe have assumed that all detected resonances are due to s-wave interaction.

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REFERENCES ll "Compilation of EAIMOC Requests of Neutron Data Measurements", report EANDC 85"U"

April 1970 2) A.D. Carlson, S.J. Friesenhain, W.M. Lopez and M.P. Fricke

Nuclear Physics A 141(1970], 577 3) A. De Keysert S. De Jonge, Т. Van Der Veen, P. Ter Meer

"Analyser Computer Interface", Proceedings of the Int. Symp. on Nuclear Elec­tronics, Paris 1968

**] L.A. Rayburn and E.O. Wollan Nuclear Physics 61Д1Э85), 381

5) F.H. Frohner and E. Haddad Nuclear Physics 71 (19653, 129

6) W. Kolar Eur. report 4760 e (1972)

Fig. 1

Fig. 2

1200 U00 1600 1800

- ' 8 6 -

ESTIMATE OF THE RATIO R = Г (3)/T f (4) FOR 2 3 5 ü ( n , f )

F . Corvi and M. Stefanon

CBNM, Euratom, Geel, Belgium

CNEN, Centro di Calcolo, Bologna, Italy

235 The knowledge of the spins of a considerable number of U neutron

resonances allows one to deduce an estimate of the average fission

width per spin state: Г.(3) and Г,(4). In the frame of the channel theory of nuclear fission of Bohr*), these quantities a re related to the number of open fission channels and then to the energetically

2) available saddle-point configurations. On these grounds, Lynn has predicted: Г, (3) - 2 • Г,(4).

235 Due to the complicated structure of the U neutron c ross section 235 in the resonance region, different analyses of U data have yielded

very different values of Г, : therefore it is preferred here to give an est imate of the ratio R = ГЛз) / Г\. (4), in the hope that this quantity be l ess dependent on the par t icular analysis used.

The calculation was carr ied out with the maximum likelihood method described in ref. 3, where a prel iminary estimate of R is given: the present evaluation differs from the old one in that it takes into

4) account also the resu l t s of Reddingius et a l .

Summarizing, the data considered a re the following: 5) - 3 spin assignments of Schermer et al. ,

6) -10 spin assignments of Poortmans et al. , 3) -14 spin assignments of Corvi et al . ,

4) -14 spin ass ignments of Reddingius et al. . This consistent set of data gives in total the spin of 31 resonances; the Tf values of both assigned and unassigned resonances below

7) 42 eV a re taken from the evaluation of Krebs et al.

The resu l t s a r e given in fig. 1, where the average likelihood

function ~A_(R) is plotted versus R: one can see that the most

probable values lie around R = 3 and that in any case is R > 1.

This resul t is in agreement with Bohr's channel theory, but 8 9) d isagrees with previous est imates ' based on smaller samples

of resonances .

REFERENCES

1) A. Bohr, P roc . 1st Conf. on peaceful uses of atomic energy, Geneva, Vol. 2, 1956, p. 151.

2} J. E. Lynn, P roc . Int. Conf, on nuclear data for reac tors , P a r i s , Vol. 2 (1966), p. 89.

3) F . Corvi, M. Stefanon, C. Coceva and P. Giacobbe, Nucl. Phys. A203 (1973) 145,

4) E. R. Reddingius et al. , Proc.of this Symposium.

5) R . I . Schermer et a l . , Phys. Rev. 167 (1968) 1121.

6) F . P o o r t m a n s et al. , Proc . 2nd Int. Conf. on Nuclear Data for Reac tors , Helsinki, 1970, p. 449.

7) J. Krebs et a l . , P roc . 3rd Conf. on Neutron Cross Sections and Technology, Knoxville, Vol. 1, 1971, p. 410.

8) C.Wagemans and A. J. Deruytter, Nucl. Phys. A194 (1972) 657.

9) R . G . G r a v e s et al. , Bull. Am. Phys. Soc. II, 16 (1971) 1181.

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11 resonances with J =3 20 " J =/» 32 not assigned Tf from Krebs et al.

/ / \ \ _ / / Л I

/ / \ \ ^ / / \ \ £Г

/ / \ \

< 1 \ \

11 \ \ 1 \

/ / \ \ ^-cr =3.5 / / 1 1 1

\ \ \ \

/ / 1 1 1 Of = oc \ \

\ \ / / Of = oc \ \

\ \ / / \ \ I \ \

1 \ \ / / \ \

/ / \ \ / / \V X *v

0

FIG.1

-289-

THE REACTION 29Si(n,Y)30Si

A.M.J. Spits FOM-RCN Nuclear Structure Group, Petten (N-H), the Netherlands

Although the lower part of the 30Si level scheme, mainly consisting of positive-parity levels, has been investigated thoroughly by means of various reactions, until recently our knowledge of the higher-lying levels was rather limited. A recent publication on (d,p) work by Mackh et al. |t|, concentrating upon the E =6-9 MeV region, improved the situation. The purpose of the present investigation of the reaction 29Si(n,y)30Si is the supplement of our knowledge of especially the higher-lying levels as well as the comparison of the mechanisms of the (d,p)~ and (n,y)-reactions.

The experimental procedure consisted of two parts:

a) singles spectra were recorded 0f the gamma radiation following capture of unpolarized thermal neutrons in an isotopically enriched target;

b) the circular polarization of three primary 7-ray transitions was measured by using a polarized-thermal-neutron beam. Because of the low capture cross section (=0.1 b) a long measuring period was needed in addition to a big amount (10g) of target material.

From the set of energies and intensities deduced from the singles spectra, the ratio of the thermal-neutron capture cross section of 28Si and 29Si was determined as 1 -6±0.2. The absolute thermal capture cross section of 28Si could be deduced from a series of runs with targets of silicon mixed with elements of which the cross sections are well-known. The cross sections thus found are a (28Si) •= 0.16+0.03 Ъ and a (29Si) = 0.10+0.03 b, at cap cap variance with the literature values 0.08±0.03 b and 0.28+0.08 b, respectively |2j. Besides, the accurate (0.14-1.2 keV errors) energies of 20 levels could be obtained together with their y'branching and a few more spin restrictions.

The circular polarization experiment yielded R-values for three primary

-290-

y-ray transitions. The theoretical polarization R as a function of a, the fraction of the 1 component in the 30Si capture state, is depicted in fig. 2. As the correlation coefficient for the sets of reduced (n,y) strengths and (d,p) strengths for 1 (d,p) = 1 levels is rather high (p=0,95, fig- 3), the measured polarization R yields the ratio of the relative pi/2- and рЗ/2-strengths |з|. The measured R-values for three primary y-ray transitions are listed in the table, together with 83/2/'^el/2+e3/2^ ai'd J a s s i g n m e n t s *

In the case of pure 2pl/2 and 2p3/2 levels R can then only take the values +1 and -0.5, as is indicated in fig. 2 by squares and circles. An admixture of channel resonance capture will become manifest as i) a value of p significantly differing from +1, ii) R-values which for Jf = 1 levels

+ deviate from the values +1 and -0.5. Indeed, when a 0 resonance contributes to the total capture cross section, the (n,y) strengths for 1 levels will be enhanced relative to those for 0 and 2 levels and on the ellipse R-values to the left of the circles (as is indicated by the arrows) are obtained.

As was demonstrated on the Budapest Conference of 1972 by Abrahams |4|, for p-levels a sum rule holds: £±l/a(l-a) « 0, where I denote the intensity of the primary y~ray transition, a again stands for the fraction of the IT +

J = 1 component m the capture state and the sum extends over all p-ТГ — —

levels. As for Jj, = 0 or 2 the terms become zero, this reduces, to 'f Z +I/a(l-a) = 0.

J*-Г As the intensity of the primary y~ray transition proceeding to the E =6.74 MeV 2p3/2- level with J^l", is 30% (table), in order that the above equation shall hold one has to assume either that 0+resonance channel capture plays a role in the capture mechanism or that the E =6.74 MeV level indeed has a certain 2pl/2 admixture. Besides one may predict that

ir — of the higher-lying levels found there are at least some with J =1 and rather high 2pl/2 purity.

As was already shown by Mackh et al. |lj, a comparison of the 29Si and 30Si. level schemes can be instructive. Within the framework of a weak-coupling model one may speculate that the 29Si E =3.62 MeV level with predominantly. 1 f7/2 character will show up in the 30Si level scheme as a

-291-

2sl/2-lf7/2 (3 , 4~) doublet, and likewise the 29Si E. = 4.94 MeV 2p3/2-level as a 2sl/2-2p3/2 ( 1 , 2 ) doublet. It is now possible to forward two candidates for the 2sl/2-2p!/2 ( 0 , 1 ) doublet, viz. E = 8Л6 MeV (Г) and E =8.80 MeV (0~, Г , 2~). Their strengths (2J+1)S as found in the (d,p) work are in agreement with this assumption, as is the 'fact that the centres of gravity of the two doublets differ by 1.36 MeV, which is near the value of 1.44 MeV found'f or the spin-orbit splitting of p-states in 29Si.

-292-

RËFEBEKCES

I 1 I H. Mackh et al.., Nucl, Phys. A202 (1973) 497.

|2J Hughes and Schwartz, Brookhaven National Lab. Report BNL-325 (1958).

J3J K. Abrahams, Contribution to this conference.

\h\ К. Abrahams, Contribution to the Budapest conference on nuclear structure study with neutrons (1972) p. 42.

J5| R.D. Syir.es et al., Nucl. Phys. 1_67 (1971) 625.

Table : Spin assignments to some 3C'Si bound states

E X

(MeV)

E Y (keV)

I Y (Z)

Previous assignments E X

(MeV)

E Y (keV)

I Y (Z) 1*>

n , .ШВА а)

nlj j T b)

6.74

7.51

8.16

3865

3102

2446

30±3

23+2

7.3+0.6

J

]

1

2p3/2 2p3/2 2p3/2

Г (0, 1, 2_)~

(0, 1, 2, 3)" >

E X

(MeV)

This work

Conclusion

E X

(MeV) RC> ,.circ.pol. d) nlj J* e ) Conclusion

6.74

7.51

8. 16

-0.41±0.08

-0.36+0.08

+0.57±0.35

2p3/2 (3>0.95±0.06)

2p3/2 (8^0.91+0.06)

2pl/2 (g<0.29±0.23)

(I, 2)"

(1, 2)"

1~

Г (1, if

г

a) Ref. | 1 | .

b) t from ref. |5|, other two spin-parities from ref. jl|.

c) The possibility of the systematic error resulting from depolarization of the beam through H-scattering is not accounted for.

d) e-e* / 2/<e* / 2 +e| / 2>. e) Based upon R,l and ground-state transition of the E = 8.16 MeV level.

2x10

0

-2х103

6x10*

_ 4x10s

с с

2 о а

3

<3

2x10

frwkm^fc** ,*ч ƒ*=„ V5 , , • ^8>»°,? "»Л й

difference spectrum

1711 I <

+2Н

«ав1

vb-J^J*

Pst

sum spectrum

3000 3500 E^ in keV

2000 2500

Ю3

-103. 4x106

13865" 3»a difference spectrum '

3x105 aMoJ ' - ^ А <

38651 3539 (^Si)

"^W^JL A ft Л a

3365 и

4934 (29SI)

2x10° sum spectrum w *уц

Щ- ' The relevant part of the circular-polarization spectrum of the 29Si(n,Y) reaction. The sum and the difference of the two spectra relating to the two different neutron-spin directions are displayed.

-295-

+ 1.0г

+ 0.5-

R

- 0 . 5 -

0 3?=0

- - ot + 1

Fig. 2 i The polarization R as function of a, the fraction of the l component in the 30Si capture state.

-296-

> 4)

s 3

p = 0.35

30_.

Si Fig> 3 : Comparison of the stripping strengths (2J+l)Snof the (d,p)

reaction (black Unes) and reduced transition probabilities after

thermal-neutron capture (open lines) with respect to 1 (d,p) = 1

levels of 30Si only. On the left-hand side as reduction factor

for the (n,y) intensities the usual value 3 3 according to Weiss-

kopf's estimate is used, on the right-hand side E~ 1 - 2. The (n,y)

partial radiation widths have been normalized in such a way that

their largest value equals the corresponding (2J+1)S value.

Correlation coefficients are given in both cases for all

1 (d,p) = I levels.

l „ (2J+1)Sn Ex(MeV) J™ Ex(MeV) ] " (d,p) (d.p)

V + C=8.47 /2_ C = 10.61 0+, 1 .+ H+

6.38 2P1/a 14"

4.94 2 P % z/l

8.80 (о'ягт

8.16 2P!4 1~

7.51 2 P % (1.2Г

6.74 2P3/2 r 6.51 1 f7/2 4"

(1) 0.13

0.34

1 0.86

1 0.55 3 2.30

/ 3.62 lf_% %_/

"~"-^u49 1f££ ЗЛ 3 1.60

29Si 30Si F i -8 - 4 : Comparison of part ial level schemes of 29Si and 3 0Si. The 1 (d,p> and (2J+DS

values are from ref. [ ] | , the 2p3/2 and 2pl/2 assignments to 30Si levels are from

the present work, as is the spin-parity of the E = 8.16 MeV 30Si level.

-298-

CIRCULAR POLARIZATION AND GAMMA-GAMMA ANGULAR CORRELATION MEASUREMENTS IN THE 39К(п,у)ц0К REACTION

A.M.F. Op den Kamp.

FOM-RCN Nuclear Structure Group Reactor Centrum Nederland, the Netherlands

Abstract:

Circular polarization measurements of the y-radiation from polarized neutron capture combined with y~Y angular correlation measurements in the 39K(n,y)'t0K reaction lead to spin assignments J = 3 , 2 , 2 and 1 to the E x = 0.03, 0.80, 2.05 and 2.42 MeV states in t,0K, respective­ly. Spin restrictions for the states at E = 2.10, 3.44 and 4.25 MeV have also been made. Multipole mixing ratios for the y-rays which de-excite these levels have been determined.

1. Introduction

The t+0K nucleus has been investigated extensively in the last few years. From a study of the 39K(n,y) reaction, precise values ft>r the excitation energies, branching ratios and the reaction Q value have been determined by Johnson and Kennett ) and Op den Kamp and Spits ) . Spin assignments to a number of excited states in ^°K, branching ratios and multipole mixing ratios for the y-decay of these states follow from the 40Ar(p,ny) reaction studiec

3 4 by Twin e£ _al. ) and Wechsung ejt al. ). The latter also report the mean lives of 13 excited states of 40К, which they determined from a study of the 37Cl(a,ny) reaction. Spins have been deduced * ) from circular polarization measurements of primary y-rays emitted after capture of polarized thermal neutrons. The

7 coherent interference of the spin components in the capture state ) makes this method not very useful for other than even-even target nuclei.

Angular correlation measurements are not affected by this interference effect, but a correlation consists of an incoherent mixture of the two correlations corresponding to the two possible capture states. These measurements therefore generally do not lead to unique spins or y-ray mixing ratios.

This article shows that a combination of both types of (n,y) experiments can be applied for the determination of spins and y-ray mixing ratios. From these experiments also follows the population ratio of the two spin components in the capture state for primary y-ray transitions.

2. Theoretical

The circular polarization of y-rays emitted after capture of polarized thermal neutrons is given by P = RP cos9, where P is Che neutron polarization and 9 (chosen as 0 or 180 ) is the angle between the neucron polarization direction and the direction of the detected y-rays; R is a function of the spin of the target nucleus (J ) , the spin of the final state (J.), the multipole mixing ratio (5) for the primary y-ray emitted and the coherent interference (л) between the two spin components J— = J + 1/2,in the cap-

8 c . ture state. The quantity л is defined ) by the relation

<J J L I J+><J+|sl J > f' ' с с' ' t

n = - > < J , L J ><J s J > f' ' с с1 ' t

where L i s the y-ray mul t ipo l t - r i ty and s the spin of the incoming neutron. +

If a i s defined as the cont r ibu t ion of the capture s t a t e J to the t o t a l

i n t e n s i t y I of a primary t r a n s i t i o n , the r e l a t i o n between a and n is given

by

(J + On 2

a = J t + ( J t +1)л2

The expression for R can then be wr i t t en as

R = (1 - a)R(J~) + /a (1-е)' R(J±) + a R(J*) , с с c

- + + 9 where the functions R(J ) , R(J—) and R(J ) , which can be expressed ) in terms of W and Z coe f f i c i en t s , s t i l l are functions, of the mixing r a t i o 6.

9 10 The coe f f i c i en t s can be found in ex i s t ing tables ' ) .

-300-

The polarization P can be determined experimentally by measuring the + — + — + —

ratio (I - I )/(I + I ) , where I and I are the intensities of the emitted y-rays corresponding to the two opposite neutron polarization directions. It is generally assumed ) that primary transitions to odd-parity levels are of pure El character. The El assumption has been tested in previous work ). Under this assumption, R is only a function of a and Jf. An example of the theoretical dependence of R on a for different spins of the final state is given in fig. 4. As can be seen, the determination of R does not lead to a unique spin assignment. The angular correlation of y-rays emitted after capture of thermal neutrons is given by

W(0) = aW(J+,9) + (1 - a)W(J~,e) •+* —

where W(J ,6) and W(J ,6) are the angular correlations of the y~rays C + c -emitted from the J and J capture states and Э is the angle between the с с - 2 two cascading y~rays. The function W(J ,6) is given bv ) W(J ,6) =

С ' С 1 + A-P^(cos6) + A,P (cosB). Here P„ and P, are Legendre polynomials. The El assumption e n t a i l s A, = 0; A i s s t i l l a function of the mult ipole mixing r a t i o of the secondary y-ray involved. The F c o e f f i c i e n t s , used in

12 13 the expression for A_, can be found i n ex i s t ing tab les ' ) , The fact tha t A, = 0 means tha t i t i s only necessary to measure a t two angles (0 and 90 ) . On the other hand, with a measurement a t more than two angles , one can t e s t again the El assumption. This procedure has been followed in the experiments described below.

3. Experimental

The experiments have been performed a t the Dutch High Flux Reactor a t Pct;:en, the Nether lands.

3^J^_T^e_x;ïaY_circular_oglarization_exDeriment

The neutrons were polar ized with a magnetic mirror system. This se t -up

has been described extens ively by Stecher-Rasmussen e t a l . ) . The neutron

flux densi ty a t the t a r g e t p o s i t i o n was about 3xl07 cm" 2 s - 1 . The degree

of p o l a r i z a t i o n was (90 +_ 5)%; the p o l a r i z a t i o n d i r ec t ion was reversed every

10 seconds.

-301-

It was necessary to use a densily packed target because (i) the thermal-

neutron capture cross section is not high (2 b), (ii) the intensities of

the primary y-rays studied are less than 10% (see fig. I), (iii) the

polarization detection efficiency is not more than 3% jref. )| and (iv)

the dimensions of the target are limited by the experimental set-up.

Therefore, 24 g of compressed potassium fluoride was chosen as target

material. The density of the KF was 857* of the theoretically possible

value. To avoid depolarization of the neutron beam by scattering on H

atoms, the hygroscopic KF target was placed in a thin (0.6 mm) quartz

holder which was filled with dry argon gas.

Two detection units, each consisting of a circular y-ray polarimeter,

a 40 cm3 Ge(Li) detector and a 4096 channel pulse-height analyser were

placed opposite to each other in a direction perpendicular to that of

the incoming neutron beam. Asymmetries in the experimental set-up should

lead to different values for the y-ray polarization measured with the

two detection units. It was found, however, that the error introduced

by these assymetries is negligible compared to the statistical error in

the experimental R values. The memory of each analyser was divided into

two groups corresponding to the two neutron polarization directions.

Each 12 h the collected data were read out on a punch-tape. The spectra

thus obtained were transformed to a reference spectrum. After this trans­

formation all spectra were summed for each detection unit, and for each

neutron polarization direction. The total measuring time was 37 days.

The measurements were calibrated with the intense primary 5.42 MeV

(capture state -*- 3.22 MeV) transition in sulphur. This transition has

pure El character ). The calibration measurements were performed at the

beginning, half-way and at the end of the experiment.

3j^_The_;£-;£_angular correlation^exgeriinent

A filtering system, consisting of one bismuth and four quartz single

crystals was used to decrease the fast-neutron component in the beam.

The experimental set-up of this filtering system has been described by 14

Van Middelkoop and Spilling ). The thermal-neutron flux at the target

position was 107 cm~2s" .

-302-

As a target 4 g К2С0з was used. The target was encapsulated in a thin-walled cylindrical teflon tube with an inner diameter of 1 cm centered on the neutron, beam.

The detection unit consisted of a 12 cm x 12 cm Nal crystal and a 60 cm3 Ge(Li) detector. The over-all resolution of the Ge(Li) detector was 7 keV at E =1.24 MeV over the whole measuring time of 25 days.

Y The NaT detector could rotate in a plane perpendicular to the neutron beam. The solid angles for the two detectors were 1% and 0.7% for the Ge(Li) and Nal detector, respectively.

A fast timing system of two constant-fraction timers and a time-to-aaplitude converter was used. The FWHM of the time spectrum was 25 ns for the full range of 0-8 MeV. The contribution of accidental coincidences in the time spectrum was 25%. Gates were placed on the Ge(Li) and Nal spectra which covered energy regions of 1.0 - 2.2 MeV and 4 - 7 MeV, respectively. With a digital discriminator15) following one of the ADC's, three windows were placed (in the 4 - 7 MeV region) on the Nal pulse-height spectrum. Gate 1 (see insert of fig. 3) could be used for (i) back­ground correction and (ii) correction for the accidental coincidences. The contribution of the accidental coincidences after the discriminator was less than 5%; the counting rate in the memory was 10 s_1.

The coincidence spectra were measured at five angles, 0 , 30 , 45 , 60 and 90 . The measuring time at each angle was 2 h corrected for dead time in the ADC. All spectra were recorded on magnetic tape, while additional information such as the neutron flux, the number of coincidences and the counting rate in each detector, was recorded separately on a typewriter. The measuring cycle of five angles was repeated many times.

4. Results

Fig. 1 shows a par t i a l decay scheme of **°К.. Only the transi t ions which have been studied in the present investigation are given. For a complete decay scheme see e.g. ref. ) . The branching rat ios for the s tates at 2.05, 2.07 and 2.10 MeV are from the present investigations. They are given, with their error, in table 1. Branching rat ios for the other s ta tes and the re la t ive in tensi t ies of the primary y-ray transit ions are from

2 ref. ) , because not a l l decaying y^ays have been observed in the present investigation.

-303-

The measured polarization spectrum with the best resolution is given in fig. 2. From the two spectra, corresponding to the two neutron polarization directions, the sum and difference spectra are given here. The background has not been subtracted. The measured effects appear clearly in the difference spectrum. The spectrum obtained from the other detection unit is essentially the same.

The relative polarization detection efficiency of the polarimeter as a function of energy is given in ref. ), while from the sulphur calibration measurements the absolute efficiency at E =5.42 MeV was determined as Q.0242+Q.0008, Peak areas in the two spectra, which correspond to the two neutron polarization directions, were calculated with the same peak and background regions. The experimental K. values for the primary transi­tions in **°К, given in table 1, are the weighted means of the values ob­tained from the two polarimeters.

The coincidence spectra measured at 90 for gate 2 and 3 are given in fig. 3. The insert shows the gate setting on the Nal pulse-height spectrum. The spectra are corrected for background and accidental coincidences. The coincidence spectrum obtained from gate 1, which covers an energy region from 6.2 - 6.7 MeV, could be used for these corrections, because the reac-tion value is 7.80 MeV Jref. )J and the primary transitions in this gate thus will feed the levels at 0.03 and 0.80 MeV (the ground state and the E =0.89 and 1.64 MeV levels are not excited), x Gates 2 and 3 cover the energy range from 5.2 to 6.1 MeV. The energies of the primary y-rays in these gates correspond to levels below 2.6 MeV. The spectra of both gates can be added because other than primary transitions, which also feed the levels below 2.6 MeV, can not enter in these gates. Nevertheless, two gates were used as a check*, because the E = 1.62 MeV transition (2.42 •> 0.80 MeV) may be observed in the coincidence spectrum of gate 3 only. As can be seen from fig. 3, the peak at 1.62 MeV complete­ly disappears in the spectrum of gate 2 after the corrections mentioned above. The peaks were analysed by a least-squares fitting of a slightly asymmetric response function. This was necessary in order to resolve the three doublets in the 2.01 - 2.08 MeV region (see fig. 3). The asymmetry and the FWHM as a function of energy were obtained from the peaks at E = 1.25, 1.30 and 1.62 MeV,

-304-

The calculated A^ coefficients for the measured angular correlations are given in table 1. For all correlations the Ац coefficient was less than the error in Ац..

A least-squares program was used to calculate the population ratio of the two capture states and the multipole mixing ratios 6 for all secondary y-rays involved; the sign convention is that of Rose and Brink ). The results from these calculations are given in table 2 together with the deduced spins for the intermediate states. All results are compared to

3 4 those of Twin _et L. ) and Wechsung £t al_. ). In fig. 4 the theoretical R values as a function of a for different inter­

mediate state spins are compared with the R(a) values obtained from the

present investigation.

5. Discussion

The El assumption l i m i t s the spins for the odd-par i ty l e v e l s , for which

a primary y~*a-y t r a n s i t i o n has been observed, to J = (0-3) .

The E = .0*03 MeV leve l This l e v e l is s t rongly exci ted in the (d,p) x • ] 7

reac t ion via a 1 = 3 t r a n s f e r ) , which l i m i t s the poss ib le spins

to J ~ (2-5) . The El assumption for primary capture r a d i a t i o n then

gives a fu r the r l i m i t a t i o n to J = (2,3) . The measured R value ( t a b l e 1)

for the t r a n s i t i o n С -*• 0 .03 MeV i s in agreement with the t h e o r e t i c a l ТГ —

value of -0.50 for J ~ 3 . Independently, one can say that the measured 18 lifetime ) excludes quadrupole character for the 0.03 •*• 0 MeV transi-1T — ÏÏ —

tion, which also leads to J = 3 . Conclusion: J = 3 .

The S = 0.80 MeV level Again, the value 1 (d,p) = 3 jref. ) | , combined

with the El assumption, limits the possibilities to J * (2,3) * The 7Г ~ TT ^

measured R value of +0.63 +_ 0.06 excludes J = 3 . Conclusion: J = 2 . The E =2.05 MeV level This level is excited by ln(d,p) = 1 transfer ) and hence J11 = (0-3) . The level decays 29% to the ground state (4 ) , 32% to the 0,03 MeV(3~) state and 39% to the 0.80 MeV(2~) state, which, in

4 . . combination with the measured lifetime ) limits the possibilities to JT = 2~ (with either a = 0.02 +_ 0.01 or 0.98 _+ 0.01). The large value for a is excluded by the result of the С -»• 2.05 -+• 0 MeV angular correlation measurement (both transitions unmixed). The angular correlation measure­ment further yields the mixing ratios of the 2.05 -»- 0.03 and 2.05 -> 0.80 3 4 MeV transitions, in agreement with previous results * )

- J U D -

The E . ° Z.07 MeV level The (d,p> work has yielded 1 = 1 | r e f . 1 7 ) l , which r e s t r i c t s the poss ib le spins to J77 = (0-3) . The decav of th i s l e v e l , 37% to the ground s t a t e (4~) , 55% to the 0.03 MeV(3~) s t a t e and 8% to the 0.80 MeV(2 ) s t a t e , combined with the measured l i fet ime ) , gives a fur ther r e s t r i c t i o n to J = (2,3) . The r e su l t s from the 4 0Ar(p,ny) r e a c t i o n , s tudied by Twin a l . ) , lead to J = 3 . The mixing r a t i o s of the secondary y-ray t r a n s i t i o n s to the ground s t a t e and 0.03 MeV s t a t e follow from the present angular cor re la t ion experiment. The r e s u l t s a re in agreement with those reported by Twin et a l . ) and Wechsung ^ t a l . ) .

The E„ = 2. 10 MeV leve l A 1 = 1 value for th i s level follows from the X _ n

(d,p) work ) , thus the pa r i t y i s negat ive . The argument for a J = 1 3

assignment given by Twin e t a l . ) , i s model-dependent; i t is based on the assumption t h a t t h i s l eve l belongs to the p , , „ d \ quadruplet . From the present experiment, only J = 0 could be excluded, because the С -*• 2. 10 -У 0.80 MeV angular co r r e l a t i on i s an i so t rop ic . Conclusion: J = (1-3) .

The E = 2290 keV level From the two leve ls at E = 2290 and 2291 x x 2

keV, only the f i r s t one is exci ted by a primary y-ray t r ans i t i on ) . The present experiment confirms th i s i n t e r p r e t a t i o n because in coincidence with the primary t r a n s i t i o n only the 1.49 MeV y-ray (2290 •+• 800 keV) has been observed ( f i g . 3 ) , whereas the 1.40 MeV y-ray , which must be i n t e r p r e t -

2 3 ed as the 2291 -»- 892 keV t r a n s i t i o n ' ) has not been observed, A J = 1 3

assignment to the 2290 keV level i s made by Twin et a l . ) .

The E = 2 . 4 2 MeV leve l The decay of th i s level proceeds 7% to the ground s t a t e (4~), 17% to the 0.03 MeV(3~) s t a t e , 73% to the 0.80 MeV(2~) s t a t e

+ 2 and 3% to the 1.96 MeV(2 ) s t a t e ) . From these branching r a t i o s , the 1 = 1 value ) and the measured l i f e t ime ) for the 2.42 MeV l e v e l , a r e s t r i c t i o n to J77 = ( 2 , 3 ) " can be made. The measured R value of -0.00 + 0.03 c lear ly excludes j " = 3 . The mult ipole mixing r a t i o for the 1.62 MeV y-ray t ran­s i t i o n to the 0.80 MeV level follows from the angular cor re la t ion experiment. The two poss ib le values ( t ab le 2) are in agreement with those reported

3 by Twin et_ al_. ) . Independently of the given branching r a t i o s and the measured l i f e t i m e , the present experiment also excludes J - (0 ,1 ,3) . Conclusion: J *= 2 .

-306-

The E = 3.44 and 4.25 MeV levels No angular correlations have been x

measured for these levels. The circular polarization results lead to

J = (1,2) and Jïï = (1,2)" (1 = 1, jref.I7)|) for the 3.44 and 4.25

MeV states, respectively.

-SOy-

R e f e r e n c e ^

1) L.V. J o h n s o n and T . J . K e n n e t t , Can. J . Phys . 4jS (1970) 1109.

2) A.M.F. Op den Kamp and A.M.J . S p i t s , Nuc l . Phys . A18Q (1972) 569.

3) P . J . Twin, W.C. Olsen and D.M. Sheppard , N u c l . P h y s . A143 (1970) 4«1.

4) R. Wechsung, W. S t r a s s h e i m and R. B a s s , Nucl . Phys . A170 (1971) 557.

5) F . S t eche r -Rasmussen , K. Abrahams and J . Kopecky, N u c l . Phys . A181

(1972) 225.

6) J . Kopecky, K. Abrahams and F. S t eche r -Rasmussen , Nuc l . P h y s . A188

(1972) 535 .

7) A.M.F. Op den Kamp £ t д 1 . , P h y s . L e t t . 391S (1972) 204.

8) J . Honzatko and J . K a j f o s z , Phys . L e t t . 38B (1972) 499.

9) A . J . F e r g u s o n , Angular c o r r e l a t i o n methods i n gamma-ray s p e c t r o s c o p y

( N o r t h - H o l l a n d , Amsterdam, 1965).

10) W.T.J . Sha rp , J .M. Kennedy, B . J . S e a r s and M.G. Hoyle , Tab les of

c o e f f i c i e n t s f o r a n g u l a r d i s t r i b u t i o n a n a l y s i s , Chalk R i v e r Report AECL-97.

11) G.A. Bartholomews Annual Rev. of Nuc l . S c i . 11 (1961) 259;

H.T. Motz , Annual Rev. of Nuc l . S c i . 20 (1970, 1,

12) K. S i egbahn , A l p h a - , B e t a - and Gamma-ray s p e c t r o s c o p y (Nor th -Hol l and ,

Amsterdam, 1965, v o l . 2 ) .

13) A.H. Waps t r a , G . J . Ni jgh and R. van L i e s h o u t , Nuc lea r Spec t roscopy

t a b l e s ( N o r t h - H o l l a n d , Amsterdam, 1959).

14) G. van Middelkoop and P . S p i l l i n g , Nuc l . Phys . _П (1965) 1.

15) P . S p i l l i n g , H. Gruppe laa r and P . C . van den Berg , I n t . Symp.

on N u c l . E l e c t r o n i c s , V e r s a i l l e s (1968) P a r t I I , Cont r . 140.

16) H . J . Rose and D.M. B r i n k , Revs. Mod. Phys . 39_ (1967) 306.

17) H.A. Enge , E . J . I r w i n and D.H. Weaner, Phys . Rev. _П5_ (1959) 949.

18) J . F . . B o u l t i e r , W.V. Prest iVich and B. Arad , Can. J . Phys .

47 (1969) 591.

-308

Table 1

Results from the present investigation

С •+ E . -+ E , l f

R ( C •+ Е £ ) В г ( % ) а ) А Ь ) с) а mt. d )

(MeV) ($L •+ E f )

С + 0 - 0 3 -+ 0 - 0 . 5 0 + 0 . 0 3 1 _

С + 0 . 8 0 -+ 0 . 0 3 + 0 . 6 3 + 0 . 0 6 0 .

0 ,

, 0 9 + 0 . 0 4

, 9 1 + 0 . 0 4

с

С + 2 . 0 5 + 0

-> 0 . 0 3

-+ 0 . 8 0

+ 0 . 0 8 + 0 . 0 3 29+2

32±2

39+2

- 0 . 0 9 + 0 . 0 2

+ 0 . 0 8 + 0 . 0 2

- 0 . 2 1 1 0 . 0 1

0 . , 0 2 ± 0 . 0 1 d

С - * 2 . 0 7 -* 0

-+ 0 . 0 3

+ 0 . 8 0

- 0 . 4 6 + 0 . 0 5 37±2

55+2

8+1

+ 0 . 0 7 ± 0 . 0 6

- 0 . 2 0 ± 0 . 0 2

1

С + 2 . 10 -*- о.оз + 0 . 8 0

- 0 . 4 1 + 0 . 0 4 72+1

28+1

+ 0 . 0 5 ± 0 . 0 2

- 0 . 1 3 1 0 . 0 2

d

с ~> глэ + 0 . 7 0 + 0 . 0 6

С •+ 2 . 4 2 + 0 . 8 0 -о.оо+о.оз + 0 . 1 9 ± 0 . 0 2 0. . 9 6 + 0 . 0 2 d

С -> 3 . 4 4 + 0 . 9 8 ± 0 . 0 9

С •+ 4 . 2 5 + 0 . 4 9 + 0 . 1 0

a) Branching ratio in percent. b) Corrected for solid angle attenuation

+ c) The fraction of the 2 component in the capture state. d) The interference in the capture state; d and с denote destructive and

constructive interference, respectively.

- 3 0 9 -

ТаЫе 2

Deduced s p i n s fo r l e v e l s i n **°К and t h e m u l t i p o l e mixiag r a t i o

fo r t h e i r 7 - r a y decay

С •* E. -»- E-1 f fi(E. * E f ) J17 б J ï ï <5

(MeV) СЕ.) r e f . 3 ) r e f . 4 )

С -*• 0 . 0 3 з~ С -> 0 . 8 0 2~

С -" 2 . 05 •+ 0 Е2 г Е2 г Е2

-+• о . о з - 0 . 0 7 ± 0 . 0 4 - O . 0 1 t 0 . 0 2 - 0 . 0 5 + 0 . 0 3

9 .0+2.0 { 9±2

- 0 . 0 5 + 0 . 0 3

9 .0+2.0

•* 0 .80 - 0 . 1 0 ± 0 . 0 4

-1 -7±0 .3

" -0 .13±0 .09 - 0 . 1 0 ± 0 . 0 5

С ->• 2 .07 ->- 0 - 0 - 0 1 ± 0 . 10 { + 12±4

3~ +0.О7±0.]0 з" +0.0710.10

-*• о . о з - 0 . 2 ± 0 . 2 { - 0 . 8 ± 0 . 3

- 0 . 2 7 + 0 . 1 0 - 0 . 2 5 + 0 . 1 5

С -*• 2 .10 -+• 0 . 0 3 ( 1 - 3 ) " ( 1 - 3 ) "

С ->• 2 .29 1

С •+ 2 .42 •* 0 .80 - 0 . 0 6 ± 0 . 0 6 {

- 1 . 9 ± 0 . 3

г - 0 . 0 5 + 0 . 1 0 2 - 0 . 0 6 ± 0 . 0 6 {

- 1 . 9 ± 0 . 3 - 2 . 0 + 0 . 6

- 0 . 3 5 + 0 . 0 5 з" С ^ 3 .44 ( 1 , 2 )

С •* 4 . 2 5 ( 1 , 2 ) "

-310-

7.80

4.25

39 K+n J * In

f,2+<fi,p)

7.3 2.7 7.1 3.0 7.0 4.1 9.8 5.1 4.5

&2>

3.44 JL2

2.42

73 2.290 -rr~ 3555 2.10 (1-3f

2.07 72 28

37558 2.05

1.96 2932 39

1.64

0.80 " ' •

0.03 100

100

40, К

Fig. 1 : Partial -y-ray decay scheme of 40K. Only those transitions have been given which are also studied in the present investigation. The intensities of the primary y-rays (per 100 neutron captures) are taken from ref. 2 ) . The branching ratios (in %) of the bound levels at E = 2.05, 2.07 and 2.10 MeV are from the present investigation; those of the other levels are taken from ref. ).

. 17ч The 1 values are from ref. ). n

8.

Fig- 2 : Polarization spectrum (sum and difference spectra) of y-rays emitted after capture of polarized thermal

neutrons in K. In background regions in the sum spectrum, the mean of each four consecutive points is

plotted; in the difference spectrum all points are plotted. Full-energy peaks are labelled with the y-ray

energy in keVr single- and double-escape peaks with the primed and double primed y_ray energy, respectively.

12 ""' Ï3

1*"ft*V«4Btf4l»p»»e^*rt

'го 2.1 -Et inMeV

Fig. 3 : Coincidence spectra at 90 for gates 2 and 3. The insert shows the gate setting.

Fig. 4 : The theoretical R values for different spins of the

final state as a function of the 2 fraction in the

capture state. The measured (R,a) values are given as

rectangles

-314-

0Ы A SYSTEM OF MODERATING NEUTRON MIRRORS TO PRODUCE AN INTENSE BEAM OF POIARÏZED THERMAL NEUTRONS

F. Stecher-Rasmussen

FOM-RCN Nuclear Structure Group, Reactor Centrum Nedsrlsnd

Petten, the Netherlands.

1. INTRODUCTION.

Polarized thermal neutrons are at the High Elux Reactor in Petten

(H.F.R.) used in two experiments:

i) measurement of the circular polarization of y-radiation after capture

of polarized neutrons by unpolarized target nuclei;

ii) measurement of the directional intensity asymmetries of Y~radiation

after capture of polarized neutrons by polarized target nuclei.

Both measurements imply an experimental determination of a small relative

difference in the intensity of the -y-radiation (of the order of a few per

cent). Therefore an intense polarized beam is needed, which should be free

from fast neutrons and Y~ra<iiation, but should not necessarily be mono­

chromatic.

At present the neutrons for the circular polarization experiment are

polarized by transmission through a system of magnetized focussing Co (50%)

Fe(50%) mirrors j]j. With this system a flux of 3*]07 n/cm2sec is obtained

at the target position.

In order to compete in the coming years with work performed at

centres, where the available neutron flux is much higher than that of the

H.F.R., it has been decided to continue the development of focussing mag­

netic mirror systems. With the system described in the following it is

possible to increase the flux of polarized thermal by an order of magni­

tude with respect to the present flux.

- 3 1 5 -

2. DESCRIPTION OF THE SYSTEM.

In fig. 1 the system is sketched. The main feature of this system is

the use of the thermal column of the HFR. as a neutron source instead of

one of the beam channels. This gives a large increase of the solid angle

under which the neutron source is viewed from the target position.

The system consists of four parts;

1) a focussing precollimator of 85 moderating graphite mirrors, to be des­

cribed below;

2) a focussing collimator of 85 Ni mirrors, which close the system for

direct transmission;

3) a polarizing system of 85 magnetized Co-Fe (50%, 50%) mirrors, and

4) a focussing collimator absorbing the neutrons, which are not reflected

in 3) and therefore unpolarized.

3. THE PRECOLLIMATOR.

According to Rauch |2| it is possible to obtain an additional in­

tensity gain from a system of neutron mirrors if the mirror material acts

as a moderator too. Such a system will combine the moderating action of

mirror material with the focussing action of the present mirror system.

Only those neutrons which reach the present mirror system under an angle

permitting total reflection will be transmitted through this system.

Almost the whole rest of the neutrons is absorbed in the mirror material

and lost. If, however, the first part of the mirror system would be made

as a Soller collimator, with moderating mirrors the otherwise absorbed

neutrons after a number of reflections will have a chance to be trans-

mi t ted.

At the exit of the moderating part of the mirror system the trans­

mitted neutron intensity results from the following processes:

i) neutrons scattered from the moderating material, and directly leaving

the Soller collimator through a channel;

2) neutrons transmitted through the system by total reflection;

3) neutrons scattered within the moderating material and reaching the

reflecting surface with an angle of incidence smaller than the cri­

tical angle for total reflection;

4) neutrons diffusing through the moderator.

The increase in neutron flux due to the moderation in the mirror material

is a function of i) scattering and absorption cross section; ii) tempera­

ture of moderator.

-.316-

For a system of 60 cm long graphite mirrors the gain caused by the moderating action will be about a factor of three at room temperature.

4. AN ESTIMATE OF THE FLUX DENSITY.

Unmagnetized nickel has about the same scattering amplitude as mag­netized permendur (50% Fe, 50% Co); if therefore the geometrical parame­ters of system 2 and 3 are chosen equal to those of the present mirror system, the final flux density Ф is simply related to the flux density of the present system Ф0 Ъу:

Ф/Ф0 = (N/N0)>:(B/B0)xFxA = ]8

N/NQ = 3 is the ratio between the number of mirrors in the new sys­tem and that of the present system. B/BQ = 4 is the ratio of the height of the mirrors in the new sys­tem and in the present system. F = 0.5 is the ratio between the flux in the thermal column and the flux in a beam channel. A = 3 is the boosting factor introduced by the precollimator.

5. BACKGROUND OF FAST NEUTRONS AND y-RADIATION.

Due to the moderation of the fast neutrons in the graphite precol­limator the flux of fast neutrons transmitted through the entire system will be reduced. This is very important since the lifetime of the Ge(Li) detectors is determined by the background of fast neutrons. The ^-background, due to neutrons captured in the mirrors is mainly coming from the uncollimated neutrons, hitting the first part of the mirror sys­tem. The low capture cross section of graphite compared with that of nic­kel will result in a decrease in this gamma background source.

6. CONCLUSION.

With a focussing .system of neutron mirrors installed at the H.F.R. in Petten-it is estimated that a flux of polarized thermal neutrons of 5*10° n/cm2.sec can be obtained. The dimensions of the polarized neutron beam allow the beam to be used by two experiments simultaneously,-

-317-

REFEREHCES.

j1I F. Stecher-Rasmussen, K, Abrahams and J. Kopecky,

Nucl. Phys. A181 (1972), 225.

|2] Friedmann and Rauch, Nucl. Instr. Meth. 86_ (1970), 55.

Fig. J; Meutron polarizing mirror system at the thermal column of the H.F.R,

-319-

A review of nuclear orientation techniques applied in experiments

with low-energy neutrons.

H. Postma

Natuurkundig Laboratorium, Rijks-universiteit Groningen,

the Netherlands.

I. Introduction

One of the main tasks for experimental nuclear physicists is to obtain

information about quantum numbers of nuclear levels; the most important ones

being the spin and parity. In this talk I will concentrate on the determi­

nation of spins of levels encounted in reactions with low-energy neutrons.

An important group of methods for determining spins depends on the measure­

ment of angular correlations of successive radiations. These methods are

fairly straightforward and fundamental if the properties of the radiation

are well understood, as for instance in gamma-gamma angular correlations.

By measuring the first gamma radiation in a fixed direction the sublevels

of the intermediate state are unequally populated. The subsequent radiation

will show an anisotropic angular distribution with respect to the detection

direction of the first transition. A disadvantage is that two gamma detectors

in coincidence are necessary. In addition fairly small solid angles must be

used; thus the counting rate will be low. Quite often it is not possible to

find suitable cascades; one of the transitions might be too weak and often

too many parameters are unknown. Thus the number of spins assigned with the

aid of Y~Y angular correlations is often rather limited.

In nuclear reactions sublevels are unequally populated if the projectile

brings in orbital momentum. The following gamma transitions show anisotropic

angular correlations. These have been very useful for assigning spins. How­

ever, this technique cannot be used in reactions with low-energy neutrons

because of their s-wave nature. An interesting possibility to mention here

is the capture of polarized neutrons. The following gamma radiation has

isotropic spatial distribution. However this radiation is circularly polarized

and can be used for assigning spins to intermediate levels. This technique

has been extensively applied in Petten. It will be discussed during this

meeting by other participants. A problem is that spin assignments on the basis

-320-

of circular polarization alone is only possible if the capture is related to one spin state.

All the above-mentioned methods for assigning spins to levels in (n,f) work have limited applicability. However, some other new methods have been developed which have shown to be useful. One of them depends on nuclear-orientation techniques. Angular correlation of gamma-transitions after neutron capture by oriented nuclei have been used in a series of experiments at the High Flux Reactor in Petten to assign spin to intermediate levels. It should be realized that it is of great value to use as many methods to assign spins to intermediate levels in (n.y) work because of the often very complicated decay schemes.

Nuclear orientation methods are based on the use of hyperfine coupling. Already the first successful nuclear orientation experiments, now more than 2 decades ago, have shown the great potential of such measurements. However, nuclear orientation depends on complicated techniques, such as for instance for obtaining extremely low temperatures. In addition the number of isotopes, which were possible candidates for nuclear orientation was extremely limited. During the past 20 years it became possible to orient many more isotopes, thus making nuclear orientation a much more general tool. It remained a rather difficult technique, but it certainly offers a great challenge because of the interaction between widely different fields in physics.

In this talk I will consider some applications of nuclear orientation in experiments with low-energy neutrons. They concern the emission of neutron capture gamma rays, the determination of spins of neutron resonances and some phenomena in fission.

2, Theoretical description of nuclear orientation.

Before discussing some of the techniques for obtaining ensembles of oriented nuclei it is of value to consider first the mathematical description of nuclear orientation. For simplicity it will be assumed that we are dealing with systems with rotational symmetry. The axis of rotational symmetry will be taken as the quantization axis; thus the probabilities a for finding nuclei with magnetic quantum numbers I em can be defined. Since Га =1 only 21 inde­pendent parameters for describing the orientation exist; I being the spin of the nuclei.

In the derivation of angular distribution formulae of radiation emitted from oriented nuclei quantities of the form

£ ( - ) 1 _ Ш C(IIv; m-m)a m m

occur. It is therefore suitable to define nuclear orientation parameters,

- 3 2 1 -

vhich are p ropor t iona l to these q u a n t i t i e s . The simplest o r i en ta t ion parameter

i s : fj = Zma / I . This i s the so -ca l l ed polarisation parameter, s ince i t

d i s t i n g u i s h e s between the two d i r e c t i o n s along the quant iza t ion a x i s . The

following parameter , which we a l so need qui te o f ten , contains the second moraent

Im2am . Since t h i s has a value l/<=l(l+l) for unoriented nucle i i t i s reaonable

to def ine the following o r i e n t a t i o n parameter:

f2 = {I m2am - V a l C I + m / I 2 . m

This is known as the alignment parameter. It does not make a difference for

the two directions along the quantisation axis.

It depends on the type of experiment which of the two orientation

parameters are important. Let us consider as an example the emission of gamma

radiation of pure parity. The emission pattern is basically mirror

symmetric with respect to a plane perpendicular to the nuclear spin. Thus the

angular distribution of gamma radiation from oriented nuclei does not make a

difference between the two directions along the quantization axis; consequently

the angular distribution function- contains f_ and other even orientation

parameters, but no odd parameters. Another well-known case is the emission of

j3-particles from oriented nuclei. As a.consequence of non-conservation in

weak interactions the angular distribution is asymmetric; thus the distribution

function contains the polarization parameter f..

3. Methods to achieve^ nuclear orientation

Since the first successful attempts to produce oriented nuclei very many

methods to achieve this goal have been developed. Some of the schemes are very

ingenious. It is not the purpose of this talk to review all these methods. It

suffices for the moment to remark that there are two main classes:

a) static metliöds in which the nuclei are in thermal equilibrium with their

direct surroundings. In these methods the unequal population of hyper~

fine levels at extremely low temperatures are used,

b) dynamic methods in which the populations of the hyperfine levels at a

given temperature are changed by "pumping" part of the nuclei from one

to another sublevel.

We will only deal with the first type of methods. Dynamic methods have been

applied in only a few neutron physics experiments. It is also outside the

scope of my experience to talk about dynamic polarization techniques. In all

our nuclear orientation experiments we have been using static methods.

The most straightforward and in principe simplest method is the direct

interaction of nuclear magnetic dipole moment, p, with an external magnetic

field, H, produced in the laboratory. The splitting of the magnetic sublevels,

-322-

given by:

E m = muH/I Ml

is extremely small even in the strongest magnetic field, which can be

generated now—a—days. Thus extremely low temperatures are necessary to obtain

considerably different populations a of sublevels, which are proportional to

the Boltzman factors:

exp(-Em/kT) = exp(tnuH/IkT).

With u/I is 1 n.m. H/T should be of the order of 107G/K. Assuming an external

magnetic field of 50 kG (e.g. generated by a superconducting solenoid) it is

necessary to cool the sample to a temperature of about 0.01 Kelvin. It depends

very much on the kind of experiment whether we can use this so-called

"brute-force" technique or not. In experiments which depend on polarization

and in which rather small effects can be tolerated it is a useful technique.

Alignment experiments cannot be done with brute-force oriented nuclei because

of the smallness of f?.

With only the brute-force method available nuclear orientation would have

been a very exotic technique. Fortunately nature is helping quite a bit with

the very large internal magnetic fields existing inside paramagnetic ions or

produced at nuclei implanted inside ferromagnetic materials. Such fields are

often of the order of 10 G. In the first nuclear orientation experiments

nuclei of paramagnetic ions have been used. Internal fields are often so

strong, that at the low temperatures which can be achieved, it is possible -

to have large values for the alignment parameter.

At this point one may still question the feasibility of static nuclear

orientation techniques because of the extremely low temperatures, which are

necessary. There are now two important methods which enable us to produce

temperatures as low as 0.0! Kelvin on a routine base. The oldest method is

adiabatio demagnetization of paramagnetic materials. A great disadvantage is

the single-shot type of operation, which has to be repeated when the sample

has been warmed up too much. It is also often difficult to apply an external

magnetic field at the target; this requires a physical separation of coolant

and target. Adiabatic demagnetizations have been used rather extensively

in some of pur measurements at the High Flux Reactor in Petten.

A relatively new cooling method is the dilution of concentrated liquid 3#e in liquid 4Ee at a starting temperature below about 0.5 Kelvin. At a

sufficiently low temperature a phase separation sets in with concentrated 3He floating above a diluted 3He phase. Cooling occurs if 3He goes from the

concentrated phase to the diluted phase. We will not consider details of this

cooling method. As an example a dilution refrigerator used for fission

-323-

experiments at Harwell in a cooperation with the nuclear orientation group in Petten is shown in figure 1.

We have now discussed the main ingredients for doing nuclear orientation experiments. However, before discussing some applications in neutron-physics experiments I like to ask your attention for two other ways to arrive at oriented nuclei, which have been important for our work. First of all I like to mention the possibility of using the interaction of the electric auadruvole moment^ Q, with electric field gradients (-7-7-). With rotational symmetry the hyperfine levels split according to:

Em " 41(21-1) { m " /3 I< I +D/.

This splitting is not equidistant; more over there are doublets + m. Thus no polarization occurs; this is a way to align nuclei. It is also necessary to use single crystals. We have been using this technique in the case of fission experiments with 23 U, 2 3 5U and 237Np (the case of 237Np is somewhat complicated because of an additional magnetic interaction) * .In fig. 2 the even orientation parameters of 2 3 5U, aligned in single crystal layers of Rb Uo„(NO-),s are shown as a function of reciprocal temperature. Even at moderately high temperatures, say 0.1 Kelvin, a reasonably large value of f_ can be obtained.

A second remark concerns the polarization of low-energy neutron beams. During this conference experiments with polarized beams will be discussed in detail by other participants of this meeting. It suffices at this point to remark that polarized neutron beams can been obtained by; a) total reflection at magnetic mirrors, b) Bragg scattering at magnetized single crystals and c) transmission through samples with polarized protons. In the second case mono-energetic neutrons of energies up to 20 eV can be obtained. The third method has been applied for the first time at Dubna; it is useful up to a few keV. Energy selection is then achieved by time-of-flight methods.

Capture of polarized neutrons by unoriented nuclei gives polarized compound nuclei. This is of value for circular polarization experiments. An interesting possibility is to capture polarized neutrons by polarized nuclei. The compound nuclei will have values for the alignment parameter according to the expressions (assuming f2(N)«f 1 (Ю) :

f2(J) = ~ I ( 2 I 2 + 71 +6)f1(n)f1(N)/(I+l)tI + .1 + If1(n)f1(N)> if J-I+i

, f 2 ( j ) = _ ~ ( 2 I 2 - 31+l)f ,<n)f j O O / t t - D O " f , (n ) f , (N)} i f Л-1-i

f.(n) and f.(N) are the neutron and nuclear polarizations. A substantial alignment of the compound state can be obtained in this way at relatively

-324-

high temperatures. In addition the sign of f2(J) can be changed by reversing the neutron polarization. This is of great value for our neutron capture gamma ray experiments as I will discuss lateron.

4. Low-energy neutron experiments vith oriented nuclei

There are several possibilities for using oriented nuclei in reactions with low-energy neutrons. The neutron reaction itself can be studied; further on there are important applications in capture-gamma emission and fission after neutron capture. Three types of applications will be discussed in the following subsections.

Да. Determination of resonance spins

On this I can be short since this' will be discussed in more detail by Reddingius. Resonance spins can be determined by considering reaction strengths with neutrons and nuclei polarized parallel respectively antiparallel. The easiest thing to due is to study the total cross section in a transmission experiment. The measured effect is:

'where N and U are the counting rates in such a transmission experiment with parallel and antiparallel polarizations. Such experiments have been carried out at Oak Ridge, Washington, Brookhaven and Dubna. In the latter case neutron-time-of flight techniques have been applied at a pulsed reactor.

In these experiments brute-force polarized nuclei can be used as is demonstrated in figure 3, which shows the transmission effects of indium and lutetium polarized in an external magnetic field of 37 kG and temperatures

5) down to 0.03 Kelvin. This experiment has been carried out at Brookhaven Reddingius will discuss another transmission experiment with 2 3 5U, which

6) has given beautiful results Let me finish the discussion with the remark that this work is important

for two reasons: a) to determine the spin dependence of thermal neutron cross sections b) for assigning spins to as many resonances as possible for statistical

analyses of neutron resonance data.

4b Capture gamma ray в from oriented nuclei

The first experiments concerning capture gamma rays from oriented nuclei have been carried out at the High Flux Reactor in Petten using aligned '•' Md nu-

7 81 clei ' . The angular distribution of the primary transitions, which are presumably of dipole nature, is given by:.

-325-

W(6) - 1 + G2(n)A2f2P2(cos9),

ïere f2 is the alignment parameter of the capturing nucleus, G?(n) is the

jrameter, which gives- the change in alignment due to the neutron capture,

id A,, depends on the 3pins of the final levels. Since the spin of the

asonance state was known, it was possible to assign in a very direct manner

jins values to several excited states of 1Ift>Nd. Similar experiments have

sen carried out for Sm, Co, Mn, and Pr in Petten and Dy and Ho in Munich.

Iso secondary gamma transitions have been studied.

Often capture of thermal neutrons is related to the two possible spin

tates J=I±i. In such cases it is not known which fraction of an observed

eak in a gamma spectrum is due to I-J capture. In addition interference ',

ccurs between the two spin states. To detect such interferences experiments

ith polarized neutrons on polarized nuclei are useful. The angular distri-

ution function is of the form:

W(0) = I + A0 fjCrOf^N) + {A2 fjOOfjCN) + A2 f2(N)}P2(cose).

11 02 11 he A2 and A2 parameters depend on the interference; Ap not. By measuring

n two directions 6-0 and 6=90 , with parallel and antiparallel polarizations 11 11 11

t is possible to derive AQ and A2 -From the vaLues of AQ the (I-i)-ractions lor the individual primary transitions can be obtained. Using

hese fractions it is in principle possible to assign spins of final levels 11

rom the A2 values. Such experiments have been carried out on 9Co(n,v) э) io)

eaction in Praha and Petten. The results are in good agreement with circular olarization measurements. In figure 4 a parameter, R(0 ) - R(90 ), essentially

11 roportional to A2 > is given for j9Co{n,y) as a function of I-i«3 fraction nd for the possible spin values of the final levels assuming pure dipole ransitions. A similar experiment is now carried cut by Bosman for 165Ho in etten. This experiment suffers from the very weak primary transitions and omplicated decay scheme. The results look, however, promising.

c. Fission of aligned heavy nuclei induced by low-energy neutrons

The last application of oriented nuclei to be considered in this talk oncerns fission of aligned 2 3 3U, 2 3 5U and 237Np after capture of neutrons, uch experiments have been carried out by Dabbs at Oak Ridge, in a cooperation f Oak Ridge and Saclay (Dabbs, Michaudon et al. ) and in a cooperation of the uclear orientation group in Petten and Pattenden from Harwell • In these joint fforts neutrons generated with electron linear accelerator have been used.

The basic idea is to find out whether the fission fragments fly away redominantly in the direction of the nuclear spin or perpendicular to this

-326-

direction. Fission of 233lj and 235li occurs via a small number of barrier

states. In the case of 237Np we are dealing with subthreshold fission;

here intermediate states in the second potential well play an important

role. The above-mentioned experiments give information about the K.-values

of the transition states; that is about the projection, K, of the total

angular momentum, J, onto the deformation axis.

Such experiments are not easy to perform. Long counting times are

necessary to obtain sufficient statistics. In the case of 237Np data have

been accumulated for 8 months at low temperatures. Dilution refrigerators

are very useful in such types of experiments. The fission fragments were

detected with Si-detectors mounted on the 1 Kelvin shield of the cryostat

shown before. As samples we used slabs of single crystals of Rb UO-CNO )

containing ^-^^13, 235y o r 237Np £n chin surface layers (3 lmg/cm2). These

crystals were cut in a special way to allow measurements of the fission

fragments in the 0 and 90 directions with roughly to same angle with

respect to the surfaces.

The results showed that 2 3 3U and 2 3 5U fission predominantly perpendicular

to the spin direction. In the case of 2-7Np the fragments fly away in the

direction of the spin; at least for the first group of subthreshold resonances

below 20 and 60 eV. To conclude the discussion about these experiments I

like to show these resonances of 237Np and the measured values of the

anisotropy parameter A2; see figure 5. These values are compared with the

theoretical values expected for (J ;K.) combinations (3 ;3); (3 ;2) and + 4)

(2 ;2). We believe that this group of.resonances is related to an inter-ТГ +

mediate state in the second potential well with (J ;K) *• (2 ;2).

5. Conclusions

I like to finish this talk with the following concluding remarks: a) Nuclear orientation techniques can give very useful information in

low-energy neutron experiments. b) Since such experiments are difficult to perform, one should be careful

in selecting useful cases. c) One should aim for a combination of several techniques to assign spins

to levels populated in (n,v) work because of the complicated decays. This is to a good extent achieved at the High Flux Reactor in Petten.

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Referenees

1. H.Postma, Nuclear Instruments and Methods 88(1970)45. 2 . N.J .Pat tenden and H. Postma, Nucl.Physics Ш ( 1971)225. 3 . R.Kuiken, N.J .Pat tenden and H.Postma; Hucl.Physics A190Q 972)401, 4. R.Kuiken, N.J .Pat tenden and H.Postma; Nucl.Physics AI96(1972)389. 5 . H.Postma, V.L.Sai lor and L.Vanneste; to be publ ished. 6. E.R.Reddingius, H.Postma, C.Olson, D.C.Rorer and V.L.Sailor; to be

publ ished. 7. H.Postma and E.R.Reddingius, Physica 34(1967)541. 8. E.R.Reddingius, J .F .M.Pot ters and H.Postma; Physica 38(1968)48. 9. J.Honzatko and J .Kajfosz; Phys .Let te rs 38B(1972)499. 10. E.R.Reddingius, J.J.Bosman and H.Postma; Phys.Let ters 41B(1972)30I. 11. J.W.T.Dabbs, C.Eggerman, B.Cauvin, A.Michaudon and S.Sanche,

Proc . 2 Symposium on phys. and chem. of f i s s i o n , Vienna (1969)321.

- 3 2 8 -

DETECTORS

H« PUMPING LINE

Dilution, refrigerator for fission experiments with oriented nuclei at Harwell.

HELIUM BATH (4 K)

NITROGEN BATH

CONDENSING LINE

HELIUM BATH (IK)

EVAPORATOR

2 !> HEAT EXCHANGERS 3

MIXING CHAMBER

SAMPLE HOLDER

-329-

Figure 2

Orientation parameters for 2 3 5U in single crystals of Rb U02,(N03)3.

+ 4

О 10 20 30 T - M i n K ' 1 )

Figure 3

Effect E in the transmission of polarized neutrons through polarized indium and lutetium targets.

Figure 4

Anisotropy effect in the emission of gamma rays after capture of polarized neutrons by polarized 59Co nuclei. The indicated regions are calculated for the various possible spin • values of intermediate levels.

0.8 0.6 FRACTION OF

0.4 0.2 3" CAPTURE

GO

3.0

2 .0-

1.0-

2 0 0 0 -

NUMBER OF

COUNTS

. 1500 -

1 0 0 0 -

500-

bO _«_. АО -.-1 - -

35 —г - 30 Г 1 ~

25 E (in oV)

l/l

№JKftï/l.C*'jwrtl J\*«^J W v ^ UL ' , £ ..•*-ЧЛ^-*-.Л\У'"л*МГ-

7 0 0 8 0 0 9 0 0

<J*;K)

( 3 * ; 3 > ~

- -C2 ' ;2) —

-<3 ' - .2 ) -

^Twy^-^^v^^-^wv^-^^v^

Figure 5 The f i r s t group of subthreshold f iss ion resonances of ^37Np and the i r anisotropy parc">eters obtained with aligned Z37Kp.

1000 1100 CHANNEL NUMBER

1200

-333-

NUCLEAR MAGNETIC RESONANCE OF SHORT-LIVING ^-ACTIVE NUCLEI FORMED BY

CAPTURE OF POLARIZED NEUTRONS.

A.D, Gulko', S . S . T r o s t i n , M . I . Bulgakov, Yu.A. O r a t o v s k i i .

I n s t i t u t e of T h e o r e t i c a l and Expe r imen ta l P h y s i c s , Moscow, USSR.

A b s t r a c t

The method for measurement function representing the profile of nuclear

magnetic resonance line of polarized short-living 3-active nuclei

(distribution of internal crystal fields), formed by capture of polarized

thermal neutrons in investigated sample is described. The line profile

is measured by destroying, with a radio-frequency magnetic field, the

angular anisotropy of 3-rays emitted by the polarized nuclei. An interesting

feature of the described NMR method is the fact that the profile of the

NMR line can be determined at frequencies very far from the resonance

point. Measurements and theoretical calculations for 8-active 8Li nuclei

(Tj =0.85 sec.) in LiF samples are made. A comparison between the theo­

retical calculation and the experimental (results demonstrates that the

internal local fields at the 8Li nuclei have a Gaussian distribution and

only wings are subject to a Lorentzian deviation.

-334-

I. ВВЕДЕНИЕ

Ядерный магнитный резонанс поляризованных р -активных ядер принадлежит к более общей категории ЯМР радиоактивных ядерных состояний. Для короткоживущих ядерных состояний клас­сические способы регистрации ЯМР оказываются не применимыми из-за чрезвычайно низкой концентрации радиоактивных ядер (10"" - 10 ). Единственной возможностью регистрации резо­нанса в этом случае является использование анизотропии угло­вого распределения продуктов их радиоактивного распада или угловая корреляция, которая разрушается В Ч -полем при резо­нансе.

Для различных методов ЯМР радиоактивных состояний харак*-терны ври этапа: I) получение системы радиоактивных ядер с неравной заселенностью магнитных подуровней; 2) облучение об­разца, содержащего радиоактивные ядра? радиочастотным магнит­ным полем; 3) наблюдение резонансного поглощения посредством частотной зависимости анизотропии излучения или угловой корре­ляции.

Одним из эффективных способов получения поляризованных радиоактивных ядерных состояний является использование ядер­ных реакций. Характерная особенность этого способа - циклич­ность создания системы поляризованных ядер, одределяемая вре­менем их жизни. В этом случае опыты по ядерному магнитному резонансу можно осуществлять в диапазоне времен жизни радио­активных состояний от I0"8ceK до I03 сек. Верхний предел вре­мени жизни определяется статистической точностью,необходимой

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при регистрации резонанса, т .е . зависит от интенсивности первичного излучения, за счет которого получаются исследуе­мые продукты реакции, сечения ядерной реакции, фона, а так­же от времени релаксации ядерной поляризации в веществе. Нижний предел определяется в основном максимальным значени­ем амплитуды РЧ -поля, которое используется для индуциро-

а р

вания переходов между ядерными звмановскими подуровнями. В последнее время ЯМР на поляризованных ядрах, получае­

мых в ядерных реакциях» получил широкое распространениеL?~?1 Измерены магнитные моменты ядер Li 8 ( ^ i /2 = °»8 5 сек),

Р 1 7 (бб сек), F 2 0 ( I M сек), 0 12(0,02 сек), Л/1 2(О,0П с е к ) / Г / 9 1 1 6 ( В сек), #5 1 Й ° ( 2 ^ с е к)» # £ 2 8 ( 2 , 3 мин.), C i 3 8 ( 3 7 , 4 мин). Для ядер F 2 0 и В 1 2 измерен электри­

ческий квадрупольный момент. Кроме возможности измерения ядерных констант ЯМР на

поляризованных короткоживущих /3 -активных ядрах весьма перспективен в исследованиях взаимодействия fi -активных ядер с кристаллической решеткой. Поляризованные (Ъ -активные ядра, находящиеся в кристаллической решетке, являются свое­образными микрозондами. Исследование формы линий ЯМР этих ядер позволяет находить распределение внутрикристаллических полей, а также сделать вывод о местонахождении в -активных ядер в решетке и характере их взаимодействия с окружэнием^с].

Взаимодействие поляризованного & -активного ядра с окружающими его неполяризованными ядрами мишени обладает ря­дом особенностей по сравнению с взаимодействием соответствую-;

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щего стабильного изотопа. Во-первых, система поляризованных Jo -активных ядер оказывается сильно растворенной в большом

количестве неполяризованных стабильных ядер (концентрация ^ 10 * 10 ). Во-вторых, О -фактор Й> -активного яд­ра, как правило, значительно отличается от Q -факторов ок­ружающих его стабильных ядер мишени. Поэтому их спин-спино­вое взаимодействие сильно ослаблено. Кроме того, энергия от­дачи jh -активного ядра, получаемого в ядерной реакции, мо­жет быть настолько велика, что оно выбивается из узла решет­ки. Такой эффект может привести к образованию вокруг остано­вившегося 13 -активного ядра значительного числа дефектов.

Все эти особенности взаимодействия ядер с окружением могут влиять на форму линии ЯМР и на механизм релаксации.

Интересной особенностью описываемого метода ЯМР являет­ся тот факт, что резонансное поглощение может наблюдаться и при больший амплитудах РЧ-поля, в то время как в обычном методе ЯМР на стабильных ядрах этоМюзможно из-за фактора насыщения. Применение больших амплитуд позволяет измерить форму линии ЯМР на очень больших расстояниях от резонансной частоты.

В настоящей работе выводится соотношение, связывающее экспериментально наблюдаемую форму линии ЯМР и естественную, определявшую локальными полями, и описывается метод вычисле­ния последней. Приводятся экспериментальные данные для (Ь --активного ядра Li ö , полученного в реакции ( У^}у) на поля­ризованных тепловых нейтронах в образцах Z.ïP при комнатной

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Ь= -

температуре.

2. Форма линии ЯМ? поляризованных А-активных ядер.

Как известно, угловое распределение (3 -распада поляри­зованных ядер анизотропно. Однако, если перпендикулярно на­правлению поляризации ядер приложить радиочастотное магнит­ное поле ларморовской частоты, анизотропия будет разрушаться.

Зависимость О-ОТ асимметрии Р> -распада поляризован­ных радиоактивных ядер £ ^ от частоты приложенного РЧ-поля V имеет следующий вид:

*л1 1-#Р1-№, + {'№&Ш

Здесь £0 -величина асимметрии в момент образования поляризованных ]Ъ -активных ядер; /I -постоянная распада; Тт- - время релаксации системы поляризованных jf> -активных ядер; т£0 -время облучения образца поляризованными нейтрона­ми; &t -время измерения асимметрии; "С -время от конца облучения до начала измерения; у -гиромагнитное отношение поляризованного ядра; 6 -коэффициент, зависящий от спина ядра и закона заселенности уровней поляризованной системы; Нт- -амплитуда вращающегося РЧ-поля; i(\)) -нормированная функция формы резонансной линии, определяемая распределени­ем внутрикристаллических полей на Й> -активных ядрах.

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Считаем (это также показано экспериментально), что под действием различных релаксационных процессов (взаимодействие с решеткой, действие РЧ-поля) поляризация ядер во времени меняется по экспоненциальному закону, а именно:

где величина W - -2- êft И{ "f-f^J называется вероятностью перехода в единицу времени, индуцированного РЧ-полем.

Использование выражения (I) для непосредственного опре­деления функции формы -f(о) практически неудобно, так как связано со знанием абсолютной величины Нт . С этой целью вве­дем функцию <£($) :

(3)

Она характеризует радиочастотное поглощение во время жизни яд­ра в поляризованном состоянии. Тогда из формулы (I), считая, как в нашем опыте, V = 0 и полагая /\ ~ Д + JL , получим:

4. U+x?- (l-e-^)(i-e-7ai) , гД б £«у» -асимметрия /?> -распада вдали от резонанса.

Величина t-v/S^ находится экспериментально, а трансцен­дентное уравнение (4) решается относительно , f графически,

- 3 3 9 -

если известны А Т0 Д Т Рассмотрим два случая расчета функции формы резонансной

линии f-(ü) .

Б первом случае, если время релаксации Тт известно, то величина Л определена, и из уравнения (А-)можко найти <% . Из уравнения (3), обозначая

*№ %(и^) > (5)

получим две функции формы резонансной линии:

{Н-ft • (б)

Величину А можно найти методом графического интегрирования экспериментальной кривой <t(V) :

wo

т .к . W ^ i M ^ i. вследствие нормировки функции формы. Таким образом, использование К позволяет определить

функцию формы l(v) без знания амплитуды РЧ-поля Hj и

параметров $ и у • Во втором случае, если время релаксации Tj неизвестно,

решение уравнения (4) ищется в линейном приближении:

-34C-

*=i*', ^*£)> (8)

где Ж -решение уравнения (4) п р и Л - Д . Коэффициент (Х& зависит от времени релаксации Tj : чем меньше Т-ц , тем он больше. Б принципе, связь между <$ и 3f нелинейна, ины­ми словами коэффициент ^ зависит от èt . Однако, для до­статочно узкой области У (&) нелинейностью можно пренебречь. Б частном случае Li численный расчет показывает, что при изменении <jf в пределах от 0,05 до 2, соответствующих диапа­зону изменений ^^/£^ от 0,9 до 0,1 , величина 6и изменяет­ся в пределах лишь 1%. Это лежит в пределах точности наших измерений.

Таким образом, вместо (6) и (7) имеем:

# " • ) -

и (Ю)

Здесь А -также площадь под экспериментальной кривой X (v) , определяемая графически. Видно, что и в этом случае использование выражения для К позволяет находить функцию формы f{Oj , причем не только без знания параметров ê , У , Ну, но и без T-J-.

- 3 4 1 -

Необходимо отметить, что уравнение (10) позволяет в принципе находить величину времени релаксации Тт . Для этого, измерив площадь под кривой <)f , и зная ê , tf , иНт , определяем функции CbTl /fAr+ )уf/iT(J , а по расчитанному гра­фину зависимости этой функции от Тт находим Тт.

Для случая одного сорта |3 -активных ядер, зная вре­мя релаксации l ö f ^ в каком-то образце, можно по измеренным площадям А (при постоянной амплитуде Hj) определить Тт эти: ядер в других соединениях:

fi' _ CLTI(I+'Z/T1IC)

где rC-^\j}\ -время жизни ƒ?> -активного ядра. Если Tj o » ^ то Cu- s I и Тт определяется из выражения

К '~ и г/т, ' (12)

Из формул (3) и (4) следует, что экспериментальная форма ли­нии ЯШ? поляризованных & -активных ядер зависит от величи­ны амплитуды РЧ-поля Нт , причем, как было отмечено ранее [~| выражение (I) справедливо при таких полях"Hj, при которых асимметрия уменьшается приблизительно до 1/2 * S^ (следствие применения теории возмущений). Экспериментальный верхний пре­дел поля Нт, при котором еще справедливы выведенные соотноше-

-342-

ния (3) и (4), можно установить, измеряя функцию Ж при различных амплитудах Hj. Яри этом "приведенная" функция пог­лощения f

*1 = ^'/CH,/HII0)Z аз)

не должна зависеть от Hj. В этом выражении величина Hj Q -достаточно малая амплитуда РЧ-поля, Нт и Ь( -соответст-венно заданная величина амплитуды РЧ-поля и фуннция поглоще­ния для этого поля»

Далее, из формул (3) и (4-) вытекает возможность измере­ния функции f (о) на очень больших расстояниях от резонанса. Форма линии вблизи от резонанса обычно измеряется при неболь­ших величинах Hj • При этом вдали от резонанса, где -ff^) ма­ла, величина Н? •4-(^) » а следовательно и ^ , малы. Поэтому изменение асимметрии Е^ будет незначительно. Приме­няя достаточно большое поле Н-г, можно сделать величины Н? . * )t(y\ и f такими большими, что изменение асимметрии £^ бу­дет заметным ( £^ 1/2' f e 0 ) . Таким образом, измеряются очень малые значения Л-(у) • Другим способом измерения функ­ции -j?(DJ 1 как следует из выражения (5), может быть метод измерения асимметрии во времени. В этом случае по наклону кривой определяется величина -1- +- -— ê fr2 Щ f-fo) * откуда может быть вычислено значение jL(yj) *

-343 -

3 . ИЗМЕРЕНИЯ, РЕЗУЛЬТАТЫ, СРАВНЕНИЕ С ТЕОРИЕЙ

Схема измерения ядерного магнитного резонанса поляри­зованных короткоаивущих 9> -активных ядер, получаемых с помощью поляризованных нейтронов, заключается в следующем, исследуемый образец, находящийся в стационарной однородном магнитном.поде, облучается в течение времени ~С0 поляризо­ванными тепловыми нейтронами. Счет электронов распада осущест­вляется двумя сцинтилляционными счетчиками, расположенными соответственно под 0 и 180° к направлению нейтронной поляри­зации (а, следовательно, и поляризации ядер), спустя любое заданное время X после перекрытия нейтринного лучка. Дли­тельность времени счета ДХ* одинакова для обоих счетчиков. По истечению некоторого времени, необходимого для распада ис­следуемых ядер и /3-фона, цикл повторяется с обращенным направлением нейтронной поляризации, что позволяет устранять приборную асимметрию. Асимметрия вычислялась для каждого ка­нала в отдельности по формуле:

где А/Л И А/^_ -отсчеты счетчика для двух направлений поля­ризации нейтронов. Радиочастотное магнитное поле, необходимое для разрушения поляризации (Ь -активных ядер, создается ка­тушкой, намотанной вокруг исследуемого образца. Катушка созда­ет на образце осциллирующее магнитное поле амплитудой 2Hj.

-344-

Аеимметрия £. измеряется как функция частоты v> РЧ-поля. В данном опыте образец подвергался действия РЧ-поля непрерыв­н о ^ в течение всего времени облучения и измерения-

Измерения ЯМР ядер Li ( i/2 - °*85 с е к) проводились на пяти образцах [th : четыре образца содержанием изотопа /с. около 3,5% и один образец с содержанием изотопа Lt ~0,2%. Образцы имели вид пластинок с толщиной 2 мм и площадью 40 х 40 мм2. Три образца представляли собой монокристаллы, вырезанные таким образом, что плоскости (100), (ПО) и (III) были параллельны большой поверхности. Четвертый образец Li F ( Lc& & 3,5%) и образец Ll*F( Z7Ó:= 0,2%) представляли собой поликристаллические порошки, изготовлявшиеся дроблени­ем. Бее образцы UF изготовлялись из одного монокристалли­ческого блока. Образцы устанавливались в центре электромагни­та, большой поверхностью перпендикулярно направлению магнит­ного поля в пределах 2°. Времена облучения "t0 и измерения A T составляли 3,73 сек и 4 сек соответственно.

Для получения 0-7Г-асимметрии ƒ3 -распада Li 8 из измеренной величины асимметрии вычиталась асимметрия ft-pac-пада ядер /~ , образующихся в образце Li F • Асимметрия F определялась как остаточная асимметрия при полной

/ ' 8 деполяризации ядер Lc наложением РЧ-поля большой ампли­туды. Фон постороннего излучения, как нетрудно показать, не влияет на величину отношения £<>/£ , а следовательно, и на форму линии ЯМР.

-345-

(15)

Типичная зависимость величины В^/В^ от частоты и ампли­туды РЧ-поля для ядер /.£ 8 приведена на рис, I и 2. Из зна­чений £//£«> по формулам (4) и (13) вычислялись функции <*f0;, приведенные для всех образцов к одному и тому же значению Hj Q . Далее находились площади А0 под кривыми №о и по (9) и (10) определялись функции формы fff). Вторые и четвер­тые моменты формы резонансных линий вычислялись по формулам:

J / -оо ~СК» - С е 0

Результаты представлены в табл. и на рис. 3-5. Значения площадей А0 для всех образцов в пределах экспе­

риментальных ошибок оказались одинаковыми. Отсюда на основании формулы (II) можно заключить, что времена релаксации Тт ядер Ц для всех образцов одинаковы. По известной величине Ну Q из (10) можно оценить, что T j> 15 сек. Более точное опреде­ление Тт этим методой требует повышения точности измерения РЧ-поля Hj Q.

На рис. 3 показаны результаты измерения функции fff) для образца с HQ || [ i l l ] с использованием различных амплитуд РЧ-по­ля. Логарифмический масштаб выбран из тех соображений, что позволяет показать функцию ^fff) на больших расстояниях от резонанса* Данные свидетельствуют о том, что значения f(^) , полученные с помощью различных амплитуд Hj, совпадают (в пре­делах экспериментальных ошибок), если амплитуды Hj таковы, что отношение SLojt^o H8 менее 0 ,1 . Это определяет область

применимости анааитического выражения (I). Аналогичные ре­зультаты получены для других 4-х образцов*

На рив, 4 и 5 приведены результаты измерения *f(0) для пяти образцов» усредненные по различным амплитудам РЧ-поля.

.Ори теоретическом расчете формы линии ядер Lc в образце Uh предполагалось, что (Ь -активные ядра U за­нимают нормальные положения ядер лития в решетке Lcr, в действительности» в результате испускания ^-квантов при переходе ядра /л 8 в основное состояние последний получает импульс отдачи (энергия около 300 эв) и выбивается из увла решетки. В процессе торможения выбитый ион производит смеще­ние соседних ионов, что моает иривести к образованию дефек­тов (вакансий и сдвоенных атомов) вблизи остановившегося ядра £ t 8 . Такой эффект нарушения кристаллической решет­ки приведет к увеличению локальных полей и, следовательно, изменению формы линии ЯМР по сравнению с формой, когда ядро

Li находится в узле идеальной решетки. Если существенную роль играет механизм отжига дефектов (он зависит от темпера­туры образца), то можно оаидать приближения формы линии ЯМР к бездефектной. В этом случае можно воспользоваться теори­ей формы линии для жесткой решетки кубического кристалл!®^*''у которая позволяет рассчитать вторые моменты формы линии, В образце Li F имеются спины трех сорков, причем g -фактор ядер LL СИЛЬНО отличается от а-факторов окружающих ядер / 7 г~ Г9 и я Г • Поэтому из гамильтониана ДИПОЛЬ-ДИПОЛЬНОГО взаимодействия едедует исключить переворачивающий член и оставить только статическую часть. Благодаря этому вторые

моменты М ^ оказываются в Э/Ч раз меньше, чем если бы об­разец состоял из ядер одного сорта. Значения вторых моментов для использованных образцов приведены в таблице.

Однако знание второго момента не дает еще возможности судить о форме линии. Важной характеристикой формы линии яв­ляется отношение ее четвертого момента к квадрату второго М^/М 2 « Например, для гауссовой формы М^/М^-З. Если фор­ма линии отклоняется в сторону кривой лоренцз, то это отно­шение больше 3, а если в сторону прямоугольной - меньше 3.

используя теоретические значения вторых моментов фор­мы ЛИНИЙ.были построены функции формы <f(ü) в виде гауссо­вых и лоренцовых кривых. Лоренцова форма отклоняется от эк­спериментальных точек как вблизи, так и вдали от резонанса. Для монокристаллов в основной части резонансной линии до J ~ 10 Jp , гауссова форма хорошо согласуется с экспе­риментом*

Для порошкообразных образцов Li'г и It /"экспериментальные кривые 4(ü) одинаковы в пределах ошибок. Однако гауссовые кривые^расчитанныв с теоретической полушириной 6~-^2^ '~ - 3,64 кгц, дают худшее согласив с экспериментом вблизи от резонанса. Лучшее согласие наблюдается для гауссовой кривой с 6* « 3»2 кгц*

Вдали от$ резонансной частоты, при f é 1 ( Р у т л к , экспериментальные точки для всех образцов отклоняются от расчетной гауссовой кривой в сторону лоренцовой.

Такому квазилоренцовому характеру кривдх f{oj соответ-ствуют полученные экспериментальные отношения М^/М ^ кото­рые для всех образцов оказались больше 3.

-348-

Таким образом, из сравнения экспериментальных данных по f(o) с теоретическими функциями формы можно сделать сле­дующие выводы. Распределение внутренних локальных полай на ядрах II 8 , образующихся при облучении образцов UF тепло­выми нейтронами, имеет гауссовую форму с отклонением на крыльях в сторону лоренцовой. Величина внутренних полей ЛНАМС, рассчитанная как ширина на половине высоты кривой 1(о) , хоро­шо согласуется с шириной гауссовой кривой, расчитанной по модели диполь-диполъского взаимодействия для жесткой решетки. Наблюдаемое для порошков сужение линий по сравнению с теоре­тическим носит, повидимому, не случайный характер, ибо наблю­далось как для образца Ц /~ , так и для Li F . Причиной этому сужению могут быть остаточные напряжения, возникшие при изготовлении порошкообразных образцов (размоле монокрис­таллических блоков).

Экспериментальные величины вторых моментов формы линий для монокристаллов превышают теоретические в среднем надии^ а 0;65 + 0,1 кгц . Т.к. влиянием спин-решеточной релаксации Ту и неоднократностью поля Н0 на форму линии в нашем случае можно пренебречь, то это увеличение следует приписать взаимо­действию р> -активных ядер с дефектами образцов, в том числе с возникшими вследствие " -отдачи ядра Li . Эксперимен­тальные величины вторых моментов формы линии для порошков луч­ше согласуются с теоретическими. Возможно это есть следствие сужения вершины кривой f(\)) , Поэтому требуется дополнитель­ная экспериментальная проверка этого факта на отожженных по­рошкообразных образцах.

-349-

В целом, анализ формы линии на различных образцах £i7~

свидетельствует о достаточно хорошем согласии с теорией ли-поль-дипольного взаимодействия и подтверждает, таким образом, существование при комнатной температуре ыеханиама отжига ра­диационных нарушений, благодаря которому Jh -активные ядра после V" -отдачи занимают нормальные места в узлах кристал­лической решетки Ltr .

Л И Т Е Р А Т У Р А

Jij H • ВадхсЖ Л - | t o i Пъ^с,и:} т ^$(4366).

1 J р}щь. UM , ijb f ПО (1Ш); М_& i 5"ХО (i$?o). [з] А.Д.Гулько, С.С»Тростин, А.Худоклин, ЖБТФ, 52, 1504, Ц967).

[4J А.Д.Гулько, С.С.Тростин, А.Худоклин, ЯФ, 6» вып.4, 657 (1967),

о( eJl} Ptu/y 1<М } М_& У«" ^ V J W /

ГЛ Н, Лск:е^илии ^.^ьсА^е^Ь З.М&^еллЬ _Л. ШСии^^и&ъj

Г8"| H, №\wiwci\AV\ föty<A&uu> fM.fa-uf?[>t 9, H&i-tj'ccnb / G-Zu Pt^itctz} H. 7- 5*оыс»1аии t РЬуь. l^tt/ 4JJI A/2. ( 1$ ?Z).

[itrlM.'USyjiVMOoe w ^ . , ЖУТр 6l}éC7 f4$?l). [k(8.J А.Лёше, Ядерная индукция, 0л, Москва, 1963.

fï$J А.Абрагам, Ядерный магнитизм, ИЛ, Москва, 1963.

Образец М5,теор I Mg, эксп ' М^, экоп. М^/М

[ктц] [ K T ^ J [КГЦ2] [КГЦ4] ЭКСП

Лн лок АН,

UF [юо] . 0,444

* 0,011

1

13,73-1 (13,76)*'

.14,42 * 0^38 .

715 ± 24

3,4 4. 13,6 ± о! ie

UF [юо]

[110] . 0,432 ± 0,011 (4 ,95)*

.5,44 151 t«8 5,1 8,2

± 0,14

jra] + 0,413 1,964 1 (2,014)* + 2;59

± 0,13 ±4 7,* ± 0,13

порошок . 0, 418 ± 0,015

6.7JI _ (б!?13)ж

* 6,72 ± о;з4

207 + 15 4,6

, 8,6 ± 0,22

U7 F порошок

0,424 +0,014

6,713 6,19 ± 0 , 3 3

194 ± 15 5,1 8,6

± 0,23

Л0К,Т90р.=

ЭКСП [эрст] г 1 ' 6 7 Д ^ 2 ( т ^ р £эрсаГ|

13,8

8,3

5,2

9,6

9,6

Ш) - при отсуготвии изогона № ,

- 352 -

Подписи под рисунками

Рис.1. Частотная зависимость асимметрии ƒ5-распада ядер Li в монокристалле Lit с Нс \\ D ï ï J } И0 - 'lb$4k в 5 \

О - 2Hr- 0,013$ ; О - 0,015 Э ; А - О}04 $ ; X, - о}ой 9 ; ® — CtB4 Э ' ф - it ?$J . ] Сплошные кривые - теоретические в предположении гауссовой формы линии f(v) с €Г = у 2 . Н 2 ( Т е с ' •= 1,66 к: га, „

Рис.2. Частотная зависимость асимметрии й-распада ядер Li для трех плоскостей монокристалла LcF при uHf- 0(ОЧэ: о - Н0 Ц [юо] , • - М [lic] х -Н0 Ц [mj .

Рис.3. Форма линии fa) для ядер 1с & в монокристалле %Uf с Hjjp'H Обозначения точек те же, что и на рисЛ. Сплошная кривая -гауссовая форма с б"'- 1,96 кгц; пунктирная кривая лоренцова форма.

РисЛ. Вершинная часть функции -fft) для ядер i t в монокристал­лических образцах Li г . Экспериментальные точки усреднены по различным величинам амплитуд радиочастотного поля* о - Ц0\\ [ice] © — It0*4) X-|(D'*U Сплошные кривые - гауссовы формы с (Г= /^Н^ТаФ ровной ? $,1Ч щ для HoWLwoJ^ïiltcb ДАЙ 'HotfCnoJ

Рис,5. То же, что и на рисЛ, но для поликристаллических образцов J U F и i ï ? F . Сплошная кривая - гауссовая форма с 6"-=ЗеУ*:л ;1

пунктирная кривая - гауссовая форма с <Г- 3 2 / с г ^ - ' $ О -порошок Ц F , • - порошок Ll^F' 'i

5-ок

'E& г Hjim)

1.0 f Q 4 - % « * — - - % ..ajfj^ — 4 ч ч ] %É 1 Yf

Q8 \ \ 1 U9 °° Jrl 1 V fn. (П f <У

: \ I\JI i > \ j II il i OM ft* ff II

0.2 : • • \ \

H i i

il -\ ^ 1 \17 / * vl ЧГ л ' /

n %-• .. • Jf / U

> i

* • . .._.! 1 ! 1

/8500 ISSQO iilOfi 1660.0 1890,0 1900.0 Ж,0 I/I-Л»

Fig. I.

ог -

НЕ 2И,'0М>.

b-HJ(iOQ} — till (110}

1850.0 1650,0 18Т0.0 I88Q0 (890,0 1900,0 19/0.0 У ,хГц

Fig. 2

- 3 5 5 -

ƒ •*

Mo1

ю- л - 4

0, 1

к mm] l | Л

,J H l i ^

ю % \

.. 1 f 1 \

N.

1 4 .

iff \ 10 - 1 ^

~ 1 '* - 1 4

' f)

*

h 1

III к —

1 •• . 1 1 "

ro Г5 20 25 V-K'**

Fig. 3.

-356 -

UF

Ï £ - & .

*0 V КГЦ

F i g . 4 .

o - LiF i>opo**K

л-Li7f-пврсшок

•i КГЦ

Fig. 5.

-358-

NEUTRON RESONANCE OF 2 3 5 U .

ж-) * * ) ж**) ж***) E.R. Reddingius , H. Postma , C.Olson , D.C. Rorer

****) V.L. S a i l o r

FOM-RCN Nuc lea r S t r u c t u r e Group, P e t t e n (N-H) , t h e N e t h e r l a n d s . **)

State University of Groningen, the Netherlands. Los Alamos Scientific Laboratory, USA. Brookhaven National Laboratory, USA.

Neutron resonance spins of 2 3 5U were determined by measuring the transmission of polarized neutrons through a target with polarized 2 3 5U nuclei. The experiment was performed at the High Flux Beam Reactor of Brookhaven National Laboratory. Fig. 1 shows the experimental set-up. A beam of polarized neutrons was obtained by Bragg reflection from a magnetized Co-Fe single crystal. The Bragg angles could be ad­justed with high precision in intervals of 3''. The best spectrometer resolution was obtained by using the (220) reflection of the Co-Fe crystal in combination with two Soller collimators; one of 3* in the primary beam and a 1' collimator between the cryostat and the neutron detector. In that case the resolution was 0.4 eV at 10 eV neutron energy, The direction of the neutron spin polarization could be reversed with a combination of a guide field rotated 180 and a current sheet. The in­tensities of the transmitted beam (for parallel as well as antiparallel polarizations of neutrons and nuclei) were measured with a neutron de­tector.

The sample was prepared by pressing 7.8 g uranium monosulfide and an approximately equal amount of lead powder in a die. Uranium enriched to 99.99% in 2 3 5U was used in order to reduce the heat production from a-decay of 231fU as much as possible.

-359-

The sample was cooled by ad iaha t ic demagnetization of i ron alumn grown

in a bundle of copper wires for good heat contact .

One end of t h i s p i l l was connected v ia a lead heat switch to a helium

b a t h , maintained at about 0.9 K, At the other end i t was attached to

the sample holder . The whole assembly could be moved up and down so

that d i f f e ren t pa r t s of the sample holder could be exposed to the

neutron beam. After ad iaba t i c demagnetization data were taken during

about e ight hours . During th i s time the sample warmed up from 0.04 К

to s l i g h t l y above 0.1 K.

During the experiments the sample was in an external magnetic f ie ld of

28.7 kOe.

Experimentally we determined the transmission effect e, defined a s :

_ N4-4- - mi . £ N++ + N-H ' t l J

where N-t-t and N++ are the numbers of counts with parallel and antiparallel

polarizations neutrons and nuclei. For low values of the nuclear polariza­

tion f„ and neglecting the influences of spectrometer resolution and neutron

depolarization in the sample, the transmission effect can be expressed as:

e = -fnfNNcrtp (2)

Here f and f are the degrees of neutron and nuclear polarization, N is n N

the number of nuclei per cm3, a is the neutron capture cross section and t

is the target thickness. The parameter p is 1/(1+1) for a resonance with

spin J=I+^ and p is -1 for a J=I-j resonance. In practice several resonances

contribute to the capture cross section and the spectrometer resolution has

to be taken into account. In that case the analysis is more complicated and

a computer programme has to be used to analyse the data.

The degree of neutron polarization at the sample position was determined by

measuring the transmission effect of an indium sample which was also attached

to the sample holder.

For 115In nuclei the degree of nuclear polarization in the external magnetic

can be calculated (brute force polarization). The value of Not was measured

and the p values are known. Hence f can be estimated using eq. 2.

-360-

The degree of nuclear polarization of the 2 3 5U nuclei can in principle be

calculated from the known internal magnetic hypefine field in US, It can

also be estimated from the transmission effects of the most prominent

resonances of 2 3 5U using eq. 2.

In our experiment we obtained f - 0.50 and f„ = 0.055. n N

The thickness of the sample was such that Nat was 1-2 for the most prominent

resonances. Inserting these numerical values in eq. 2 shows that transmission

effects of few percent can be expected which are positive or negative depending

on the spin of the compound nucleus.

The experimental results are shown in figure 2. In the lower part the cross

section (Not) of 2 3 5U as measured with the spectrometer is shown for the

energy region of 1.7-15 eV. In the upper part the measured transmission ef­

fects are given. The final results are listed in table I and compared to results

from a) an earlier experiment with polarized neutrons and polarized nuclei |l|

b) resonance scattering experiments |2,3|

c) intensity of primary gamma transition experiment |4)

d) intensity ratio of secondary gamma transitions experiment J5|

It is clear that several new spin assignments have been obtained and that

our results compare reasonably well with the results of the previous

experiments mentioned above.

-361-

REFERENCES

jl] R.I. Schermet e.a-, Phys. Rev. _167 (1968)1121 [2J F. Poortmans e.a., Proc. 2nd Int. Conf. on Nuclear Data for Reactors,

Helsinki (1970) 449. |3| F.B. Simpson e.a., Nucl. Phys. _164_ (1971) 34. \й\ W. Kane, Phys. Rev. Lett. 25_ (1970) 953. )5| F. Corvi e.a., Nucl. Phys. J203 (1973) 145.

-362-

Table I

NEUTRON RESONANCE SPINS OF 235ü

E n E

J

E n E present previous

0.275

1.4

2.04

3.15

3.61

4.85

6.15

6.39

7.08

8.79

9.28

10. 16

1 1.67

12.39

14.0

- 0.515 + 0.025

+ 0.618 +_ 0.019

- 0.88 +_ 0.13

- 0.72 _+ 0. 14

+ 1.51 +_ 0. 16

+ 1.09 +_ 0.06

-0.18 +_ 0.05

+ 1.39 ^ 0.23

+ 0.79 +_ 0.10

+ 1.30 ^ 0.13

+ 0.94 +_ 0. 14

+ 0.51 _+ O.IO

+ 0.34 _+ 0.07

- 1.09 _+ 0.10

-1.18 _+ 0.22

•3

4

3

3

4

4

3

4

4

4 (+30% 3)

4

4

4

3

3

за

4a

3c,d,(a)

4d,(c)

зъ

4b,d 3b,d

Polarized neutrons, polarised nuclei. Resonance scattering. Intensity of primary gamma transitions. Intensity ratio of secondary gamma transitions.

SCALE IN meter

FIG. 1

-i 1 1 1 г "T • 1 Г ело2

-* г

2.04 £15 I

2.84 3.61 I I

W г 4.85

3.46 \ 8.79 10.16

I I 9.28

2.0 3.0 4.0 . 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 neutron energy (eV)

FIG. 2

- 3 6 5 -

i

MAGNETIC UOüENTS Oï? l 6 8 E r STA2ES EXCISED БХ XEITSRON

САР'ШЕЕ

Alfi iuenkov V . P . , Zhukov G . P . , Ziiain G.H. , Lason L . , blareGV Y U . D . ,

Ovcb.irm.ikov O.N. , P i k e l n e r L . B . , S a l a m a t i n I .ГЛ., T i s h i n V . G . ,

S h a p i r o 3? .L. , Sharapov E . I . (ЛШ)

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ï.ïajpietic moments of nuclear compound states, eiccited oy the

neutron capture are the most unstudied characteristics. A laethod

for measuring JU- iiad been proposed for the first ti ie in rof.

/1*2/. The method is based on observing the shift of the neutron

resonance energy due to the hyperfino interaction in experiments

with polarized neutrons or nuclei. There are two ways to perform

such eicpcriments. One is the transmission of polarised neutrons

through the unpolarized target in the e:cternal aiagnetic field,

which have to orientate internal magnetic fields on nuclei. The

othezis the transmission of the unpolarised neutron beau, through

the tai-get whose nuclei arc polarized in internal Kinetic fields.

The values of the resonance shift (compared with those in case of

the absence of the polarisation) are the following:

where д£ is the resonance shift, ÏÏ - the hyperfine magnetic

field, f and fjy - the polarization óf neutrons and nuclei

respectively, I - the spin of the target nucloous , J - the spin

of the compound nucleus, J-tz and A; - the magnetic moments of the

corresponding states.

In both cases it is very difficult to perfora the experiment

because of small effects, indeed, wiüh the maximum value of the

hyperfine field Н-Ю^ое, lOG>ó polai-ization and the difference h;-hz being equal to one nuclear magneton J4M the value of the

shift is of about p x 10 J eY, while the total resonance width is

is about 10 eY. The first nieasurcment of magnetic moments of

™Er neutron resonances 0.450 eY and 0.534- eV had been performed

J Щ

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at Broolthavcn ITational Laboratory. L poiarined neutron l;raas«iacion method had been used / 3 / . The following values of magnetic ыо-ments had been obtained; <ч-/огч<ьо) =г (-0,45+. O(>Y].^N

\'Ie measured magnetic moments of these states as well, using another method: the transmission ox" unpolariacd neutrons through polarised and unpolrased 3Sr tarcets. The experiment was performed at the pulse reactor IBB-30 using the time-of-flight method with the 53.5 meters flight path. The scheme of the experiment is pre­sented in l?ig. 1*

I'Mg.l. The scheme of the experiment. 1) Vacuum tubes* 2) Colli­mators, p) The cryostat. 4) lir targets. 5) The plug. 6) The detec­tor .

To polarize Er nuclei up to f, 0.97 the sample was cooled to the temperature 0.02°K. The polarization was destroyed by heating the sample up to the temperature 0.5°K (residual polari­zation fT,=0.12). The internal magnetic field on the nucleus was 7.1 x 106 oe /3/.

In order to detect a small resonance shift a high, statisti­cal accuracy of spectrum is needed and it follows that a high count rate is nessesary. In our experiment the inatanteneons count rate was of about 5 x I06icc "1. Thus the current method of detection, which is free of counting losses caused by the limited high-S7)e-uu

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responce of the instrument тас used in our experiment. The Eh _ filter having the resonance at '1.257 eV was placed in the beam to choclc the time scale of the analyser. Besides, the neutron Ъеош was devided iito two ones by means of the collimator having two

2 50 x 80 mm holes. One of the boards passed through the main targe' and the other one through the control Er target. The later was placed in the sane cryostat but its temperature was constant and equal to 10°K. Behind the cryostat there was the plug which in turn shut off beams (approximately in JO Seconds). In accordance with this the time-of-flight spectrum had been registered.in the first and second parts of the analyser's memory. The temperature of the main target was chanc;ed after three hours of measurements.

j

Thus in every eight hours we had four time spectra: two for,' the case of the transfixssion of neutrons through the main target j; under the 0.02°K and 0.5°K respectively, and two for the transmis-j sion through the control one under the temperature 10°K. Pig. 2 t

represents one of the measured time-of-flight spectra. !

100 300 too 500 t

Pig. 2. The time-of-flight spectrum, t - is the number of the channel of 15 Msec, H - the number of the counts per channel,

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AQ a whole there were obtained twenty five pairs of i ain spectra and the same number of control ones. To put aside not proper results of ineasureiaents due to the instrument fault, and to jualce the correct evaluation of the accuracy of the obtained results, each pair of spectra had been analyzed separately. From the point of veiw of possible accidental errors pairs are indepen­dent, so the defined froia theia Sr resonance shifts should be dis­tributed near the real values following Gaussian distribution with the dispersion, which characterizes the accuracy of measurements. •BIG energy shifts with the normalization to Ida resonance were ob­tained on the computer B2Si-'i-4- using the least square method. From twenty five pairs five were excluded since bad fit of Pli resonance. The results obtained from the rest pairs gave energy shifts presen­ted in Fig. p. The following values of energy shifts and their errors for both J3r resonances were obtained:

bE ( 0,44,0) = (П7 t>*J-/0**.\f

A£(ots4$) = (НЧ ±t£)iÓ(' &/

On the control pairs (as a consequence of the absence of the pola­

rization) the shift must be zero, in fact the following values of

shifts were obtained in the exoerbient: <*.(**«>)-t-*9 ±*)-<oc*f/ A&(o.S?4) =• (~ц +IHJ-/06 cv>

0,O2'h 0,460eV

1

uE-(2?±tyeY

ft 1 3 r~ -Л-, Чл

0,584 QV A E-(44*№jjeV —

г-, ^ >L - П ,-ГТ rh— •fS0-fO0-5O 0 50 № (50 AEjieV

Ю'К-10'К Q460QV

l\ rrrm

&E-t-QA±:6} peV

0,5B4oV

BE ka I

uE-C-11*14))l9V

TD-... -150400-60 0 50 WO t50

UEJJOV

Fig. J. 'L'he distribution of experimental де values for the main

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and conti"ol pairs of spectx a. 'To find out possible system,

the above described experiments a fistic methodical errors apart v/ere peri'ox'iiied: the Liodclling of thew extra control -measurements due to the mechanical movej-ent of t;s shift usint -::-iie Dopier effect temperature change (with unpolarisehe sample, the i.uCiuencc of the resonance. A- role of the шсап resd nuclei) on the shape of the estimated as well. By all these iuea:idual polarisation had been errors in limits of accuracy of the as the absence, of systematic With the help of the obtained shift experiment had been shov/n. magnetic moments of two Er states and using formulae 5 and 4

Л1; (O,H(.Ö) - (o,<) -t o, s were defined: J4 • (0,52.4) = it* *O,4)J4„

Tiiese valjzes differ from ones obtai^J^^ the 0.584 eV resonance. It is diffincd in ref»/^/ especially for but it; should be noted that the con cult to point out the cause , ty brings the magnetic scattering i siderable additional uncertain-interfere with nuclear scattering, a the experiment /p/ which

ffihe obtained results are in a theory of magnetic moments of the с good agreement with the preseni (as it was shov/n in ref. />,6/) ausoupound states of nuclei, which

* the single-particle values* not differ greatly from lief erencos. ;*

1. P. L.Shapiro "He search Applicatioi p.176, Vienna, IAJ^, 1967. ls o£ H a c l e a r p a l G G d systems",

2. E.L.Shapiro'Tolarized Targets ш "° 7 * id Ion Sources",p03^9,Saclay CIüA

3« IC.II.BecIcurts, G.Brunhart Phys.Ia 4. А.й.Бескрозыый, Ю.Ы.Осганзвич, UVa cn 7 2 G (1^70) 5 . V.G.Soloviev, V.V.Voronov, P r e p ] - ^ jj7"5 c ï p . 5 4 ( I 9 7 I ) .

c in t ЛКй 34-G437, Dubna 1972.)