Nuclear Physics A137 (1969) 445--466; (~)North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

INELASTIC SCATTERING OF 61 MeV PROTONS FROM Sgy

AND THE ASSOCIATED REACTION MECHANISMS

A. SCOTT t and M. L. WHITEN tt

University of Georgia, Athens, Georgia, USA tit

and

W. G. LOVE

Florida State University, Tallahassee, Florida, USA

Received 16 June 1969

Abstract: The differential cross sections for the excitation of the first seven resolved excited states of sgy by 61.2 MeV protons have been measured over the angular range 17°-120 °. One of these is the weakly excited state at 2.62 MeV. The inelastic scattering data are analysed using the collec- tive model and a microscopic model including both core polarization and a central spin- dependent effective interaction.

El NUCLEAR REACTION 89y(p, p,), Ep = 61.2 MeV; measured a(Ep,, 0). ] 89y deduced levels, ilL. I

1. Introduction

There has been much interest recently in the microscopic description of the in- elastic scattering of protons by nuclei 1). In this description, the effective interaction that produces the inelastic transition is taken to be a sum of two-body interactions between the projectile and each of the target nucleons. In order to determine the parameters of this effective interaction, the first nuclei chosen for study are those in which the initial and some final states are believed to be well described by simple shell-model configurations. Once this effective two-body interaction is determined, it is hoped that it can be used in the microscopic model to describe the inelastic ex- citation of states with more complicated configurations, and hence deduce the struc- ture of these states. Recent calculations indicate that even when these relatively simple shell-model states are excited, the effects arising from the active participation

t Part of this work was carried out while an Oak Ridge Associated Universities Summer Research Participant at the Oak Ridge National Laboratory operated for the U. S. Atomic Energy Commission by the Union Carbide Corporation.

tt Graduate Assistantship provided by the University of Georgia. *it Research supported in part by the Office of General Research and the Work-Study Program

at the University of Georgia. Travel funds provided by the Oak Ridge Associated Universities. Research sponsored in part by the U.S. Atomic Energy Commission while an Oak Ridge Gradu-

ate Fellow from the University of Tennessee at the Oak Ridge National Laboratory and in part by the National Science Foundation (Grant Number GP-7901).

445

446 A. SCOTT et al.

of the core should be included 2). The inclusion of these core polarization effects have helped to remove the state dependence of the remaining part of the effective interaction, which may be used with greater confidence to study more complicated

excited states. The primary motivation for the present experiment was to obtain the differential

cross section for the excitation of the low-lying levels in 89y in order to gain in- formation about the microscopic-model effective interaction. In particular, the study of the excitation of the excited state at 0.908 MeV seemed to offer the best opportunity to "calibrate" the effective interaction used in the microscopic model, because the ground state and this 0.908 MeV state are well described by simple shell-model wave functions 3). Since there is a parity change of the nuclear states, this transition involves only the odd-parity multipole components of the interaction when exchange is neglected 4). The second and third excited states of 89y at 1.51 and 1.74 MeV are believed to be predominantly single-hole configurations with odd parity, there- fore the even-parity multipoles of the effective interaction are involved in the ex- citation of these states when exchange is neglected. If one assumes a simple form for the effective interaction in which a knowledge of one multipole determines the others, the excitation of the 1.51 and 1.74 MeV states may be regarded as tests of the inter- action which describes the cross section for the 0.908 MeV state or as tests of the assumed single-hole structure of the 1.51 and 1.74 MeV levels. A recent 9°Zr(d, aHe) 89y experiment has confirmed that the low-lying levels of 89y have simple shell-

model configurations 5). Although it is more difficult to obtain good overall resolution, this experiment was

performed at 61 MeV in the expectation that the reaction mechanism would be simpler and the shape of the differential cross section more strongly structured than at lower projectile proton energies. It was considered that this experiment would therefore more stringently test the assumptions made about the reaction mechanisms used in the microscopic-model calculations than in other recent experiments at lower proton energies, particularly since the differential cross sections reported were somewhat incomplete 6-8). In addition, comparison of this experiment with those at lower proton energies would yield information about the energy dependence of the effective

interaction. The experimental differential cross section for the excitation of the 0.908 MeV

level for the major portion of the angular range 17°-120 ° was reported in a previous paper 9), but the work reported here closes the gap in the very interesting region 23°-30 °, where the inclusion of spin flip and exchange could produce significant differences from calculations which do not include these effects.

In addition to providing stringent tests of the microscopic model of inelastic scattering, the present experiment may be used to test the weak-coupling model, in which the excited states of 89y are described by the coupling of a 2p½ proton to the excited states of the 88Sr core. Previous experiments have shown that this weak- coupling model does not describe the excitation of the low-lying levels of 89y without

89y(p, p,) 447

changing the deformation parameters of that model 6, 8,10,11). A recent experiment 12) and the present experiment show that all of the states were not resolved in the earlier experiments.

The experimental differential cross sections for the excitation of the first seven excited states in 89y with 61 MeV protons are analysed using the weak-coupling model and, where appropriate, the microscopic model including core polarization 2). The sensitivity of the analysis to the inclusion of core excitation and spin-flip con- tributions is also investigated.

2. The experiment

Since the primary objective in studying the inelastic scattering of 61 MeV protons from 89y was to obtain the differential cross sections for the excitation of the weakly excited low-lying single-particle levels, the best energy resolution possible was needed to separate these peaks from the strong peaks due to elastic scattering from carbon, nitrogen and oxygen contaminants. For this reason, the broad-range spectrograph facility at the Oak Ridge Isochronous Cyclotron (ORIC) Laboratory was used. A de- tailed description of this facility has been given by Ball 13). The nominally 61 MeV proton beam from the ORIC was analysed by an n = ½, double-focussing magnet with a 183 cm radius of curvature. With entrance and exit slits of this magnet set to the same opening of 1.8 mm, an energy resolution of 1 part in 1000 was obtained. Beyond this analysing magnet, the beam was focussed into a spot about 2.5 mm wide at the centre of the spectrograph scattering chamber by two successive triplet quadrupole magnets and the height of the spot limited to 8.5 mm by tantalum slits. The beam intensity was monitored by a small Faraday cup placed inside the scattering chamber, because it is of the "windowless" type, in which a steel band attached to the spectrograph moves relative to the wall of the scattering chamber when the scattering angle is changed.

The protons scattered from the 89y target were deflected by the magnetic field of the spectrograph and detected at the focal plane with Ilford 5.2 x 25.4 cm nuclear track plates, which had G5 emulsions 50 ¢tm in thickness and extra plasticizer. An aluminium absorber of thickness 1.78 mm was placed directly in front of these plates to stop all heavier particles from proton-induced reactions with the same rigidity, but a 25 l~m thick mylar sheet thickness was placed between the absorber and the emulsion to protect the emulsion from damage by the aluminium absorber. In earlier exposures, Kodak NTB and Ilford K2 emulsions were tested, but the 54 MeV protons entering the emulsions produced tracks, which were practically invisible against the background silver grains. The discrimination of proton tracks was quite clear in fresh Ilford G5 emulsions, even though they are more sensitive to the relatively high X-ray and gamma-ray background present in this experiment.

The Ilford G5 nuclear track plates were developed for 10 rain in "Brussels" amidol solution, stopped for 8 rain in 2 ~ acetic acid solution, fixed for 75 rain in 30 ~o sodium

448 A. SCOTT et al.

thiosulphate solution and washed for 75 min in tap water. During early tests, it was discovered that it was advisable not to exceed a temperature of 19 ° Celsius at any stage of the processing in order to avoid distortion of the emulsion and curling of the proton tracks. The number of proton tracks in successive strips 0.5 mm wide (about 19 keV for 60 MeV protons with the magnetic field at 8 kG) and 20 mm long was counted by the track counting group at the University of Georgia. A magnification of 200 times was used on Bausch and Lomb binocular "Dynazoom" microscopes with stages modified by the Search Corporation, Tallahassee, with dark field il- lumination.

Proton spectra were obtained from plates exposed in the broad-range spectrograph with its entrance collimator successively set at angles ef scattering over the range 17°-120 ° . The angular acceptance in the scattering plane was 3 ° for most of the data, but at angles where difficulties were encountered from contaminant peaks, an angular acceptance of 0.5 ° or 1.0 ° was used. The absolute solid angle of the spectrograph and the effective target thickness were estimated by comparing the elastic scattering from the 89y target with elastic scattering from a 9°Zr target at a number of angles of

scattering using the identical spectrograph solid angle as in the inelastic scattering exposures for the S9y experiments. The differential cross section for the elastic scattering of 61.4 MeV protons from 9°Zr had been measured earlier by Fulmer et al. 14) using a Na(TI) scintillation detector, but at this proton energy the resolution was not good enough to measure the elastic cross section for 89y without errors caused by oxygen and carbon contaminants. The cross section for elastic scattering of 61.4 MeV protons from 89y was assumed to be the same as for 9°Zr at the same energy. The absolute error in the elastic differential cross section for 9°Zr was about 7 ~ , therefore this calibration contributes the same uncertainty to the absolute values of the inelastic cross sections for s 9y. Another estimate of the solid angle using the Magnet Spectrograph Data Analysis Code 15), assuming the target to be of uniform thickness, agreed with the estimate f rom the comparison of the 90Zr elastic-scattering measurements described above.

The inelastic scattering data for s g y were accumulated in several different beam runs, and different solid angles were used on some occasions. The relative normaliza- tion of data was determined by making short plate exposures during each beam run at a number of selected angles to observe the elastic scattering from 89y with the identical solid angle, effective target thickness and Faraday cup calibration as in the corresponding inelastic-scattering measurements.

Since the differential cross sections for the single-particle states are small and the intensity of the proton beam in the Faraday cup was only from 10--20 nA for most of this experiment, it was necessary to use relatively thick (9.6 and 6 mg/cm 2) 89y targets. The relative importance of elastic scattering from surface contaminants is reduced if thicker targets are used. These target thicknesses do not significantly influence the energy resolution at this energy, because the energy loss of 61 MeV protons in S9y is small (approximately 6.5 keY" cm2/mg).

Sgy(p, p,) 449

4 0 0

3 5 0

3 0 0

E E 250 u3

200

o o

150

I00

50

ny (paJ}

Ep- 61,2 MIV 8 "33" • '~O -=,

¢

3.61 4.31

,

80 100

PJ.

2.87

14 N

?..~3

2.22

1.5i

] ["/

140 160

O,90B

' I

+,, , l _ 0 120 180 220

D!STANCE ALONG PLATE(ram)

89 Yet

2GO'

Fig. 1. Spectrum of protons scattered at an angle of 33 ° from sgy with the spectrograph acceptance angle set to 1 °. The elastic cross section at this angle is three orders of magnitude greater than that

for the 0.908 MeV state.

5 0 0 -

89y (p,p,) 16 !i Ep = 61.2 MeV (3/

I 8 : 2 5 * I 400~- AS= ~* /

~ 3 0 0 +2c t

Z

8 zoo ]

,oo 7 I L / / , [4 N

40 35 30 26 DISTANCE ALONG PLATE(mm)

Fig. 2. Spectrum o f protons scattered at an angle of 25 ° f rom the 9.6 mg/cm 2 .R9y- target with the spec t rograph acceptance angle set to 1 °. This shows the difficulties caused by elastic scat ter ing from

contaminants.

/

e9y 0.908 MeV

500:

E E i£)

g

i

J E I

150 L

• 160 t . . . . 89y (p,p,) Ep= 61,2 MeV 0- Z7 ° A0=0"5° /

egy

12C 0.908 MeV

45 50 55

DISTANCE ALONG PLATE (ram)

Fig. 3. Spectrum of protons scattered at an angle of 27 ° f rom the special 6 mg/cm 2 89y target. The spec t rograph acceptance angle was 0.5 + . The focal p lane was shifted to minimize the widths of the elastic peaks from contaminants .

4 5 0 A. SCOTT e t al.

The first 89y target used was rolled into a 9.6 mg/cm 2 thick foil by the O R N L Isotopes Division, and the thickness was determined by weighing. Since elastic scat- tering calibration plates were exposed during each run, the non-uniformity of the target introduced a negligible uncertainty into the cross sections. An example of the spectra observed is shown in fig. 1. An overall energy resolution (FWHM) from 39 to 50 keV was obtained due mostly to the energy spread in the incident 61 MeV beam. With this initial 89y target, it was found that the peaks due to protons elastic- ally scattered from carbon, nitrogen and oxygen contaminants obscured the 0.908 MeV 89y peak in the interesting angular range 24°-32 °. This difficulty is illustrated in fig. 2.

Since it was believed that good data at forward angles would more stringently test the microscopic model of inelastic scattering, we obtained a new 89y target which was specially prepared to minimize the content of carbon, nitrogen and oxygen con- taminants. This target was prepared by the O R N L Isotopes Division, by vacuum distillation and the metal was then rolled in an argon atmosphere into a self-supporting 6 mg/cm 2 thick foil. This foil was then stored in an argon atmosphere until used.

To obtain data with this new target in the angular range 24°-32 ° where contaminants were troublesome, the angular acceptance of the spectrograph in the scattering plane was reduced to 0.5 ° , and the focal plane position was set so that the first-order focus- sing was appropriate for the oxygen, nitrogen and carbon contaminants. These changes reduced the width of the contaminant peaks markedly. The much improved spectrum near the 0.908 MeV peak of 89y is shown in fig. 3 for a scattering angle of 27 °, the low-contaminant target, an angle of 0.5 ° in the scattering plane and the focal plane adjustment described above. Normalization of data with this new target to that taken with the other a9y target was made by repeating elastic and inelastic scattering with both targets at a number of angles using the same solid angle. The Faraday cup calibration was the same, because these measurements were performed close together in the same beam run.

A peak corresponding to an 89y level at 2.62 MeV excitation may be clearly seen in fig. 1, and at most other angles, although the cross section is small and its peak is on the side of the much stronger peak of the 2.53 MeV collective level. This 2.62 MeV level was not reported in other recent inelastic proton scattering experiments 6,8), but its existence was demonstrated in earlier (n, n'7) and beta-decay experiments 16,17) and was confirmed again recently in an inelastic proton-scattering experiment with 9 MeV protons 12). The large errors shown in fig. 15 for the differential cross section for this 2.62 MeV level are due to its low intensity and the uncertainty associated with the subtraction of the nearby peak of the 2.53 MeV collective level.

According to a recent experiment by Hinrichsen et al. 12), the 2.53 and 2.87 MeV peaks each include two levels. The second level at 2.572 MeV excitation is only about 15 ~o of the 2.53 MeV peak intensity in their work, but the second peak at 2.890 MeV excitation was too close to the 2.879 MeV peak to be resolved even in their experiment with 9 MeV protons.

89y(p, p,) 451

The experimental differential cross sections for all the 8 9y levels studied are shown

in figs. 4-18 with the results of collective-model and microscopic-model calculations, which are discussed in sect. 4. The errors shown with the experimental data include those due to counting statistics, an estimate of the error due to background sub- traction and an estimate of the scatter of the track counting itself. The reproducibility of the track counting was found to be within + 5 % by having a fraction of the plates scanned more than once by different individuals. The track counting was slower than with lower-energy protons or heavier particles because, even in the G5 emulsions used, the stopping power of the 54 MeV protons produces significantly lower track density, and there was an appreciable background of gamma rays.

3. Theoretical models

The calculations of the inelastic scattering amplitudes were all carried out in the distorted wave approximation 1). Exchange effects between the projectile and target nucleons were not included explicitly, although some of these effects will be hidden in the effective interactions or form factors.

The optical model used to describe the elastic scattering was of the form used by Fricke e t al. ~ 8). The actual optical-medel parameters used in these inelastic scattering calculations are those found by Fulmer e t al. 14) for the scattering of 61.4 MeV protons from 9°Zr with the average geometry parameters

r o = 1.16fro, a = 0.75 fro,

rs = 1.064 fro,

The other optical-model parameters were

V = 42.9 MeV, W = 4.7 MeV,

t r o = 1.37 fin,

as = 0.738 fro.

W D = 4.0 MeV,

a ' = 0.63 fro,

V s = 6.04 MeV.

3.1. THE WEAK-COUPLING MODEL

In this model, the ground state of 89y is considered to be a single proton occupying a 2p~ state outside a 88Sr core. The excited states of 89y are then formed by coupling this 2p.~ proton to the various excitations of the 88Sr core. Since the excited states of the S8Sr core may be expected to contain some components in which the 2p~ proton state is occupied, these states are expected to be modified by the blocking effects caused by the Pauli exclusion principle. In particular, it is expected that the magnitude of the deformation parameter /~L found for the excitation of the Lth multipole in 88Sr will be an upper limit to the value found when exciting the corresponding multipole in 89y.

When the collective model is used there arises an interesting sum rule relating transition probabilities. In particular, if the extra-core particle has a total angular momen tumj , then one expects 2 j+ 1 excited states of the composite system for each core excitation in which J~or~ is greater t han j . In the case of a9y, j = ½ and one

452 A. SCOTT et al.

expects a sequence of doublets if this weak-coupling model is valid. The sum rule is

E a,,,,~(0) = ao.~(0)oo~o, If

o r

E B(EL; I i --+ If) : B(EL; 0 --+ L, core). I f

The above sum rules may be combined by introducing a partial deformation parameter

flL(Ie) = ( 2 I , + l ) ( 2 L + l ) J ilL.

The sum rule then becomes

Z flLZ(If) = / 32. If

From the above discussion (since all of the transition probabilities are proportional to f12), it is expected that the transition rates of the 88Sr core will be an upper limit to the sum of the corresponding transition rates in 8 9 y .

In the collective model of inelastic scattering, the form factor for a transition of multipolarity £ is given by 1)

<fllVlli> oc tic dU(r) , dr

where the deformation parameter ]?L is the only unknown parameter in the theory. The flL may also be determined from the relevant electromagnetic transition strength if it is known. In this work, it is assumed that both the real and imaginary parts of the optical potential undergo shape oscillations characterized by the same deformation parameter.

3,2. T H E M I C R O S C O P I C M O D E L

In this model, the zero-order ground state of s 9 y is taken to be a single 2P½ proton outside a SSSr core, but the excited states are described by either exciting this particle to a higher-lying shell-model orbit or by promoting one of the core particles to one of the unoccupied levels lying above the closed shell. By zero order is meant the simple individual particle state without the inclusion of core polarization. The single- particle states are taken as eigenstates of a Woods-Saxon potential. The relevant bound-state parameters are given in ref. s). In this microscopic description, the form factor is given by the nuclear matrix element of some effective interaction 1I. Following Johnson et al. ~), we write V = ~ V~v, where V~p is an effective two-body interaction between the projectile p and the ith target nucleon. This interaction V~p is assumed to have the following central form:

v , , = - { + V o e % " + . + .

89y(p, pt} 453

This yields the form factor

Fus(rp) = [ML 6(S, O) + N u 6(S, 0]IL(rp),

where the quantities are defined by Johnson et al. 1). The subscript S on FLss(rp) corresponds to the transferred spin angular momentum, L to the transferred orbital angular momentum and J to the total angular momentum transfer which obeys J = L+S. The first two terms of the interaction Vip above give rise to S --- 0 am- plitudes, and the last two terms are associated with S = 1 amplitudes. It has recently been shown 2) that the inclusion of core polarization requires the replacement of

FLsj(rp) by FLsj(rp), w h e r e

TL(rp) = Iz(rp) +(4hi/o)- ~yL(Q)(n212 jzlko[n, l, j~ )kp(Fp). H e r e kp(rp) is the usual collective form factor, and the other quantities are defined by Love and Satchler 2). As indicated by the assumed form of the effective inter- action Vip, there is an isospin dependence of the Fzsj(r~, ), but we deal exclusively with the excitation of protons by protons, therefore the combination Vs~+ Vs# will always participate and will henceforth be denoted by V s. The form of g(ri,) in the expression for V~p above will be restricted to a Yukawa interaction of range 1 fm.

Corresponding to each FLsj(r) or Fzsj(r) there will be associated one amplitude and a labelling triad (LSJ). Since the amplitudes belonging to different values of J are rigorously incoherent, and those corresponding to different values of S are approximately incoherent s), we may write

-~ (0) = const 2Jr+ 1 E azss(O), 2J i + 1 LsJ

where aLsj(O ) is the partial cross section corresponding to the form factor FLss(r) or /~Lsj(r). The relevant nuclear matrix elements ML and Nza for this microscopic- model analysis of 8 9y are given in ref. 8).

4. Analysis of the experiment

4.1. THE 0.908 MeV STATE

The experimental cross section for the excitation of this level in 89y is given in table 1 and shown in figs. 4-7. Since this excitation is thought to be a single-particle transition, it is analysed principally in terms of the microscopic model, but for comparison the collective-model calculation is shown in fig. 4. The deformation parameter f15 = 0.0451 from this calculation is smaller than that found at lower proton energies 7,8). This disagreement is probably because the experimental angular distribution in the present experiment is more complete and strongly structured than for lower proton energies, thus less freedom is allowed in choosing the normaliza- zation of the calculation to the experimental data.

454 A. SCOTX et al.

In the microscopic model, a particle is excited from the 2p~ state to the lg~ state.

The par t ic ipat ing triads (LSJ) for this t ransi t ion are (505), (515), (514) and (314).

The S = 1 part ial cross section is domina ted by the (314) triad, because small

angular m o m e n t u m transfers are favoured, and in addi t ion the (514) nuclear matr ix

element is small. An upper limit to the sp in- independent part of the interact ion V0

was obta ined by setting the S = 1 cross sections equal to zero and ignor ing core

polarizat ion. The result ing fit to the data is shown in fig. 5 for Vo = 100 MeV,

TABLE 1

Differential cross sections for the excitation of the 0.908 MeV state in 89y by 61.2 MeV protons

0 . . . . O" . . . . ( 0 ) Overall error a) in cr .... (0) (deg) (mb/sr) (mb/sr)

17.20 1.51 × 10- t z~0.68 × 10-1 18.20 1.67 ±0.22 19.22 2.04 3:0.20 21.23 1.86 ~0.19 23.26 1.88 ~0.27 24.27 1.54 ~0.15 27.30 1.78 ~0.40 29.32 1.55 ~0.45 33.36 1.77 ±0.14 34.37 1.84 &0.11 36.39 1.97 :£0.15 38.40 1.70 ~0.16 40.42 1.31 ~0.11 43.44 9.93 x 10 -z ~1.12 × 10 -z 46.47 6.61 -~0.75 50.50 3.84 ~0.69 55.53 3.09 ~0.45 60.56 2.12 ±0.28 65.59 1.19 ±0,17 75.63 1.44 ~z0.21 80.64 7.68 x 10 -3 ~1.38 × 10 -3 90,65 3.10 +0.60

100,64 1.69 J-0.35 105,63 2.02 i0.51 120.57 5.38 × 10 -~ -k2.69 x 10 -~

a) This includes counting statistics, an estimate of uncertainties in the subtraction of backgrounds from elastic peaks of contaminants and an estimate of the reproducibility of the track counting.

bu t the shape is not very good. Therefore the normal iza t ion is no t well determined.

Similar calculations were performed by varying the inverse range ~ of the Yukawa

interact ion between 1.4 and 0.714 f m - 1 with no significant change in shape. An upper

limit on the spin-flip strength V1 was obtained by setting Vo = 0 and ignoring core

polarizat ion. The max imum value of V1 from the compar ison of this calculation with

the experimental data was found to be 47 MeV as shown in fig. 5. The more forward

peaking of this S = 1, L = 3 cross section probably accounts for the b u m p in the

SOy(p, p,) 455

PC"

f .~ -zl = I 0 ~ . . . . .

I

b

I

20

I - - ¥ (p, ~'l . ~ . gp:61.2 MeV

- - ~ ~- - O : - 0.908 MeV

1 ~ . ~ Collective Model - - ~ ~ #5 (9/2)=0.030

,8~ :0.0451

0 40 60" 80 I00 120 140 8c.M.(degrees)

Fig. 4. Experimental data compared with a col- lective-model calculation for the excitation of the 0.908 MeV state. The bars on the data points are overall errors including uncertainties in sub-

traction of background from contaminants.

I ~ ? Q=-O.9OSMeV" F ~

- 2 ', ÷ io

_--Vo:,OOMeV I-- - t ,d . . . . v,:.U ey I , t , -

0 20 4.0 60 80 I00 120 14.0 Oct.(degrees)

Fig. 5. Experimental data compared with micro- scopic-model calculations for the excitation of the 0.908 MeV state without core polarization.

Upper limits for Vo and V~ are determined.

"2

0 20 40 60 80 I00 120 140 Oc. M. (degrees)

Fig. 6. Exper imenta l data compared with a micro- scopic-model calculat ion for the 0.908 MeV state including core po la r iza t ion but excluding S = 1

transfer.

I I I P L / -[ --~ Q=-O.908MeV-- - - - 7

,~ I ~ 1 - - C+D, Vo=~O, v,:2o - ~ . r J / T , ( ~ [ ~ . - . . . . C + D V o = 3 0 , V = O i

' ~ ~/...:'L ~ - - D,Vo=O,V,=2o~

• ! ,, , ]

P , - ~ , ' - x

0 20 40 60 80 I00 120 140 ~C.ll (degrees)

Fig. 7, Experimental data compared with micro- scopic-model calculations for the excitation of the 0.908 MeV state including both core polar-

ization and S = 1 transfer.

456 A. SCOTT et al.

experimental cross section at about 20 °. These upper limits to Vo and V1 for 61 MeV protons of 100 and 47 MeV may be compared with the corresponding values of 164 and 63 MeV for 24.5 MeV protons 8). By adjusting the ratio of V1 to Vo until the fit is optimized, a more reasonable value for V1 could be determined, but this was not done because core-polarization effects have not been included up to this point.

An estimate of the core participation may be made using the value for the core- coupling parameter Ys(Q) of 1.61 x 10-3 MeV-1, which was obtained from the elec- tromagnetic excitation 2) of the 5- state in 9 0Zr" With this value of the core-coupling parameter, a real Vo of 50 MeV predicts the correct magnitude of the cross section when the S = 1 contribution is ignored. This calculation is shcwn in fig. 6. If the S --- 1 contribution is included with a strength V1 = 20 MeV in addition to core polarization, a value for Vo of 30 MeV is sufficient to account for the magnitude of the experimental cross section. Fig. 7 shows that this calculation also fits the shape of the experimental cross section better than the other calculations. From calculations for the excitation of the 1.51 MeV state, a spin-flip strength Va = 20 MeV is as much as can be permitted by that experimental cross section t. Scott et al. 19) have found that I V l o - V I ~ I = 10 .5+4 .7MeV by exciting the 3.475 MeV 4- state in 2°spb with 61 MeV protons. Austin et al. 20) obtained a value for V 1 in the range 28-74 MeV for protons scattered from 6Li, but this may not represent the effective inter-

action for heavier nuclei. For 61 MeV protons, olae may be guided by the impulse approximation. If one

fits the Fourier transform of a Yukawa of range 1 fm to the absolute square of the antisymmetrized, free two-nucleon t-matrices as generated by the Hamada-Johnston potential 21) at zero momentum transfer, one obtains

IVjol ~ 3.4MeV, IVall ~ 13.5 MeV.

These values are consistent with the above V1 from the neutron excitation in Z°SPb and with the V1 = IV10 + V111 = 20 MeV assumed in the calculation for this proton excitation in 89y. The data for 6Li indicate 2o) that 1Ilo lies in the range 20-50 MeV,

which is definitely inconsistent with these other estimates. The present values of the interaction strengths must be regarded as tentative, since

the effects of exchange were not explicitly included. The work of Atkinson and Mad- sen 4) without core polarization indicates that the effects of exchange may be rel- atively more important for this high multipolarity transition than for a transition of lower angular momentum transfer.

4.2. THE 1.51 AND 1.74 MeV STATES

The excited states of 89y at 1.51 and 1.74 MeV are believed to be negative-parity levels with spins of ~ and ~, respectively 7,1 o.11). Such a doublet suggests the weak coupling model, because these are the values of J~ expected from the coupling of a p~ proton to the 2 + collective excitation of 88Sr. Although the B(E2) values to these levels

t See subsect. 4.4.

89y(p, p,) 457

are about one single-particle unit ~a), and recent 9°Zr(d, 3He)99y measurements ~) indicate a single-hole character of these states, the weak-coupling model including Coulomb excitation was applied to these leveL. The comparisons of these calculations with the experimental cross sections are shown in figs. 8 and l 1 for the excitation of the 1.51 and 1.74 MeV levels, respectively. The deformation parameters obtained from this comparison are listed in table 2 with parameters from other experiments.

TABLE 2

Deformat ion parameters for transitions in s9y

Nucleus E~, Electromagnetic ~) Other (p, p ' ) ~) (MeV) jzr L flL(lO i lL( l ,)

Present (p, p ' ) experiment

89y 0.908 ~+ 5 0.0408 0.0305 0.00112 0.045 s9y 1.505 ~]- 2 0.0378 ~-0.0183 0.0404 0.032 0.001 0.051 Roy 1.742 ~ - 2 0.0413+0,006 0.0512 0.045 0.002 0.058 *SSr 1.84 2 + 2 0.111 ±0.003 0,017 ~) 0.13 ~) s9y 2.217 ~+ 3 0.116 --0.005 0.103 0.095 0,009 0.14 g9y 2.525 ~+ 3 0.123 ±0.005 0.115 0.100 0.010 0.13 89y 2.622 (~-+) (5) 0.0372 0.00139 0.055 a) s9y 2.873 (~+) 3 0.114 ±0,005 0.0975 0.089 0.008 0.12 SSSr 2.74 3 - 3 0.180 ±0.003 0.040 ~) 0.200 e)

") See Peterson and Alster ~a). ~) See Benenson et al. s). d) This value of f15 assumes If = -~+.

¢) See Stautberg et al, 6).

F F • T~ e%y (p, ~ ) Z

~ ~ Ep:6t.2 MeV ~ - - - ~ - - - = -I Q = -1.51 M e V

,0]~ _ I __] Conectve Mode

- I . . . . .

0 20 40 60 80 IO0 120 0c. M (degrees)

140

Fig. 8. A collective-model fit to the experimental cross section for the excitation of the 1.51 MeV state. The bars on the data points are overall errors including uncertainties in subtraction o f back-

ground from contaminants.

458 A. SCOTT et al.

These deformation parameters for 61 MeV protons are in reasonable agreement with the other values, but they are both slightly lower than from the experiment with 24.5 MeV protons ~). The shape of these collective model angular distributions in figs. 8 and 11 are in reasonable agreement with the experimental cross sections, and the cross sections are approximately proportional to 2J~+ 1 as predicted by the weak- coupling model, but the transition strengths to this doublet exhaust only 30 or less of the sum rule. This disagreement with this sum rule was also found in the experiments with lower-energy protons 6,~).

Bey (p,p,)

Ep= 612 Me',/ Q = - 1.51MeV

I0 o C+D :+ - 1.5 o- [C

- ~ ' ~ -' D Vo=BOMeV "2 " k 3 ,== I.O fm-

"o -2 - - I / .~ • t

I . , [

0 20 4 0 60 80 I00 120 140 OC.M. (degrees)

Fig. 9. Experimental data compared with a micro- scopic-model calculation for the excitation of the 1.51 MeV state including core polarization but excluding S = 1 participation. The mixing param-

eters are a = 1, b = 0.

eey (p,p,)

F I Q= -- 1.51MeV , - = - I I ~ - - I °=o.8 b:O.6 ~z-'~a

I ol ] - - e * o [ ] 0 ~ _ . . . . . C

D Vo=6 9 MeV a = LO f m - I ~

"o

1-2 3

0 20 4 0 6 0 80 I00 120 140 0c. M. (degrees)

Fig. 10. Experimental data compared with a micro- scopic-model calculation for the excitation of the 1.51 MeV state including core polarization but excluding S = 1 transfer. The mixing parameters

are a = 0.8, b = 0.6.

A more reasonable description of the excitation of these two levels is believed to be given by the microscopic model. In this model, the ground, 1.51 MeV and 1.74 MeV levels are believed to be described as

Hz-, g.s.) = 12p~)188Sr),

I~-, 1.51 MeV) = 12p~ 1){alp~) + b[g~)},

I~-, 1.74 MeV) = Ilf~-l){a'lp~) + b'lgZ)},

assuming the k - and ~- states are excited from the ground state by promoting a p~ proton or a f~ proton, respectively, to the p~ state. Spectroscopic factors from a

89y(p, p,) 4 5 9

9°Zr(d, 3He)SgY experiment indicate s) that the choice a = a' = 1 is reasonable, and that b and b' are small. This set of "mixing" coefficients leads to theoretical cross sections which are compared with the experimental results in figs. 9 and 12 for the 1.51 and 1.74 MeV levels, respectively. Core polarization and Coulomb excitation are included, but S = I transfer is not included. A range of core coupling parameters y2(Q) is possible 8) due to the range of B(E2) values allowed by the errors in the electron-scattering experiments from which the B(E2) values are deduced. Using those values of y2(Q) in the analysis of the present experiment leads to a range of values of the direct strength V o for these two transitions

½- ~ ~ - 60 MeV < Vo < 100 MeV,

½- ~ ~ - 90 MeV < Vo < 120 MeV.

These values of Vo are upper limits because the S = 1 part of the interaction has been neglected thus far. The quality of the fit to the cross section for the k - level is poorer than that for the ~- cross section. The ratio of the strength V o required in the 25-- excitation to that in the ~ - excitation is smaller than this ratio was for excitation with 24.5 MeV protons. This calculation for the ~- excitation with the direct contribution alone is not as good a fit as the collective one alone, whereas for excitation with 24.5 MeV protons the direct calculation alone was almost as good as the collective one alone 8).

Since for protons the relative amount of core participation depends upon the mixing parameters a and a', new values of 0.8 were taken and the above calculation repeated. These values for a and a' are the same as for the ground state of 9°Zr [ref. 5)]. The results of the calculations with these new mixing parameters are shown in figs. 10 and 13 for the 1.51 MeV and 1.74 MeV levels, respectively. No significant improve- ment in the fits to the angular distributions was found, but with this mixture the ranges of Vo were

½- ~ ~ - 40 MeV < V0 < 100 MeV,

1-- ~ - - ~ --+ 110 MeV < V o < 145 MeV.

Apparently a much larger change in the mixing parameters a and a ' is required to significantly alter the shape of the calculated cross sections. Much smaller values of these parameters would be inconsistent with available spectroscopic information 5).

Up to this point, the analysis for these states has neglected the S = 1 contributions, but these two states are particularly interesting in this respect since excitation of the ~ - state introduces the (LSJ) triads (01 I), (211), (202) and (212) and excitation of the ~- state involves the triads (212), (202), (213) and (413). The interference between triads of different S or J is neglected. Small nuclear matrix elements associated with the (211) and (213) triads cause these contributions to be negligible. In the case of the excitation of the z2-- state, the nuclear matrix elements N0~ and N22 are approximately equal, but the calculation favours the lower L transfer. For the excitation of the ~--

460 A. SCOTT et al.

Sgy (p,#)

Ep =61.2 MeV Q = - 1.74 MeV

10 ° Collective Model _ ~z c % ) : o . o 4 5

"E B 2 =0.058

3 _ _ _

0 20 40 60 80 I00 120 140 Oc. M.(degrees)

Fig. I 1. A collective-model fit to the experimental cross section for the excitation of the 1.74 MeV state. The bars on the data points are overall errors including uncertainties in subtraction of

background from contaminants.

~- -oy (p,p.)

E p =61.2 MeV Q=- - 1.74 MeV 0'=0.8 b':O.6 ~2--5/2

o ~ - - C-~D I0 Core + CE

~ . . . . . D Vo== ll6,a : ,.Ofm -'I

Z

:J?, 0 20 40 60 80 tO0 120 140

8c.kt (deqrees)

Fig. 13. Experimental data compared with a microscopic-model calculation for the excitation of the 1.74 MeV state including core polarization but excluding S = 1 participation. The mixing

parameters are a ' ~ 0.8, b' = 0.6.

"2

E 3

b

0 20 40 60 80 I00 120 140 8c-~t (degrees)

Fig. 12. Experimental data compared with a microscopic-model calculation for the excitation of the 1.74 MeV state including core polarization but excluding S = 1 transfer. The mixing pa r a m-

eters are a ' = 1, b' ~ 0.

~..~t j egV =,p,p ~ i

Ep= 61.2 MeV Q = - I .51MeV _ . o=I b=o, ~ - ' ~ / ~

, , , , , , / " " { ' , ~ . . . . C÷D.Vo=3OM,V,V,=O I ( ~ l ~ i ! ----- D, Vo=O,VI=2OMeV

~ = ; ~ - - C+D, Vo = 30,Vl = 2 0

,,~,,

0 20 40 6 0 8 0 I00 120 140 8C.M.(deorees)

Fig. 14. Experimental data compared with a microscopic-model calculation for the excitation of the 1.51 MeV state including core polarization and S = 1 transfer. The mixing parameters are a = 1, b = 0. An upper limit for V1 is determined.

"2

¢

89y(p, Dr) 461

state, the matrix element N4a ~ 2N22, therefore, despite the fact that small L transfers are favoured, the triads (212) and (413) contribute about equally. These nuclear matrix elements are listed in ref. s).

The result of including the S = 1 contribution to the excitation of the ~- state is to introduce an additive cross section ten times as large as the direct S = 0 cross

section if V t = Vo, but for the excitation of the 5 - state the S = 1 cross section is about the same magnitude as the direct S = 0 cross section. Clearly the excitation of the 5 - state is much more sensitive to S = 1 participation than is the excitation of either the 5 - state or the ~+ state. An upper limit to the magnitude of the spin-flip strength V1 may be obtained by ignoring any S = 0 contribution to the excitation of the az- state. This gives [Vll < 24.5/a MeV. The fit of this calculation to the experi-

mental cross section is very poor, thus V1 is undoubtedly less than this. The value of a is very near unity, therefore ]VI] N 25 MeV. The excitation of the 5 - level can tolerate a much larger V1.

For comparison with the excitation of the ~-+ state, fig. 14 shows the experimental and theoretical cross sections for the excitation of the 2 a-- state when one includes core

polarization and S = 1 contributions with V0 = 30 MeV and V1 = 20 MeV as in the calculation for the excitation of the ~+ level. The mixing parameter b = 0 for this calculation. The agreement with experiment is perhaps slightly improved at forward

angles, but for angles greater than 50 °, the theoretical cross section is far too small. This same feature is present in the ~+ cross section to a much lesser extent. Several changes in the calculations could improve the fit. One change would be to decrease the range of the interaction, but for the ~-+ excitation, it was found that changing the

parameter e in the Yukawa interaction from 1.4 to 0.714 fm-1 caused no significant change in shape. Stronger core participation may also help, although the weak-

coupling calculation indicates that the core contribution is slightly deficient at back

angles also. The inclusion of exchange effects might increase the cross section at back angles.

Including the S = 1 amplitudes in the calculation for the 5 - excitation has very little effect if V~ is taken to be about 20 MeV even with b' = 0. Using a much larger

V~ of 50 MeV only reproduces about 10 or 20 ~ of the total differential cross section with a ' = 1, therefore a strength V0 of about 100 MeV is required even when S = 1 contributions are included. This suggests at least four possibilities. There may be another mechanism not already included which might enhance this cross section, our estimate of VI which accounts for the cross sections for the 29-+ and ~- states may

not be correct, the 5 - state may not be as well described by the shell model, or the S = 1 interaction may have a shorter range. A shorter range would significantly reduce the difference in the S = I cross sections for the excitation of the ) - and 5- states, because the ratio of the (314) cross section to the (514) cross section (ex- cluding nuclear matrix elements) is about 2 for a zero-range interaction and about 4 for a Yukawa with ct = 1 fm-1. Even more pronounced differences are expected to occur for the (011) and (413) cross sections which arise in the excitation of the

4 6 2 A. SCOTT et al.

~:- and ~- states. Since exchange effects were not yet included in the calculations, no further attempt was made to investigate the effects of changing the range of the interaction.

4.3. T H E 2 .62 M e V S T A T E

This level has not been well enough resolved in recent experiments at lower proton energies 6,8) to determine a complete angular distribution. The experimental cross section for the excitation of this level in the present experiment with 61 MeV protons

is shown in fig. 15 with a calculation using the weak-coupling model for an L = 5

89y (p,p,)

E p =61.2 MeV

~\! I Q ~ - 2 . 6 2 M e V Collective Model

L . . . .

3

b ~1 -3:

IO _

I

0 20 40 60 80 I00 120 140 OC. M. (degrees}

Fig. 15. A collective-model fit to the experimental cross section for the excitation of the 2.62 MeV state. The bars on the data points are overall errors including uncertainties in subtraction of the

nearby collective 2.53 MeV state.

transfer. The agreement is quite satisfactory and a deformation parameter ilL(If) = 0.0372 is obtained. The weak-coupling model predicts a doublet of states associated with the excitation of the 5- core state in 88Sr with a J~ of 2 ~+ and ~-+. This state at 2.62 MeV excitation may be one of those two states or at least possess a large com- ponent of one of them. From the study of the beta decay of 89Zr ' Van Patter and Shafroth have proposed the (2p~)Z(2p~)2(lg~) proton configuration for this state 17).

The small deformation parameter extracted for this state from our collective-model calculation suggests that this is not a collective transition. In their 9°Zr(d, 3He)89y experiment, Preedom et al. 5) did not see a peak at 2.62 MeV excitation in 89y but pointed out that this reaction would not be expected to excite a (2p~)Z(2p~)Z(lg~) configuration at this excitation. This configuration would be consistent with their

8Oy(p, p,) 463

failure to see a peak at this excitation energy. In the present (p, p ' ) experiment, this 2.62 MeV state is excited as strongly as the 0.908 MeV ~+ state, but the excitation of a state with this proton configuration in this reaction is first-order forbidden. The present experiment thus appears to rule out this configuration. The results of an 89y(n, n'7) experiment by Shafroth et al. 16) indicate that a spin assignment of 1@+

is unlikely, thus existing evidence points towards a ~+ assignment but against the proposed configuration.

4.4. THE 2.22, 2.53 AND 2.87 MeV STATES

These three strongly excited levels, which are believed to have spin assignments of }+, ~-+ and ~+, respectively, have differential cross sections that are well described

iJ "2

u~

E

3

b

e9y {p, p,) Ep :6r.2 MeV

~ ~ Q:- 2.22MeV

Collective Model -~-~ ~,~3 (%1=o.o9s ,83=0J4

f

I _5 0 20 40 60 80 I00 120 140

8 c. M. (degree s)

Fig. 16. A collective-model fit to the experimental cross section for the excitation of the 2.22 MeV state.

by the collective model if one assumes an L = 3 transfer. The experimental cross sections and collective-model calculations are shown in figs. 16-18 and the deforma- tion parameters are shown in table 2. These deformation parameters for the ex- citation of the 2.22 and 2.87 MeV levels are both smaller by about 10 ~ than the corresponding values of/~3 from the experiment with 24.5 MeV protons 8). The/?3 for the 2.53 MeV excitation is about 15 ~ smaller for 61 MeV protons than for 24.5 MeV protons, which is probably because the 2.62 MeV peak was not resolved from the 2.53 MeV peak in the lower-energy experiment. In a recent experiment with 9 MeV protons, Hinrichsen et al. 12) found that the intensity of the 2.572 MeV peak was only about 15 ~ of the 2.532 MeV peak intensity, therefore the shape of

464 A. SCOTT et al.

the experimental cross section and the deformation parameter deduced for the excitation of the 2.53 MeV level with 61 MeV protons is only slightly affected, if the relative intensity of the 2.572 MeV cross section is the same at the higher energy. Comparison of the shapes of the cross sections for excitation of the 2.22 MeV and 2.53 MeV levels with 61 MeV protons supports this assumption.

I _ _ _ ~ ~ @gy (p,p,} ~ i - - - - ~ / c 7 ~ E p =61.2 MeV

Q= - 2.53 MeV

2 I v _ _ _ Collective M o d e l - - - #3 ( 7 / 2 ) = o . l o --

i - - #3=o.13 ]

: - ++_

20 40 60 80 I00 120 140

Oe. ~.(degrees)

Fig. 17. A collect ive-model fit to the exper imenta l cross sect ion for the exci ta t ion of the 2.53 MeV

state.

E

3

b i

0 20 40 60 80 100 120 140 0c. ~t (degrees)

Fig. 18. A col lect ive-model fit to the exper imenta l cross sect ion for the exci ta t ion of the 2.87 MeV

state.

The 2.87 MeV peak was not resolved from another peak at 2.89 MeV excitation which was suggested by Hinrichsen et al. 12). The shape of the experimental cross section shown in fig. 18 for this 2.87 MeV excitation looks quite similar to the ex- perimental cross sections for the 2.22 MeV and 2.53 MeV excitations and to the shape of the L = 3 collective-model calculation. Contributions f rom the 2.89 MeV level are not expected to be important at 61 MeV, because an L = 3 transfer has been found adequate 6) above 19 MeV, even though at 14.7 MeV, the 2.89 MeV level had prevented a good fit to the 2.87 MeV cross section with an L = 3 transfer 7).

As in other experiments at lower proton energies 6,8), all three octupole tran- sition rates must be included to exhaust the weak-coupling-model sum rule, which is difficult to understand in terms of this model.

With the assumption that the same microscopic description of collective wave functions is valid at different projectile proton energies, the very small variation of the deformation parameters/ /3 with proton energy for these states at 2.22, 2.53 and 2.87

sgv(p, p') 465

MeV excitation clearly suggests that the energy dependence of the effective inter- action is very closely related to the energy dependence of the collective-model form factor.

5. Conclusions

The weak-coupling-model analysis yielded reasonable fits to the shapes of the cross sections for excitation of the first seven resolved states in 89y. Using the values of the partial deformation parameters fl2(lf) deduced for the L = 2 doublet at 1.51 and 1.74 MeV exhausts only 30 % or less of the weak-coupling sum rule. From the L -- 3 calculations for the excitation of the states at 2.22, 2.53 and 2.87 MeV, it was found that all three transition rates must be included to exhaust the corresponding sum rule. This is difficult to understand in terms of this model. These conclusions are in agreement with similar analyses of other experiments 6, 7,8, l 0), thus confirming that this simple weak-coupling model is not a complete description. The experimental cross section for the excitation of the 2.62 MeV state is very similar in shape and

9+ magnitude to that for the z state at 0.908 MeV excitation. The collective-model + for this 2.62 MeV state, but calculation is compatible with a spin assignment of

the configuration is uncertain.

A microscopic-model description has been attempted for the excitation of the ~+, ~ - and ~ - states at 0.908, 1.51 and 1.74 MeV respectively. The corresponding values of the S = 0 strength Vo required to describe the cross sections for exciting these levels are about 50 MeV, 80 MeV and 105 MeV, respectively, when a real Yukawa with range 1 fm is used and core polarization is included but the S = 1 amplitudes are ignored. These values of Vo are about 20 MeV smaller than those required in similar calculations for 24.5 MeV protons 8). I f the S = 1 amplitudes are

included, V o can be made as small as 30 MeV and a better fit obtained to the shape of the cross section for excitation of the 0.908 MeV state. The core-coupling parameter for the excitation of this 0.908 MeV state was estimated from that for the excitation of the 5- level in 9°Zr, therefore this may have made the estimate of the direct strength Vo somewhat low. Using the core-coupling parameters found from the excitation of the first 2 + state in 90Zr would overestimate the core participation in the ~:- and ~-- states in s 9 y by a factor of about 3. In the limit of no core participation in the excitation of the 0.908 MeV level, one would obtain a value of V o of about 100 MeV. Less core participation in this excitation would therefore tend to make the values of Vo for the excitation of the 0.908, 1.51 and 1.74 MeV states more compatible.

The transition to the ] - level is the most sensitive to the participation of S = 1 amplitudes in the microscopic model, therefore it was used to place an upper limit on V~ of 25 MeV, but a more reasonable value is about 20 MeV. There is some evidence that the S = l part of the interaction may have a shorter range than 1 fro.

The cross section for the excitation of the ~- state requires a larger value of Vo than does the cross section for the z a - state, because the form factor for exciting the 2 a - state is about , /2 larger than that for exciting the 5 - state. In view of the strong

466 A. SCOTT et al.

similarity of the shape of the cross sections for these two states, it seems likely that

one of these is rather poor ly described by the simple shell-model configurat ion

adopted in this work. Similar conclusions were noted from the analysis of the ex-

ci ta t ion of these states with 24.5 MeV protons 8). Alternatively, the core-coupling

parameters deduced from the electromagnetic t ransi t ion rates may not adequately

describe the par t ic ipa t ion of the core in the inelastic scattering process.

F inal conclusions abou t the react ion mechanism cannot be made at this time,

because effects of exchange were no t explicitly included, and the Yukawa interact ion

may not well represent the realistic in teract ion 22). Finally, the inclusion of the tensor

force may be impor tan t for the S = 1 amplitudes.

We are indebted to G. R. Satchler for his cont inued interest and helpful discussions.

Two of us (A.S. and M.L.W.) wish to thank the staff of the Electronuclear Divis ion

for their warm and helpful hospitality, part icularly the advice and encouragement

f rom J. B. Ball, and R. S. Lord, A. W. Riikola and the O R I C operat ing crews for

their friendly cooperat ion. A. S. and M. L. W. also thank K. A. Amos for helpful

discussions and R. H. Rhodes, J. N. D e F o o r and R. L. Roth for assistance with the

t rack count ing.

References 1) H. O. Funsten et al., Phys. Rev. 134 (1964) Bl17;

N. K. Glendenning and M. Vcneroni, Phys. Rev. 144 (1966) 839; G. R. Satchler, Nucl. Phys. 77 (1966) 481 ; V. A. Madsen, Nucl. Phys. 80 (1966) 177; W. S. Gray et aL, Phys. Rev. 142 (1966) 735; M. B. Johnson et al., Phys. Key. 142 (1966) 748; 154 (1967) 1204; G. R. Satchler, Nucl. Phys. A95 (1967) 1; K. A. Amos, V. A. Madsen and L E. McCarthy, Nucl. Phys. A94 (1967) 103

2) W. G. Love and G. R. Satchlcr, Nucl. Phys. A101 (1967) 424 3) I. E. McCarthy, private communication 4) J. Atkinson and V. A. Madscn, Phys. Rev. Lett. 21 (1968) 295;

W. G. Love, to be published 5) B. M. Preedom, E. Newman and J. C. Hiebert, Phys. Rev. 166 (1968) 1156;

C. D. Kavaloski et al., Phys. Rev. 161 (1967) 1107; D. C. Shreve, University of Washington Nuclear Physics Laboratory Annual Report (1968) p. 22

6) M. M. Stautberg, J. J. Kraushaar and B. W. Ridley, Phys. Roy. 157 (1966) 977 7) Y. Awaya, J. Phys. Soc. Jap. 23 (1967) 673 8) W. Benenson et al., Phys. Rev. 176 (1968) 1268 9) A. Scott, M. L. Whiten and J. B. Ball, Phys. Lett. 25B (1967) 463

10) J. Alster, D. C. Shreve and R. J. Petcrson, Phys. Rcv. 144 (1966) 999 11) G. A. Pcterson and 3. Alster, Phys. Rev. 166 (1968) 1136 12) P. F. Hinrichsen, S. M. Shafroth and D. M. Van Patter, Phys. Rev. 172 (1968) 1134 13) J. B. Ball, IEEE Trans. Nucl. Sci. NS-B(4) (1966) 340 14) C.B. Fulmer, J. B. Ball, A. Scott and M. L. Whiten, Phys. Lett. 24B (1967) 505; Phys. Roy., in press 15) J. B. Ball and K. L. Auble, Oak Ridge National Laboratory, unpublished 16) S. M. Shafroth, P. N. Trehan and D. M. Van Patter, Phys. Rex,. 129 (1963) 704 17) D. M. Van Patter and S. M. Shafroth, Nucl. Phys. 50 (1964) 113 18) M. P. Fricke et al., Phys. Rcv. 156 (1967) 1207 19) A. Scott, N. P. Mathur and G. R. Satchler, to be published 20) S. M. Austin et al., Phys. Rev. 176 (1968) 1227 21) W. G. Love, Phys. Lett. 26B (1968) 271 22) G. R. Satchler, private communication