gamma–ray spectroscopy! part vi nuclear lifetimes and...

Gamma–ray spectroscopy !Part VI!!!

Nuclear Lifetimes and Moments!Measurement!

! Lifetime measurements!–  bound excited nuclear states!–  determination of absolute transition matrix elements!–  reduced transition probabilities!

–  B(E2;2+à0+) – ground state deformation!–  collectivity of exited states!–  shape coexistence!

!

! Nuclear moments measurements!–  sensitive probes of the structure of the nucleus!–  magnetic moments !

–  sensitive to the single particle configurations (mixing)!–  quadrupole moments !

–  sensitive to collective properties (polarization, deformation, effetive charges)!

! ! !!!

Objectives!

µ = gI

Q = e 3zi2 − r 2( )

i=1

A

∑

! Excited nuclear states!–  remain excited for a lifetime τ

τ >10–22 s width becomes smaller than the separation between ! states!!!!where M is the operator for the decay and ψi, ψf are the wavefunctions of the initial and final states!!

if more decay modes are concurrent:!!!! ! !!

!

Nuclear Lifetimes!

Γτ =

Γ =τ=6.58×10−22MeV ⋅s

τ

Γ∝ ψf M ψi

Γ = Γii=1

n

∑

! Nuclear lifetimes transition probabilities!!

= reduced transition probability! ! τ = lifetime, = gamma ray energy!! ! !!!!! ! !! B is given in units of e�fmL µN�fmL–1!

Transition Probabilities!

Tfi λL( ) =8π L +1( )

L 2L +1( )!!( )2

Eγ

c!

"#

$

%&

2L+1

B λL;Ji → Jf( )

B λL;Ji → Jf( )

T =1 τ s−1( ) Eγ MeV( )

T E1( ) =1.587 ⋅1015Eγ3B E1( ) T M1( ) =1.779 ⋅1013Eγ

3B M1( )T E2( ) =1.223 ⋅109Eγ

5B E2( ) T M2( ) =1.371⋅107Eγ5B M2( )

T E3( ) = 5.698 ⋅102Eγ7B E3( ) T M3( ) = 6.387 ⋅107Eγ

3B M3( )

Nuclear Lifetimes!

Nuclear decay

Nuclear decay

T1/2 = 1.5, � = T1/2/ ln(2) = 2.16

0

20

40

60

80

100

0 2 4 6 8 10

Num

ber o

f ato

ms

[%]

Time [arb.]

T1/2

2T1/2

3T1/2

!

NUCS 342 (Lecture 4) January 19, 2011 10 / 34

a collection of N0 nuclei produced at the time t=0 will decay with a mean lifetime τ according to the law:!!!where with λ the transition probability (decay rate)!!

N t( ) =N0e− t τ

τ =1 λ

the half–live!

T1 2 = τ ln2

! Collective E2 transitions!!! = intrinsic quadrupole moment! !! !! = Clebsch–Gordon coeficient!!!!! ! !!

!

Quadrupole Deformation!

B E2( ) = 516π

Q02 JiK 20 JfK

2

Q0 =35π

ZR 2β2 1+18

5πβ2 +

58π

β22 + ...

!

"##

$

%&&

JiK 20 JfK =3 J −K( ) J −K −1( ) J +K( ) J +K −1( )

2J −2( ) 2J −1( )J 2J +1( )

1τ=1.223 ⋅Eγ

5 516Q0

2 JiK 20 JfK2

B E2( ) = 0.081642 ⋅Bi

τ ps( ) Eγ MeV( )"# $%51+α( )

Feeding of Excited States – Lifetimes!

τΜ

. . .

τι

the observed lifetime of a state depends on the lifetimes of the states feeding it apparent lifetime the relation between apparent lifetime and intrinsic lifetime of the levels is given by the Bateman equations of radioactive decay where Ni(t) is the population of level i at time t assuming

dNi t( )dt

= Nj t( )λ j −Ni t( )λij=i+1

M

∑

τ2

τ1

M

M-1!

i!

. . . i-1!

2!

1!

N0!

Ni t( ) =N0 c je−λ jt

j=i+1

M

∑ ci =λ j

j=i+1

M

∏

λ j − λi( )j=i+1

M

∏

NM−1 0( ) =NM−2 0( ) = ...=N1 0( ) = 0


τ2

τ1

2!

1!

N0! The Bateman equation

Two-decay chain: abundance for a special case

Blue: parent T1/2=1.5, N1(0) = 100%Red: daughter T1/2=3, N2(0) = 0%

20

40

60

80

100

0 2 4 6 8 10 12 14

Num

ber o

f ato

ms

[%]

Time [arb.]



τΜ

. . .

τι τSF(i-1)

τSFι

τSF(Μ-1)

Side

feed

ing

the observed lifetime of a state depends on the lifetimes of the states feeding it apparent lifetime the relation between apparent lifetime and intrinsic lifetime of the levels is given by the Bateman equation of radioactive decay where Ni(t) is the population of level i at time t if there is a side feeding:

dNi t( )dt

= Njλ j −Niλij=i+1

M

∑

τ2

τ1

τSF1

τSF2

M

M-1!

i!

. . . i-1!

2!

1!

N0!


j=i+1

M

∑ + NjSF t( ) ⋅

j=i

M−1

∑ c jSFe−λ j

SFt c je−λ jt

j=i

M−1

∑

NM−1 0( ) ≠ 0;NM−2 0( ) ≠ 0;...;N1 0( ) ≠ 0


τΜ

. . .

τι τSF(i-1)

τSFι

τSF(Μ-1)

Side

feed

ing

the Bateman equation is not a single equation but a method for setting up a differential equations describing the decay of the chain of interest as a function of time based on the decay rates and the initial population of the states

where Ni(t) is the population of level i at time t if there is a side feeding:

dNi t( )dt

= Njλ j −Niλij=i+1

M

∑

τ2

τ1

τSF1

τSF2

M

M-1!

i!

. . . i-1!

2!

1!

N0!


j=i+1

M

∑ + NjSF t( ) ⋅

j=i

M−1

∑ c jSFe−λ j

SFt c je−λ jt

j=i

M−1

∑

NM−1 0( ) ≠ 0;NM−2 0( ) ≠ 0;...;N1 0( ) ≠ 0


τΜ

. . .

τι τSF(i-1)

τSFι

τSF(Μ-1)

Side

feed

ing

in case of fusion–evaporation reactions large side feeding from unresolved states in the continuum with unknown lifetimes

the feeding times from such states are usually much shorter than the in band decay times

τ2

τ1

τSF1

τSF2

M

M-1!

i!

. . . i-1!

2!

1!

N0!


τΜ

. . .

τι τSF(i-1)

τSFι

τSF(Μ-1)

Side

feed

ing

in case of fusion–evaporation reactions large side feeding from unresolved states in the continuum with unknown lifetimes

the feeding times from such states are usually much shorter than the in band decay times

side feeding effects on the lifetime measurements can be avoided by using coincidence sets on transitions above the state of interest

τ2

τ1

τSF1

τSF2

M

M-1!

i!

. . . i-1!

2!

1!

N0!


τ2

τ1

2!

1!

N0! Independent decay of radioactive mixture

Independent decay of two radioactivities

N(t)=70⇥ exp

�� t

ln(2)1.5

⇥+30⇥ exp

�� t

ln(2)15

⇥

10

100

0 5 10 15 20 25 30 35 40

Num

ber o

f ato

ms

[%]

Time [arb.]


N1!

NRF!Coulex!Indirect Methods!

Direct Methods!

t (s)!10-18! 10-15! 10-12! 10-9!

FEST→ Electronic !

DSAM! RDDS!RFD!

RSAM!

GRID!

GRID: Gamma ray induced Doppler broadening !DSAM: Doppler shift attenuation method !RFD: Recoil straggling method !RDDS: Recoil distance Doppler shift method !RSAM: Recoil shadow anisotropy method !FEST: Fast electronic scintillation method !NFR: Nuclear resonance fluorescence !Coulex: Coulomb excitation cross section!

Techniques for Lifetime Measurement!

Direct Methods!- determine directly τ

Indirect Methods!- determine the width Γ

Irradiation and Counting!

Lifetimes ~ sec – min!-  sample irradiated to produce isomeric state!-  fast transport system: rabbit or gas jet!-  counting decays with a Ge detector!

19 YRAST STATES IN Fe, Mn AND THE DECAY OF Fe~ 19&9

TABLE I. Summary of measurements made on Ca+ N reactions.

ExperimentTarget thickness

(mg/cm~)Incident energy

(Me V)

Prompt p-ray singlesPr ompt p-p coincidencePrompt n-y coincidenceDelayed p-ray singlesBelayed p-y coincidenceDelayed P-p coincidence

0.30.50.52.02,00.5

29, 30, 32, 34, 36, 3832, 3630, 32, 34, 36454530, 35, 40, 45, 50, 55

Ca isotopic enrichment 99.9%; natural calcium was used for the other targets.This experiment is discussed in Ref. 3.

trogen beams with energies from 29 to 55 MeVwere obtained from the Stony Brook FN tandemVan de Graaff accelerator.In order to identify a possible E4 decay branch

from the "Fe isomer it was necessary to obtaina precise energy for a least one of the cascade y.

rays which would result. To this end "Fe yrasttransitions were studied in-beam in y-ray singles,and y-y and neutron-y coincidence experiments.Relatively low bombarding energies of 29 to 38MeV mere employed to favor the direct populationof low-spin yrast states below the isomer. In asecond set of experiments, delayed y rays fromthe decay of "Fe were studied in singles and y-ycoincidence at a somewhat higher energy (45 MeV).Table I summarizes experimental facts about thevarious measurements. The delayed p-y coincid-ence excitation function measurement was doneessentially as described earlier' and is not dis-cussed further here.Calcium metal targets 0.3 to 2.0 mg/cm' thick

were evaporated on gold or tantalum backings.Natural calcium was used except in the n-y coin- .

cidence experiment where enriched isotope(&99.9/p ~OCa) was employed to avoid possible in-terference from the "Fe 2;- g.s. transition (whichhas nearly the same energy as the correspondingtransition in "Fe). Targets were changed at fre-quent intervals-to minimize the buildup of long-lived activities. Targets used for in-beam experi-ments were mounted 45 to the incident beam ina small glass chamber.y rays were observed in large-volume Ge(Li)

detectors with efficiencies of 10-15/~ relative tostandard NaI detectors. The y-ray detectors usedfor in-beam measurements were placed at 90' tothe incident beam. Usually a graded absorber ofa few mm Pb and brass was employed to reducethe flux of low-energy (&500keV) y rays. Absolutedetector efficiencies were obtained by recordingy rays from various radioactive sources placed

ACCELERATOR

INLINE )gVALVE c

TURBO

i PUMP

INLINE CONCRETEVALVE BLOCK

ROUGHING PUMP

ARGON CONCRETEBLOCK

IO

DETECTOR

ARGON

ROUGHINGPUMP

FIG. 1. The pneumatic rabbit system used for delayedactivity measurements. A plastic rabbit is transported10 ft through a stainless steel tube between the irradia-tion and detector stations. A blast of argon gas followedby roughing pump action is used to achieve transporttimes 0.5 s. Sequencing of all valve operations is ac-complished with a programmable electronic sequencer.

at the target position. Energy calibrations wereobtained from these sources and known y-raylines in the spectra.In the n-y coincidence experiment neutrons were

detected in a 23 cm diameter by 5 cm thick NE213liquid scintillator placed at 0' to the incident beambehind a 1.3 cm thick lead y-ray absorber. Neu-tron and photon interactions in the detector weredistinguished by both pulse-shape analysis andtime-of-flight analysis. For each event, pulsescorresponding to liquid scintillator pulse-shape,relative interaction time, and y-ray energy weredigitized and written event-by-event on magnetictape under the control of a PDP-9 computer. Thetapes were later analyzed using the same computerby setting gates on various combinations of theparameters. Similar event-mode recording tech-niques were used in the y-y coincidence experi-ments. In the delayed activity y-y coincidence ex-

rabbit system: 3 m in 0.5 s!

1942 GEE SAMAN, McGRATH, NOR, AND MAL MIN

45.94%0.60 sec.( I 2+) 68I5 0 I30

I

I

I

I

& 0.4%

2385

CO

O

IO

4- 849

52mF

I 870

10

4IO—

I525 4~mSC

I535

IOO

(9+)+ '* " 2908(8+) 2286

849

0+ iF 052F

2& IOIIPP

I

I I30 I 160

3IO—

I I90 2000Chonnel

I I

2030 2060 2090

7+ ' 870

6' ~F F 0

Mn

FIG. 5. I evels and decay schemes of 52Fe and Mnfound in the present work. In Mn the y-ray intensitiesare given relative to the 11+ 9' transition. Intensitieswere obtained from delayed y-ray singles data.

to search for a direct y-ray decay branch. Thesedata also establish a revised level scheme for"Mn.Spectra of y rays in coincidence with four de-

layed y rays from "Mn are shown in Fig. 4. A

IO5

FIG. 7. Delayed y-ray singles spectra in the energyregions encompassing the Fe 2+ g.s. and 4+ 2+ trans-itions at 849 and 1535 keV, respectively. The absenceof observable y ray peaks at these energies provides anupper limit on direct E4 y-decay branch of ~2Fe .

previously unreported weak 2286 keV y-ray is incoincidence with the 929 and 622 keV y rays. The"Mn level scheme shown in Fig. 5 is constructedon the basis of these coincidence spectra togetherwith the delayed y-ray singles data. The "Mnspin-parity assignments are taken from Avrigeanuet al.' and from Stefanini et al." Qur coincid-ence data confirm that the ' Mn 8' state is at 2286keV. (Originally this state had been placed at1492 keg, with the ordering of the 622 and 1416 '

keV transitions reversed —see Ref. 3.) Other re-cently published papers, citing our preliminaryresults, have reported the same level scheme us-ing less direct methods. ' '"' The y-ray energies

COUNTS

IOIO-

c6-

'Q

50M rnMn

x Sc4~S ~o Fe (xIO)-

0

I

3II

62TIME

I

93 0 x~oI I I I

50 40 50l4N Inc. Energy (MeV)

FIG. 6. Decay rates of the six y rays in the Mn high-spin decay scheme. The y-ray singles data were obtainedwith the rabbit system shown in Fig. 1.

FIG. 8. Excitation functions for some delayed y-rayactivities from 40Ca+ ~4M reactions.


45.94%0.60 sec.( I 2+) 68I5 0 I30

I

I

I

I

& 0.4%

2385

CO

O

IO

4- 849

52mF

I 870

10

4IO—

I525 4~mSC

I535

IOO

(9+)+ '* " 2908(8+) 2286

849

0+ iF 052F

2& IOIIPP

I

I I30 I 160

3IO—

I I90 2000Chonnel

I I

2030 2060 2090

7+ ' 870

6' ~F F 0

Mn




IO5




COUNTS

IOIO-

c6-

'Q

50M rnMn


0

I

3II

62TIME

I

93 0 x~oI I I I





45.94%0.60 sec.( I 2+) 68I5 0 I30

I

I

I

I

& 0.4%

2385

CO

O

IO

4- 849

52mF

I 870

10

4IO—

I525 4~mSC

I535

IOO

(9+)+ '* " 2908(8+) 2286

849

0+ iF 052F

2& IOIIPP

I

I I30 I 160

3IO—

I I90 2000Chonnel

I I

2030 2060 2090

7+ ' 870

6' ~F F 0

Mn




IO5




COUNTS

IOIO-

c6-

'Q

50M rnMn


0

I

3II

62TIME

I

93 0 x~oI I I I




D.F.Geesaman et al., PRC19(1979)1938!

Irradiation and Counting!

Lifetimes ~ sec – min!-  sample irradiated to produce isomeric state!-  transport sample to a low–background area! (tape transport)!-  counting decays with a Ge detector !

39Ca produced in REXTRAP at ISOLDE

B.Blank et al., EPJ A44 (2010)363!

radioactive ions

detection - β gas counter - γ germanium

GSI tape system

Irradiation and Counting: FEST!

-  poor Ge time resolution limit τ > several ns!-  LaBr3 detectors excelent time resolution (< 400 ns)!-  Ge–(LaBr3–LaBr3) coincidences!

Figure 1. Schematic of the setup at the moving tape collector. Three LaBr3 detectors wereplaced in close geometry around the measurement position, to which the activity was carried bythe tape. An additional Ge detector was placed in order to take a high-resolution spectrum inparallel.

B(E2) strength versus neutron number in rare-earth isotopic chains decreases when approachingmid-shell (see Fig. 1 of Ref. [3]). The same (inverted) e!ect has been observed in g factors ofthe 2+

1 states within these isotopic chains [3].A qualitative explanation for the saturation was found [3] by the argument that neutrons

are filling di!erent angular momentum orbitals near mid-shell than protons, therefore thewavefunction overlaps and hence collectivity do not simply increase as a function of neutronnumber. In [3], calculations within the interacting boson model (IBM) were performed, takinginto account fractional filling of the shells, therefore e!ectively reducing the number of activevalence bosons, in order to model a reduced raise of B(E2) strengths near mid-shell. A moremicroscopic approach was found with in the projected shell model [4].

However, recent measurements of 2+1 lifetimes in the region found large discrepancies to

literature values, and gave rise to the need of new, high-precision measurements of the lifetimesinvolved. For example, using fast timing techniques we corrected the lifetime of the 2+

1 state in172Hf by about 15 % [5]. Within the present work, we tested the isotopes 168Hf and 174W. Again,fast timing techniques were applied, but using newly available LaBr3 scintillators instead of BaF2

scintillators. A brief overview of the techniques used, the advantages of the new material, andpreliminary results are given in the following.

2

!1 0 1 2 3 4 5 6 7 8 910

0

101

102

103

!T [ns]

Co

un

ts p

er

5.6

ps

Fit to data

Figure 3. (Color online) Samplefinal time di!erence spectrum, witha line fitted to the linearly down-sloping part. The slope directlyyields the lifetime of the state ofinterest.

(1,2) (1,3) (3,1) (2,3) (3,2)1.28

1.3

1.32

1.34

1.36

1.38

1.4

Detector Pair

" [ns]

" = 1.339(8) ns

"lit

= 1.64(10) ns174W

(1,2) (2,1) (1,3) (3,1) (2,3) (3,2)1.15

1.2

1.25

1.3

Detector Pair

" = 1.237(10) ns

168Hf "lit

= 1.28(6) ns

Figure 4. (Color online) Lifetimes obtained for di!erent detector pairs for the 2+1 state in 174W

(left) and 168Hf (right).

prompt time di!erence spectra, and adding background gate 3) back in (which has been over-subtracted in the first step) results in a proper background correction in the time di!erencespectra. The individual contributions are included in Fig. 2. It should be noted, that such abackground treatment was only possible because of the excellent energy resolution of the LaBr3scintillators. A simple line-fit, as shown in a sample in Fig. 3, has then be made to each of the sixresulting time di!erence spectra on logarithmic scale, including only the region su"ciently faraway from prompt contributions. The results for the six detector pairs, shown in Fig. 4, yieldedidentical results within error, and the weighted average was taken. In case of the tungstenexperiment, only 5 pairs of detectors could be used due to a broken channel in the electronics.

3. ResultsFrom the technical aspect, the new LaBr3 detectors proved to be extremely valuable becauseof their energy resolution, which is superior to comparable BaF2 detectors, whereas timeresolution is similar. It is only because of the energy resolution that we were able to correctlysubtract background from Compton events from higher-lying states when gating on the peakscorresponding to the decays from the 2+

1 or 4+1 states. Still, monitoring the spectrum with a

high-resolution Ge detector is imperative in order to ensure the absence of further contaminants.

4

!1 0 1 2 3 4 5 6 7 8 910

0

101

102

103

!T [ns]

Co

un

ts p

er

5.6

ps

Fit to data

Figure 3. (Color online) Samplefinal time di!erence spectrum, witha line fitted to the linearly down-sloping part. The slope directlyyields the lifetime of the state ofinterest.

(1,2) (1,3) (3,1) (2,3) (3,2)1.28

1.3

1.32

1.34

1.36

1.38

1.4

Detector Pair

" [

ns]

" = 1.339(8) ns

"lit

= 1.64(10) ns174W

(1,2) (2,1) (1,3) (3,1) (2,3) (3,2)1.15

1.2

1.25

1.3

Detector Pair

" = 1.237(10) ns

168Hf "lit

= 1.28(6) ns

Figure 4. (Color online) Lifetimes obtained for di!erent detector pairs for the 2+1 state in 174W

(left) and 168Hf (right).

prompt time di!erence spectra, and adding background gate 3) back in (which has been over-subtracted in the first step) results in a proper background correction in the time di!erencespectra. The individual contributions are included in Fig. 2. It should be noted, that such abackground treatment was only possible because of the excellent energy resolution of the LaBr3scintillators. A simple line-fit, as shown in a sample in Fig. 3, has then be made to each of the sixresulting time di!erence spectra on logarithmic scale, including only the region su"ciently faraway from prompt contributions. The results for the six detector pairs, shown in Fig. 4, yieldedidentical results within error, and the weighted average was taken. In case of the tungstenexperiment, only 5 pairs of detectors could be used due to a broken channel in the electronics.

3. ResultsFrom the technical aspect, the new LaBr3 detectors proved to be extremely valuable becauseof their energy resolution, which is superior to comparable BaF2 detectors, whereas timeresolution is similar. It is only because of the energy resolution that we were able to correctlysubtract background from Compton events from higher-lying states when gating on the peakscorresponding to the decays from the 2+

1 or 4+1 states. Still, monitoring the spectrum with a

high-resolution Ge detector is imperative in order to ensure the absence of further contaminants.

4

the slope yields directly the lifetime

V.Werner et al., J. of Physics312(2011)092062!

169Tm(12C,7n)174Re à 174W* β

In–beam FEST with LaBr3 Detectors !-  Ge–(LaBr3–LaBr3) coincidences!-  LaBr3 detectors excelent time resolution – fast decay time (26 ns)!

better than 400 ps!-  relatively good energy resolution – large photon yield (63 photons/keV)!

2.6% @ 662 keV (137Cs)!

Detectors @ LNL!!BrilLanCe 380 Integrated Design!Model 51S51/B380/PMT2,2!Ø  Crystal 2''x 2'' !

Ø  XP5500B 8–stages 2.2'' PMT!

Ø  AS20 Voltage Divider!Performance (data sheet)!Ø  PHR@662keV ≈ 2.6% !Ø  CRT@511keV ≈ 0.45 ns!Connectors!Ø  1 output from Anode (DC coupl.)!Ø  1 negative HV supply !

In–beam FEST with LaBr3 Detectors !Typical energy spectra!

60Co, 88Y, 137Cs!

Int. activity!

2.8% 2.4% 2.1% 1.9% 1.6%

Typical time spectra!

88Y γ–γ coinc.!

Good agreement with data sheet specifications!

Eγ [keV]

Cou

nts

Cou

nts

Time [a.u.]

88 38Sr

00+

1836.0872+

2734.1353–3218.5072+3584.7835– 0.

065

850

.647

0.00

7 3

218.

48

0.02

1 1

382.

406

(M1+

E2)

484.

53

0.71

273

4.08

6

93.7

898

.042

E1

99.2

183

6.06

3 E

2

stable

0.162 ps

0.78 ps 0.13 ps 0.14 ns

88 39Y !

5.5% 9.81

94.4% 6.90.028% 9.410.065% 6.9

4– 0106.65 d

QEC=3622.6

2344

138 56Ba

00+

1435.8112+ 66 1

435.

795

E2

stable

0.206 ps

138 57La !

66.4% 17.22

5+ 01.05"1011 y

QEC=173766.4%

4779

138 58Ce

00+

788.7442+ 34 7

88.7

42 E

2

stable

138 57La!

33.6% 18.02

5+ 01.05"1011 y

Q#$=104433.6%

4781

32 keV X–rays (Kα1) !

1436 + 32 keV X–rays !789 + β–!

α 227Ac!

In–beam FEST with LaBr3 Detectors !330 The European Physical Journal A

LaBr3 PMAnodeDynode

CFD CFDLongdelay

Shortdelay

LaBr3multiplicity

! 2

Ge multiplicity ! 1 AND

Delay

Gate &delaygener.

TAC

Start

Stop

Gate

Energy

Fig. 1. Part of the electronic scheme detailing the timing processing for one of the five LaBr3:Ce detectors.

was recently reported for the determination of lifetimes ofhigh-spin states in 122Cd populated in the !-decay of a(9!) isomer of 122Ag [8].

In this work we present a development of the fast-timing method which is suitable for in-beam "-ray spec-troscopy measurements. Triple-gamma coincidences aremeasured with an array containing both HPGe andLaBr3:Ce detectors. The high-energy resolution of the Gedetectors is used to select the desired "-ray cascade, andthe array of fast LaBr3:Ce to build the delayed coinci-dence time spectra for selected levels. In order to fully usethe e!ciency of the LaBr3:Ce array, that is, all "" coin-cidence combinations between these detectors, a specialmethod is necessary for the processing of the time infor-mation from the LaBr3:Ce detectors, and this is presentedin some details. The method is illustrated by two in-beamlevel lifetime measurements, one in 107Cd, populated withthe 98Mo(12C, 3n") reaction, and the other in 199Tl, fol-lowing the 197Au(#, 2n") reaction.

2 Experiment arrangement

The measurements were performed with beams deliveredby the Tandem van de Graa" accelerator in Bucharest.In the first experiment, a 1.3mg/cm2 98Mo target with a29.5µm Pb backing was bombarded with a 50MeV 12Cbeam with intensity of about 10 pnA. In the second exper-iment, a 9.65mg/cm2 Au foil was bombarded by a 24MeV#-particle beam with intensity around 10 nA. The detec-tion of the "-rays was made with 7 HPGe detectors eachwith relative e!ciency around 50%, five of them beingplaced at 143" and the other two at 90" with respect to

the beam, and five LaBr3:Ce detectors placed at 45" withrespect to the beam. The LaBr3:Ce detectors, deliveredby Saint-Gobain Crystals, had crystals of 2## ! 2## (one),1.5## ! 1.5## (two), and 1## ! 1## (two) and photomultipli-ers XP5500B. Energy and e!ciency calibrations of thedetectors were performed with standard sources of 60Co,137Cs, and 152Eu. Coincidences between all these 12 de-tectors were registered on-line and processed after the ex-periments. The energy information of the detectors wastreated by conventional amplification chains.

Figure 1 shows details of the electronics that are rel-evant for the LaBr3:Ce detectors and the treatment oftheir time information. For each LaBr3:Ce detector wehave used the anode signal for the timing, and the signalfrom the last dynode for the energy information. Althoughthis non-standard choice does not ensure the optimumtiming signals, we used the weakest signal for the energychain such that one does not rapidly reach the saturation(because of the large light output). For each detector wehave chosen the high voltage at which the best linearity inenergy was achieved, which simplified the o"-line energyalignment of the di"erent detectors. The timing signalswere passed first through constant fraction discriminatormodules (type ORTEC 935) —fig. 1. Because the Ge de-tectors are much slower than the LaBr3:Ce ones, the sig-nals from these CFDs had to be delayed by about 500 ns,and this was done by using only long cables, avoiding addi-tional electronic time jitter. Then, the signals were passedagain through CFDs to rebuild their front. From theseCFDs, one signal, appropriately delayed for synchroniza-tion (by a short delay) was sent as start signal of a time-to-amplitude converter (TAC). The other signal from CFDwas sent to a coincidence/multiplicity unit. The resulting

N. Marginean et al.: Measurements of sub-nanosecond nuclear lifetimes with an array of HPGe and LaBr3 detectors 331

signals with multiplicity equal to or larger than 2 were fedinto another coincidence unit where the trigger signal ofthe experiment was built from an “and” operation withthe multiplicity one signal separately built for the germa-nium detectors. This trigger signal was used, on one hand,to generate a gate signal for the TACs such as to reducetheir load. On the other hand, because the front of thissignal was given by the LaBr3:Ce detector multiplicity sig-nal, it could be distributed as a “common” stop signal toall the TAC units. This was done again only by cabling,therefore avoiding additional jitter. In this way, exactlythe same stop was used for all TACs, and in the o!-lineanalysis the time di!erences between di!erent detectorsdo not a!ect the time resolution.

Because we finally look at time di!erences of pairs ofLaBr3:Ce detectors, it is of utmost importance to prop-erly treat the time information from the detectors, in or-der to be able to add up the contributions from all pairsof detectors. The following o!-line processing procedurewas adopted. A 60Co source was placed precisely at theposition of the beam spot. The 60Co source represents aperfect case of prompt coincidence between two !-rays.One chooses one of the scintillator detectors as a timereference (therefore only events of fold two and contain-ing signal from that detector are chosen). Then, for eachof the rest of scintillator detectors one builds a matrixE!"T , where "T is the time di!erence with respect tothe reference detector, and a gate was set on the 1332 keVtransition in the reference detector. In this way one getsthe response of the CFD as a function of energy, for allenergies smaller than 1173 keV. Such a time response isshown in fig. 2(a) for a certain pair of detectors (the 2!!!2!!detector refered to one of the 1.5!! ! 1.5!! detectors). Oneobserves a non-linear dependence of the time responseon the energy (a time walk), that was found to be in-dependent of the detector chosen as a reference, thereforeit represents the instrumental time response for that de-tector —CFD combination. Di!erent detectors will havedi!erent such time walks, which would make it impos-sible to combine the time information from all of them.Therefore, for each such matrix one fits the average en-ergy dependence of the time response with a polynomialfunction. This function was composed of polynomials upto the second order, separately applied on successive en-ergy domains and smoothly joined between them. Then,by using this function one corrects the time response ofthat detector such that one completely removes the en-ergy dependence, leading to an optimum time resolution(fig. 2(b)). This is equivalent to the alignment of the timeresponse for any energy to the position of the prompt full-energy peak coincidence 1173-1332 keV, which is very pre-cisely defined (fig. 2). This procedure is repeated for alldetectors, therefore resulting in a perfect time alignmentof all pairs of detectors. The time calibration of the spec-tra was performed with a standard time calibrator. Therange of the TACs was of 50 ns. Typical time resolutions(FWHM, for the 60Co source peak-to-peak coincidences)were about 150 ps for the small (1!!! 1!!) detectors, about180 ps for the middle-size (1.5!! ! 1.5!!) ones, and about

Fig. 2. Example of time walk correction to the LaBr3:Ce de-tectors. (a) Time di!erence —energy matrix having as startone of the 1.5!! ! 1.5!! LaBr3:Ce detectors, and as stop thelargest (2!! ! 2!!) LaBr3:Ce detector, measured with a 60Cosource placed in the target position, and gated by the 1332 keVtransition. (b) The same matrix after applying the time walkcorrection as described in the text. Note that the correctionwas not applied at the lowest energies, which were outside therange of interest.

300 ps for the largest (2!! ! 2!!) one. One should note thatthe alignment of the time signals is independent of thistime resolution, and its accuracy is that of the centroid ofthe prompt coincidence, that is, a fraction of one channel(fitting a polynomial curve to the time response and thencorrecting for the determined variation with the energy isequivalent to the procedure of aligning the energy gain oftwo detectors by matching their peak centroids) —whichin our case (fig. 2) is of the order of 5 ps.

After all these corrections, a E!1E!2"t coincidencecube was built for the LaBr3:Ce detector coincidences,using all the data. We briefly describe how this cube isconstructed. Assume that a double-!! coincidence eventis recorded, consisting of !-ray number 1 (!1) detected bythe detector number i and !-ray number 2 (!2) detected bythe detector number j (with i, j being any of the numbersbetween 1 and 5). The projection in the energy plane willbe a symmetric E!1E!2-matrix constructed in the usualmode, that is, we record one event in the x = E(!1),y = E(!2) position, and a second one in the x = E(!2),y = E(!1) position. The time di!erence for the first eventis recorded as "t + T , where "t = t1,i " t2,j and T isan arbitrary o!set (channel). For the second event a timedi!erence ""t + T is recorded. In this way, the two axesare distinguished, with the x-axis assuming, say, the roleof “start” axis, and the y-axis the one of “stop” axis, re-spectively.

332 The European Physical Journal A

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845.5

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956.0

798.1

514.8

205.0

640.5

107Cd

Ge gates

Fig. 3. Relevant part of the level scheme of 107Cd [9]. Thedashed rectangle comprises the three transitions used for gat-ing in the HPGe detector spectra.

3 Measurements

3.1 Test measurement: the lifetime of the 205 keVstate of 107Cd

States in 107Cd were populated in the 98Mo(12C, 3n)107Cdreaction at 50MeV beam energy. Figure 3 shows the rel-evant part of the level scheme [9]. Di!erent matrices andcubes were sorted out from the !!! coincidences. Fig-ure 4(a) shows the Ge-energy axis projection of a !!!cube. By gating on this axis on the strong yrast transi-tions of 956, 798, and 515 keV in this spectrum, one selectsthe 640-205 keV decay sequence (fig. 2) in the LaBr3:Cedetectors, which contains the 7/2+ level of interest. Thetwo transitions can be seen in fig. 4(b), while the spec-trum in fig. 4(c) shows the scintillator spectrum gated byboth the Ge detectors (yrast transitions above the 11/2!states) and the 640 keV transition detected in the scintilla-tors. Figure 5(a) shows the resulting delayed coincidencetime spectrum for the 205 keV transition, resulted fromgating on the two !-rays on an energy-energy time di!er-ence !!"T cube constructed for the LaBr3:Ce detectorsgated by the HPGe detectors. This is the typical time-delayed spectrum, obtained when the start was given bythe transition above the level (640 keV in our case) andthe stop by the transition de-exciting the level (205 keVin our case), respectively (cf. the discussion above aboutthe “start” and “stop” axes). It clearly shows an expo-nential tail due to a decay time larger than the width ofthe prompt coincidence spectrum. The exponential decaye!t/! was convoluted with a Gaussian obtained by fittingthe prompt coincidence peak (determined by gating on theCompton background near the 205 keV peak), and the fitto the experimental data (continuous line) provides a valueT1/2 = 0.69 ± 0.03 ns, which agrees, within uncertainties,

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Fig. 4. (a) Projection of the HPGe axis of a !!! (HPGe-LaBr3-LaBr3) coincidence cube; (b) the energy projection of aE!E!"t cube constructed for the LaBr3:Ce detectors, gated bythe transitions 515, 798, and 956 keV detected in the HPGe de-tectors (highlighted in fig. 3); (c) gate on the 640.5 keV transi-tion in spectrum (b), obtained from the !! coincidence (LaBr3-LaBr3) matrix projected from the cube described at (b).

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(b)

.

"t

Fig. 5. (a) Delayed coincidence time spectrum of the 205.0 keVlevel. The continuous line is a fit to the data with an ex-ponential decay convoluted with a Gaussian representing theprompt coincidence time spectrum, that provides a half-lifeof 0.69 ± 0.03 ns. (b) Delayed coincidence time spectra ob-tained for the 205.0 keV level with two alternatives: i) startwith the 640.5 keV transition and stop with the 205.0 keV one(this is identical with the spectrum shown in (a)); ii) start withthe 205.0 keV transition and stop with the 640.5 keV one (seefig. 3). The dashed lines indicate the centroids of the two dis-tributions, their time di!erence being twice the lifetime of thelevel.


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Ge gates

Fig. 3. Relevant part of the level scheme of 107Cd [9]. Thedashed rectangle comprises the three transitions used for gat-ing in the HPGe detector spectra.

3 Measurements

3.1 Test measurement: the lifetime of the 205 keVstate of 107Cd

States in 107Cd were populated in the 98Mo(12C, 3n)107Cdreaction at 50MeV beam energy. Figure 3 shows the rel-evant part of the level scheme [9]. Di!erent matrices andcubes were sorted out from the !!! coincidences. Fig-ure 4(a) shows the Ge-energy axis projection of a !!!cube. By gating on this axis on the strong yrast transi-tions of 956, 798, and 515 keV in this spectrum, one selectsthe 640-205 keV decay sequence (fig. 2) in the LaBr3:Cedetectors, which contains the 7/2+ level of interest. Thetwo transitions can be seen in fig. 4(b), while the spec-trum in fig. 4(c) shows the scintillator spectrum gated byboth the Ge detectors (yrast transitions above the 11/2!states) and the 640 keV transition detected in the scintilla-tors. Figure 5(a) shows the resulting delayed coincidencetime spectrum for the 205 keV transition, resulted fromgating on the two !-rays on an energy-energy time di!er-ence !!"T cube constructed for the LaBr3:Ce detectorsgated by the HPGe detectors. This is the typical time-delayed spectrum, obtained when the start was given bythe transition above the level (640 keV in our case) andthe stop by the transition de-exciting the level (205 keVin our case), respectively (cf. the discussion above aboutthe “start” and “stop” axes). It clearly shows an expo-nential tail due to a decay time larger than the width ofthe prompt coincidence spectrum. The exponential decaye!t/! was convoluted with a Gaussian obtained by fittingthe prompt coincidence peak (determined by gating on theCompton background near the 205 keV peak), and the fitto the experimental data (continuous line) provides a valueT1/2 = 0.69 ± 0.03 ns, which agrees, within uncertainties,

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798.1

956.0

Fig. 4. (a) Projection of the HPGe axis of a !!! (HPGe-LaBr3-LaBr3) coincidence cube; (b) the energy projection of aE!E!"t cube constructed for the LaBr3:Ce detectors, gated bythe transitions 515, 798, and 956 keV detected in the HPGe de-tectors (highlighted in fig. 3); (c) gate on the 640.5 keV transi-tion in spectrum (b), obtained from the !! coincidence (LaBr3-LaBr3) matrix projected from the cube described at (b).

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(T1/2 = ln2 "t/2)

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(b)

.

"t

Fig. 5. (a) Delayed coincidence time spectrum of the 205.0 keVlevel. The continuous line is a fit to the data with an ex-ponential decay convoluted with a Gaussian representing theprompt coincidence time spectrum, that provides a half-lifeof 0.69 ± 0.03 ns. (b) Delayed coincidence time spectra ob-tained for the 205.0 keV level with two alternatives: i) startwith the 640.5 keV transition and stop with the 205.0 keV one(this is identical with the spectrum shown in (a)); ii) start withthe 205.0 keV transition and stop with the 640.5 keV one (seefig. 3). The dashed lines indicate the centroids of the two dis-tributions, their time di!erence being twice the lifetime of thelevel.

select the channel!

Εγ–Eγ–Δt matrices!for LaBr3 detectors!

START 640 keV!STOP 205 keV!! vs!!START 205 keV!STOP 640 keV!

Fit prompt Gaussian !+ exponential decay!

Δt = 2τ

N.Marginean et al., EPJ A46 (2010)329!

Pulsed Beam Technique!-  width of the beam pulse ! < τ (∼ ns)

-  beam repetition rate ! 100 ns – µs!-  record spectra in between

the pulses! low background!-  exponential decay of the

isomer during the no–beam period!

J.Wrzesinski et al., EPJ A10 (2001)259!


et al. [9] found the main !-cascade from the one-particleone-hole state with the highest spin 14! by inelastic scat-tering of 64Ni and 82Se on 208Pb. The experiments, pre-sented here, used heavier beams on 208Pb targets andfound with more e!cient detector systems new levels andtransitions. Parts of the present results have been pre-liminarily reported already at earlier conferences [10,11].In this article the advances of theory are compared andtested with the new experimental results.

2 Experiments

In an earlier experiment, performed at the INFN Legnaro,the 420 MeV 76Ge beam from the ALPI linear acceleratorbombarded a thick ( 50 mg/cm2 ) 208Pb target, placed inthe center of the GASP Ge-detector array. The very lowbeam intensity of around 0.2 pnA, available at that time,limited the statistics of the collected coincidence data. Onthe other hand, the beam pulsing with 400 ns repetitiontime and the low intensity provided a very clean identifi-cation of the !-rays preceding the 10+ isomer (T1/2 = 500ns) by prompt delayed coincidences.

In two later experiments at the UNILAC of GSI,Darmstadt, a thick 208Pb target was hit by beams of 5.7MeV/u 136Xe and 6.5 MeV/u 208Pb and !-rays were de-tected by 5 Ge-CLUSTER detectors of the EUROBALLproject [12] placed in a ring close to 180" and 132 NaIscintillators of the CRYSTAL BALL [13]. This set-up hasalready been described together with the data on 209Pband 210Pb [14,15]. The beam was pulsed with 110 ns dis-tance between pulses. These experiments provided betterstatistics on prompt-prompt coincidences. The data fromall three experiments were used, to deduce the final re-sults.

3 Results

Figure 1a shows the spectrum of prompt !-rays in co-incidence with delayed !-transitions occurring in the de-cay of the 10+ isomer, as measured with the 76Ge beamand the GASP spectrometer. All lines, that are placedinto the level scheme (fig. 2) above the 10+ isomer areindicated. Table 1 lists the energies and intensities as de-rived from this spectrum and also the prompt !-intensitieswhich were obtained from a best fit of the prompt-promptcoincidences of the experiment with the 208Pb beam andthe cluster detectors. This fit was performed for the levelscheme of fig. 2 with the program ESCAL8R as describedin ref. [16]. The intensities from both experiments agreesurprisingly well. Apparently the feeding pattern is notvery di"erent for the various beams used, and the impactof the angular distribution of !-rays is not important, al-though the detector arrangement of GASP is isotropic,while the cluster detectors were all placed close to 180".The highest-lying transitions at 290.7 and 947.6 keV aresuppressed in the Pb-data by the prompt time window,because they are partly fed from a higher-lying isomer.

865

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Fig. 1. a) Spectrum of prompt and short delayed !-rays incoincidence with lines below the 10+ isomer, 284, 583, 1412and 2614 keV. b) Spectrum in prompt-prompt coincidence withthe 1508 keV line from the experiment with the 208Pb beam.A “banana” gate has been used for the coincidence time thatis narrow at high energies and wider for low energies; thereforethe 948 keV line is not evident.

The previously known lines [9] below the 14! state areevident and confirm the known yrast scheme between the10+ and 14! states. The 1508 and 1553 keV lines are new;they are E3 crossover transitions from 14! to 11+ and 13!to 10+ states, as proven by coincidence relationships andtheir matching energies. The spectrum in coincidence withthe 1508 keV line (fig. 1b) shows the preceding lines abovethe 14! level and the following 340 keV transition to the10+ isomer.

A new !-cascade of 351 and 681 keV proceeds fromthe 12+ level to the second 10+ state through a newstate at 5749 keV. The selection rules for the connect-ing !-transitions limit its spin to 10, 11, or 12. Thereare very few one-particle one-hole configurations, that cangive these spins around this energy. The four expected10+ states and the one 12+ level are known already,

Methods Based on the Doppler Effect!-  relativistic Doppler shift !

!-  in the case of the usual fusion–evaporation reactions β<<1 (few %) so that!

-  allows to distinguish gamma rays emitted by stopped or in–flight nuclei!-  Doppler shift of the gamma rays allow for the determination of the emitting nuclei

velocity!

-  Doppler shift lifetime measurement methods!

-  Recoil Distance Doppler Shift (RDDS) 1 ps – 1 ns!-  Doppler Shift Attenuation Method (DSAM) 100 fs – 1 ps !-  Fractional Doppler Shift Method 5 fs – 50 fs!

Esh θ( ) =E01− β 2

1− β cosθ ; β=v

c

Esh θ( ) ≈E0 1+ β cosθ( )

β ≈Esh θ( )−E0

E0

cosθ

Recoil Distance Doppler Shift (RDDS) Method!

-  thin target ~500 µm/cm2 (movable)!-  thick stopper (‘plunger’ foil) usually in Au!-  recoils decay in–flight over the distance x!-  recoils decay as stopped in the stopper!!-  both stopped and in–flight emitted gamma

rays are detected!-  sh: shifted component!-  u: unshifted component!

Measure the difference of intensity of the two components as a function of the target–to–stopper distance!

Det.

EshEu

Eu

Esh

θ

Esh θ( ) ≈Eu 1+ β cosθ( )

Recoil Distance Doppler Shift Method!P. G. BIZZETI et al. PHYSICAL REVIEW C 82, 054311 (2010)

FIG. 1. (Color online) Evolution of the ratio E(4+1 )/E(2+

1 ) asa function of the proton number in the isotone chains with N =62, 64, 66, 68, 70, 72 (from left to right). The data are reported versusA = N + Z, to avoid overlapping of the different curves. A thickerline outlines data pertaining to the N = 66 isotone chain. Horizontallines show the theoretical values predicted by harmonic vibrator (V),X(5) model, and rigid rotator (R).

II. EXPERIMENT

A. Thick-target measurement

The level scheme of 122Ba was investigated via the108Cd(16O,2n)122Ba reaction at 62 and 64 MeV beam energy.The target consisted of a 1 mg/cm2, 69% enriched 108Cd foil,followed by a 10 mg/cm2 208Pb backing. The GASP arraywas mounted in its Configuration II (i.e., with the Comptonsuppressed Ge counters at an average distance of 22 cm fromthe target). Triple and higher-fold coincidence events havebeen recorded in 55 h of measurement. From the raw data,we have constructed three- and two-dimensional coincidencematrices, containing approximately 1.9 ! 107E! " E! " E!

coincidences and 1.5 ! 108 E! " E! coincidences. Thesematrices have been used for the search of weak ! transitionsin coincidence with known transitions in 122Ba.

Most of the transitions belonging to the bands reportedin the previous works [6,18] have been identified. A revisedversion of the excitation energy pattern of 122Ba will bepresented in a forthcoming paper, which will also include thelifetime measurements of the yrast band levels of J ! 10 [22].Here, we restrict the analysis to the known positive paritybands.

The yrast ! cascade, reported in [18] (see Fig. 2) wasobserved at least up to the 20+

1 # 18+1 transition. As to the

band based on the 3+1 state at 1168 keV, reported by Fransen

et al. [6], it was extended by two more transitions. They showthe typical angular distribution of stretched E2 transitions andtherefore the suggested spin for the corresponding levels are13 and 15. In addition, a new interband transition connectingthe 11+

1 and 10+1 states was found.

Fransen et al. [6] have also observed two ! transitions,of 587 and 422 keV, in coincidence with one another andwith a 196-keV transition that could originate from the firstexcited J = 2+ state of 122Ba. In the present measurement, itwas possible to extend the 196-, 422-, and 587-keV cascade

FIG. 2. (Color online) Partial level scheme of 122Ba relevant forthe present analysis. The two levels on the top of the band based onthe 3+

1 state and the 11+1 # 10+

1 transition have been identified in thepresent work.

to higher-lying levels, decaying with ! transitions of 722,838, and 880 keV (in order of decreasing intensity). We haveidentified the entire cascade as a part of a known band of121Xe, based on the 7/2" level at 196 keV [23]. Indeed, the121Xe nucleus is populated in the n2p exit channel of the usedreaction.

Moreover, we have observed two transitions, of 199and 514 keV [belonging to the band (4) reported byPetrache et al. [18]], which are close in energy to thoseof the first and third transition of the ground-state band(196 and 513 keV, respectively), and are in coincidence withthe transitions de-exciting the 8+

1 and the 6+1 levels. In the

following, for the sake of simplicity, they will be mentionedas 199-keV-band(4) and 514-keV-band(4) transitions.

In view of the analysis of the data obtained with the RDDSmethod (described in the following section), for which anoverlap of the 514-keV-band(4) and 513-keV transitions couldbe somewhat problematic, we have determined the relativeintensity of the two transitions. They are in coincidence withthe 8+

1 # 6+1 , 620-keV and the 4+

1 # 2+1 , 373-keV transitions.

054311-2

TRANSITION PROBABILITIES IN THE X(5) . . . PHYSICAL REVIEW C 82, 054311 (2010)

Through an accurate analysis, where a reference transition wasexploited, it was found that the intensity ratio of the 514-keVband(4) to the 513-keV line, in coincidence with both the620- and 373-keV transitions, is (1.6 ± 0.5) 10!2, whereas itis larger (5.0 ± 1.4) 10!2 when in coincidence with only the373-keV transition, because of the fact that several transitionsfrom band (4) of [18] directly feed the 6+

1 or the 4+1 level.

Because all the transitions of interest are stretched E2, weexpect that their intensity ratio is almost independent of thedetector angle.

We have also checked that a weaker 14!2 " 13!

2 , 371-keVtransition in band (3) of [18] has practically no effect on ourresults.

As to the 0+2 state (the band head of the ! band), the

systematics of heavier barium isotopes (see, e.g., [6,7]) wouldsuggest an excitation energy of about 1.1 MeV, which is veryclose to the X(5) prediction. Particular care was devoted to thesearch, in the coincidence data, of possible " -ray de-excitingstates belonging to the ! band. In particular, the energyspectrum gated on the 2+

1 " 0+1 transition was thoroughly

analyzed, but no indication for such " ray was found. At themoment, the ! band of 122Ba is still to be identified.

B. Lifetime measurements

In a separate experiment, performed at LNL, the lifetimesof the excited states of the g.s. band in 122Ba have beenmeasured by means of the RDDS method, with the Plungerdevice of the Cologne group installed in the GASP array(in Configuration 2). Counter rings 1, 2, 6, and 7 (at34.6#, 59.4#, 120.6#, and 145.4# to the beam direction,respectively) provided sufficient separation of the Doppler-shifted part and the unshifted part for most of the " -raylines. Excited states in 122Ba were populated via the reaction108Cd(16O,2n)122Ba. The target consisted of 0.5 mg/cm2 108Cdon a 2.3 mg/cm2 Ta foil (facing the beam). A 6.4-mg/cm2

gold foil was used to stop the recoils. The beam energy was69 MeV and was reduced to about 65 MeV at the entrancein the 108Cd target. Measurements have been performed at 17target-to-stopper distances, in the range from point of electriccontact between target and stopper and 1389 µm. Because theaverage velocity of the recoiling nuclei was v $ 10!2c, thecorresponding values for the time of flight were in the range$0.5–463 ps.

Typical examples of the evolution of the line shape with thetarget-to-stopper distance are shown in Fig. 3.

As to the 2+1 " 0+

1 transition, it is seen that, even at thelargest distances, the intensity of the unshifted line is still largeand that of the Doppler shifted line is still far from saturation.To extend the data to larger distances, thus improving thereliability of the result, a new measurement was performedvia the 112Sn(13C,3n)122Ba reaction, at the Tandem acceleratorof the IKP of the University of Cologne. The target consistedof a 0.3-mg/cm2 112Sn layer, evaporated on a 1.7-mg/cm2 Tabacking (facing the beam). A 4.0-mg/cm2 gold foil was usedto stop the recoiling nuclei. The beam energy was 61 MeV(corresponding to 59 MeV at the entrance in the Sn target).In this case, the average recoil velocity was v $ 8 % 10!3c.A total of 11 Ge counters were mounted in two rings, five at

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FIG. 3. Evolution of the line shape of the 2+1 " 0+

1 of 196 keV (a),4+

1 " 2+1 of 373 keV (b), and 6+

1 " 4+1 of 513 keV (c) " transitions

at different target-to-stopper distances, in the experiment performedat LNL. These spectra have been taken at the most forwardring (34.6# with respect to the beam), in coincidence with theDoppler-shifted part of the directly feeding transition. The size ofthe small 511-keV peak is visible in the lowest part of the right-handpanel.

143# and six at 29#, whereas a further counter was placed at0# with respect to the beam direction. The average distanceof the counters from the target was 11 cm for the backwardring and 20 cm for the forward one. A Plunger device [24],like in the case of the previous measurement, was used.Measurements have been performed at eight target-to-stopperdistances ranging from 10 to 3000 µm, so that the significantpart of the decay curve of the 2+

1 state was almost completelyincluded. The quality of the data obtained from this experimentis illustrated in Fig. 4. In spite of the relatively small averagerecoil velocity the evolution of the unshifted and shiftedpeaks with increasing target-to-stopper distance is clearlyvisible.

For the data analysis, the differential decay curve method(DDCM) [25,26] (described in the next section) was used.When necessary, the finite stopping time of the ions in thestopper material (Fig. 5) was taken into account.

Moreover, a new method, the integral decay curve method(IDCM) [27] was exploited in the analysis of the data collectedat LNL, concerning the lifetime of the 2+

1 . Such a methodshould be particularly advantageous when the most significant

054311-3

122Ba!

21+ → 01

+ 41+ → 21

+ 61+ → 41

+

P.G.Bizzeti et al., PRC 82 (2010)054311!

θ = 35oGASP+Koln plunger!

Stop flight

Recoil Distance Doppler Shift Method!

-  intensity of the in–flight component!

!-  Intensity of the stopped component!

!-  the ratio of the unshifted component to the

total intensity !!! depends on the lifetime τ

Det.

EshEu

Eu

Esh

θ

Ish =N0 1−e−

xvrecτ

"

#$$

%

&''

Iu =N0e−

xvrecτ

R =Iu

Iu + Ish= e

−x

vrecτ

Volume 303, number 3.4 PHYSICS LETTERS B 15 April 1993

120

80

O. o 40 vl

z + t-

ff ~oo

0 "~ 300 z

200

100

0 0

163 Lu yrast I ~ ~ l ~ l l l ~ l ~ l ' l

396keV

l l l L . l i l i l i l ' r " ~ ' .

~ ' 1 ' 1 ' 1 ' 1 '

471 keV

, l l l , l l [ i l J l l

8 16 24

1000

800

600

400

200

0 1000

800

600 400

2OO

163Lu [ 66031/2* [ I I ' I ' I ' I ' I ' I

386 keY / 2"--~21/2 *

I i I ' I , I i I , I 1

315keY

~ 2 1 ~ , I I I i [ I I i I , I , ~

8 16 24 Time of Flight(psi

1000

800

600

400

200

0 1000

8O0

600 400

200

163yb ymst T l l l ' l l l l J ' l ' l

t &63keY

I I I I I I , J I I , I L I l l l l l l I l ] l I l l l

~ , ~ 345keV

I I I I I I

0 8

Fig. 2. RDM decay curves of several transitions in '~Lu and 'O3Yb.

I i I , I , I

16 24

2 0 ' ' I . . . . I . . . . I . . . . . . . I ' , , , , r , ~ • , I . . . . I ' ' ' ' I ' ' '

15 1¢,3Lu [660] 1/2 ~

c~

C

- - , 9 ~ 2

163I.u Yrast

0 i , , I . . . . I . . . . I , , , I , , ~ L I , , , ,

5 10 15 20 25 ~,

I . . . . I . . . . . I ' ' ' 1 . . . . . . ' ' ~ . . . . . . . .

163yb Yras!

, , , I . . . . I . . . . . . . . . . . . I i , , ,

5 Io 15 > > .~o Spin Ihl

. . . . I , , , , I . . . . I ~

5 10 15 2O 25 ~(

Fig. 3. Transition quadrupole moments of the [ 660 ] 1/2 intruder band and the negative-parity yrast band (assuming K = ] ) in 163Lu and the positive-parity yrast band of J¢'3Yb. Filled and open symbols are quadrupole moments measured in the RI)M and DSAM experiments, respectively. The estimated uncertamt) of the stopping power is included m the DSAM results.

s t r u c t u r e f avour s the o c c u p a t i o n o f the i~3/2 p r o t o n o rb i t a l s on ly for Z > 73 [ 14 ], h o w e v e r at t r i ax ia l de- t b r m a t i o n a large ene rgy gap in the s ingle par l i c le s p e c t r u m occu r s a l r eady for l u t e t i u m wi th Z = 7 1 . T h i s is to o u r k n o w l e d g e the first case whe re one ob-

t a ins the coex i s t ence o f r a t h e r s t ab le t r iax ia l m i n i m a at pos i t i ve a n d nega t ive ,' va lues in an i n t r u d e r con- f igura t ion . W i t h the d e f o r m a t i o n p a r a m e t e r s g iven a b o v e we ca lcu la te a q u a d r u p o l e m o m e n t o f Q , ..... = 10.7 b us ing lhe r e l a t ion g iven by N a z a r e w i c z et al.

233

R

xvrec

Decay curve

W.Scmitz et a., PLB 303(1993)230

Stop flight

Recoil Distance Doppler Shift Method!

-  precision of the distance ~0.1 µm!-  target–to–stopper distance measured as a

capacitance between the 2 plates!-  well stretched target and stopper and good

parallelism!-  distance scale transformed in time scale from

average velocity !!-  in complex level schemes the result is altered

by!-  multiple exponential decay components!-  feeding from states above with

comparable lifetimes!-  use Bateman for the feeding of the states and

make a global fit of the level scheme !-  doesn’t work for unknown feeding!

Det.

EshEu

Eu

Esh

θ

Differential Decay Curve Method!

-  the Bateman equation can be reformulated in terms of the observed unshifted intensity for different target–to–stopper distances!

! ! where bji are the branching ratios for the feeding transitions !!Coincident Differential Decay Curve Method !

gate from above – eliminates the problems of unknown feeding! – selects the feeding path of the states!

τ idNi t( )dt

= bjiN j t( )−Ni t( )j∑

B

A

B – A coincidence has 3 components (gate set on B):!

I BA = IssBA + Isu

BA + IuuBA

IusBA it is not possible

Coincident DDCM!

-  gating from above on B (A is measured) !-  gate on (s+u) à eliminates background & side feeding!-  gate on u à direct lifetime measurement with no need of solving the ! Bateman equation!

τ =IsuBA x( )

vrecddx

IssBA x( )

P. G. BIZZETI et al. PHYSICAL REVIEW C 82, 054311 (2010)

FIG. 8. (Color online) Line-shape analysis of the 6+1 ! 4+

1 ,513-keV ! -ray transition measured at three different distances andregistered by detectors from the forward ring 1 and determinationof the lifetime of the J " = 6+

1 state in 122Ba. On the left-hand sidethe spectra obtained by setting a gate on the shifted component ofthe 620-keV transition, which feeds directly the level of interest, areshown. The meaning of the other panels is the same as in Fig. 6.

The precise knowledge of the time evolution of the velocitydistribution of the recoils is critical for the description of theline shapes. The best way to obtain this information is byperforming a full Monte Carlo (MC) simulation of the creationof the recoils, slowing down in the target, free flight in vacuum,and slowing down in the stopper. At a second stage of the MCsimulation, the velocity histories are randomized with respectto the two detectors between which the ! -! coincidences arerecorded. Numerical simulations reveal that a summation over10 000 MC histories is sufficient for a stabilization of theline shapes. We performed a Monte Carlo simulation of theslowing-down histories of the recoils using a modified [29,32]version of the program DESASTOP [33], which allows for anumerical treatment of the electron stopping powers at ionenergies relatively higher than those of the original version. Onthis basis, a procedure for the analysis of the measured data wasdeveloped [29,32]. To fix the stopping power parameters of thetarget we considered the spectra at large distances, where onlyshifted peaks are present for shorter lifetimes. Their line shapesare satisfactorily reproduced by using the simulated velocitydistribution. Hence one can conclude that the stopping powerof the target material is correctly taken into account. The effect

FIG. 9. (Color online) Line-shape analysis of the 8+1 ! 6+

1 ,620-keV ! -ray transition measured at three different distances andregistered by detectors from the forward ring 1 and determinationof the lifetime of the J " = 8+

1 state in 122Ba. On the left-hand sidethe spectra obtained by setting a gate on the shifted component ofthe 694-keV transition, which feeds directly the level of interest, areshown. The importance of the DSA contribution (short-dashed line)is evident. The meaning of the other panels is the same as in Fig. 6.

of the momentum carried out by evaporated neutrons fromthe compound nucleus is also taken into account in the MCprocedure. Concerning the slowing down in the stopper, for theexperiment performed at LNL, the mean time interval neededby the recoils to come to rest is predicted to be about 0.8 pswhereas the whole process is fully completed within about1.4 ps (see Fig. 5). The time step used for the digitalization ofthe velocity histories was #t = 8.87 fs.

To illustrate the application of the procedure followed inthe analysis, we show in Figs. 6–9 examples concerning thelifetime determination for the 196-, 373-, 513-, and 620-keVtransitions that depopulate the J " = 2+

1 , 4+1 , 6+

1 , and 8+1 levels,

respectively. On the left-hand side of the figures, the lineshapes, recorded at the indicated distances, are displayedtogether with the fits. We would like to state that the lifetimevalue reported in each figure is obtained from the data collectedin the ring mentioned in the caption, whereas the correspondingone given in Table I is an average value deduced from the datacoming from all the relevant rings.

Possible contaminations of the relevant transitions havebeen accurately evaluated in the analysis. For the 196-keV,2+

1 ! 0+ transition they could be from the 199-keV-band(4)

054311-6

122Ba!

61+ → 41

+

Differential RDDS Method!

-  for use with in setups that require the detection of the recoiling nuclei!-  stopper replaced with a degrader! CLARA & AGATA + PRISMA!

PIAVE


PIAVE

J.J.Valiente-Dobon et al, PRL102(2009)242502!

CLARA + PRISMA!


PIAVE

Differential RDDS AGATA measurement at LNL with 76Ge + 238U reaction!

Plunger IKP University Köln TU Darmstadt!

Spectra taken at 50 kHz per capsule counting rate!AGATA-PRISMA RDDS measurement θG=55º!

E.Sahin, A.Görgen, M.Doncel!

Doppler Shift Attenuation Method (DSAM)!

v(t) from Monte Carlo simulation with stopping power

-  thin target ~500 µm/cm2!-  target backing of a high Z stopper material

(Au/Pb/Ta)!-  recoils decay in–flight while stopping in the

target!-  lineshape depends on the nuclear lifetime!



-  DSAM applies when the lifetime is of the order of the slowing down time of the recoils in the target (10–13 – 10–12 s)!

-  analysis of the gamma ray lineshapes as a function of the detection angle to determine the nuclear lifetime!

-  the lineshape will depend on the velocity of the recoil (from v0 to 0) when the gamma ray was emitted!

-  the centroid of the lineshape is a measure of the average recoil velocity !

-  the centroid is expressed usually in terms of Doppler Shift Attenuation Factor!

Esh θ( ) ≈E0 1+ β cosθ( )

F τ( ) = vv 0=

1v 0τ

v t( )e−tτ dt

0

∞

∫



-  v(t) is determined based on the stopping powers!

-  stopping powers:!-  electronic stopping!-  nuclear stopping (scattering of the

nucleus) – Monte Carlo simulations of the recoil velocity profiles!

-  the lineshape dN/dE can be directly related to the nuclear lifetime!

-  a knowledge of the velocity distribution dv/dt allows for the calculation of the lineshape for a given τ

-  the accuracy of the method is limited by the !-  inaccuracy of the stopping power

models (10 – 15% systematic error)!-  unknown side feeding of the states!

dN t( ) = 1τe−tτdt



Steps for the simulation of the lineshapes!-  simulate the slowing down history of the

recoils in the backing; provides v(t) and θR(t)!-  calculate the Doppler shift observed at the

angle θγ as a function of time!-  calculate the population N(t) of the state by

solving the Bateman equation!-  simulate the energy spectrum in a gamma

ray detector from N(t)!-  compare with the experimental lineshape

and minimize χ2!


0

500

1000

1480 1535 15900

50

100

2080 2170 2260

0

100

200

1840 1930 20200

50

100

2340 2480 2620

0

50

100

1950 2025 2100

E� (keV)

�=72o

1535 keV 4+1 - 2+ 2168 keV 8+

2 - 6+1

1941 keV 6+1 - 4+

1 2488 keV 6+2 - 4+

1

2035 keV 8+1 - 6+

1

Cou

nts

0+ 0

2+ 850

4+ 2384

6+ 4325

8+ 6360

10+ 7381

8+ 6493

6+ 4872

4+ 3585

4396 3–

5137 5–

12+ 6820

849.

515

34.5

1941

.020

35.3

1021

.4

888.5

2167

.6

1620.8

2488

.0

1286.7

2735

.0

2753

.0

740.

6

3546

.3

1553

130+-T1/2=45.9 sec 52Fe

Gate from below

Fractional Doppler Shift!

-  in the case of superdeformed bands with large Qt lifetimes are very short (<100 fs)!-  gamma ray emission occurs before significant slowing down of the recoils ! à large Doppler shift with angle and no significant lineshape!-  use of F(τ) for the analysis of the centroids shift!

case. The beam was delivered by the XTU Tandem accelera-tor of the Legnaro National Laboratories. The target con-sisted of a 1 mg/cm2 100Mo foil evaporated on a 10 mg/cm2gold backing which completely stops the recoiling nuclei. !rays were detected by the GASP array consisting of 40 highefficiency Compton-suppressed HPGe detectors and of aninner ball of 80 bismuth germanate "BGO# detectors. Eventswere collected when at least 3 suppressed Ge detectors andfive BGO detectors of the inner ball fired in coincidence. Atotal of 2.13!109 events were collected on tape, which, afterthe data unpacking resulted in 3.94!109 threefold coinci-dence events available for off-line analysis.The Ge detectors in the GASP array are placed symmetri-

cally with respect to the beam direction in seven rings, asfollows: six at 35°, six at 60°, four at 72°, eight at 90°, fourat 108°, six at 120°, and six at 145°. In the off-line analysisthe highest spin states of 144Gd "including SD states# wereenhanced by setting proper conditions "high sum-energy andhigh multiplicity# on the inner BGO ball. In order to simplifythe analysis, the data were reduced by sorting only the eventswith energy comprised between 750 and 1625 keV, whichcorresponds to the region where the SD band transitions lie.The analyzed spectra were obtained by double gating on in-band transitions seen by all detectors and projecting on theseven rings of detectors available in the GASP geometry.Typical double-gated spectra at forward and backwardangles are shown in Fig. 1.The experimental fractional Doppler shift, F($), was de-

termined according to the following relation:

F"$#"%E!

2&E!0 cos ' fwd, "2.1#

where %E! is the energy difference between the centroids ofthe shifted ! rays corresponding to the forward and back-ward angles (' fwd and (#' fwd , respectively#, E!0 is theunshifted !-ray energy, and &"v 0 /c, where v 0 is the meaninitial recoil velocity. The resulting F($) values versus theenergy of the SD band transitions are presented in Figs. 2and 3; the error bars drawn in the figure are the statisticalerrors derived from the spectra of the 35° and 145° detec-tors. The points corresponding to the 1084 and 1134 keVtransitions are taken only from the forward ring, since thesetransitions are strongly contaminated in the backward ring.The slowing down process of the recoiling nuclei and the

velocity profile have been simulated using the codes devel-oped by Bacelar et al. )12*, as modified by Gascon et al.)13*. The stopping power and the multiple scattering of therecoils were described using a Monte Carlo simulation basedon the LSS parametrization )14*. We used a number of 5000histories and up to 1600 steps of 1 fs. The electronic stop-ping power was calculated according to the formalism ofBraune )15*. The calculation of the theoretical F($) valuesdepends on the mean decay time of the state "often called

FIG. 1. Double-gated coincidence spectra corresponding to thedetectors of the 35° and 145° rings with respect to the beam direc-tion. Gates are set on clean transitions belonging to the 144Gd yrastSD band. The shifts of the ! rays are indicated by arrows. The linemarked with an asterisk corresponds to the 1018 keV 12$!10$

transition in the low-spin part of the level scheme.

FIG. 2. Experimental "filled circles# fractional Doppler shifts for!-ray transitions depopulating states of the 144Gd SD band abovethe backbending. Tha data are taken from the spectra correspondingto the most forward and backward rings of detectors. The solid linerepresents the best fit to the data when keeping the same value forthe SD band and the side-feeding quadrupole moments leading toQ0"13.7 e b. The limits to the Q0 value as obtained by a standard+2 minimization procedure are also drawn. The inset shows thetwo-dimensional +2 minimization surface as a function of Q0 andQsf . The star represent the absolute minimum in the surfacewhereas the dashed line corresponds to Q0"Qsf .

C. A. UR et al. PHYSICAL REVIEW C 60 054302

054302-2

48Ti (@214 MeV)+ 100Mo à 144Gd!!target 100Mo 1 mg/cm2 on Au 10 mg/cm2!

!GASP – congiguration I

Fractional Doppler Shift!

-  in the case of superdeformed bands with large Qt lifetimes are very short (<100 fs)!-  gamma ray emission occurs before significant slowing down of the recoils ! à large Doppler shift with angle and no significant lineshape!-  use of F(τ) for the analysis of the centroids shift!

‘‘apparent lifetime’’!, which is defined by the mean lifetimeof the state and the entire decay history above the state,including the unknown sidefeeding. The program we used isa modified version of the one reported in Ref. "4# and isdealing with a rotational cascade, having a constant intrinsicquadrupole moment Q0, where each state has a sidefeedingprovided by a rotational sideband with the same dynamicalmoment of inertia I(2) as the SD band and an intrinsic quad-rupole moment Qsf .The assumption is furthermore made that all sidebands

feeding the SD band levels have the same Qsf , as suggestedpreviously by Ref. "16# and measured more recently "4# forthis mass region. Since the cranked shell model calculations$see Introduction! predict a configuration change associatedwith the backbending, we have chosen to fit separately thedata points above and below the backbending. In the follow-ing we will therefore denote by Q0

up the intrinsic quadrupolemoment of the states above the backbending and by Q0

do theone for the states below the backbending. It is clear that theanalysis will be more accurate for the states above the back-bending where a larger number of experimental points isavailable.The intensity of the sidefeeding was taken from a previ-

ous measurement using thin target "2# and recalculated ac-cording to the double gating procedure employed to build thespectra. For a better description of the in-band decay historywe took into account in the calculations all four %-ray tran-sitions above the one of 1418 keV, the last one for which wecould measure the F(&) value $see Fig. 1!. The side-feedingeffects are stronger in the upper part of the SD band wherethe side-feeding intensities are large compared with the in-band decay. In order to reproduce the side-feeding effects theprogram allows to add on top of the SD band a cascade ofvirtual %-ray transitions having the same J (2) as the SD bandand a quadrupole moment Qsf . In our case, the best fit of thedata was obtained by adding a cascade of three virtual %-raytransitions on top of the known SD band transitions.In the inset of Fig. 2 we show the two-dimensional mini-

mization of the '2 values in the space defined by Q0up and

Qsf . One can notice the large covariance between Q0up and

Qsf which results in a wide minimum. The absolute mini-mum '2 value correspond to Q0

up!14.2 e b and Qsf!9.6 e b $that point is marked with a star on the figure!.This would imply a slow sidefeeding which is not consistentwith the data since the apparent lifetime of the highest levelsof the SD band is very short $about 10 fs or less!. The samesituation has been encountered in the case of the yrast SDband in 152Dy "16# and, following that work, we have alsoassumed that the side-feeding bands have the same feedinghistory as the SD band leading to equal values for the sidefeeding and effective in-band feeding times. This assumptionis also supported by a more recent work on several neigh-boring nuclei "4#. In order to derive the SD band quadrupolemoment we have then followed the Q0

up!Qsf line marked inthe inset of Fig. 2 by a dashed line. The minimum '2 valuecorresponds to Q0

up!13.7"0.9#1.1 e b. The calculated F(&)

curves for the best fit of the experimental data and for theerror limits are also shown in Fig. 2 together with the experi-mental points.

Once obtained in this way the quadrupole moment of theSD band above the backbending we extended the analysis toinclude also the points below the backbending. In the inset ofFig. 3 we show the two-dimensional minimization of the '2

values in the space defined by Q0up and Q0

do . The minimumvalue correspond to Q0

up!13.7 e b $with practically thesame error limits as from the analysis of the points above thebackbending! and Q0

do!11.6"1.0#1.4 e b. We also show in Fig.

3 the F(&) curve calculated for the entire band with Q0up

!13.7 e b and Q0do!11.6 e b and the limits defined by the

errors on the Q0do .

The errors on the final values of Q0 both above and belowthe backbending, as obtained from the '2 minimization pro-cedure, are rather large. This implies that the two Q0 valuesoverlap at 12.8– 13.0 e b and a unique Q0 of about 13.0 e balong the whole band could also fit the data. This gives onthe other side a much higher '2 and we therefore believe thatthe data are indicative of a decrease of the quadrupole mo-ment when going from states above to states below the back-bending. If we take the values corresponding to the best fit ofthe data (Q0

up!13.7 e b, Q0do!11.6 e b! a 15% change in

deformation is derived. A drop of collectivity $but not quan-tified! has been also reported for the SD band 2 in 149Gdbelow the backbending observed at low frequencies "4#.We have also to note that the results are, as usual, subject

to 10–15% systematic errors due to the uncertainties on thestopping power parametrizations. However, this does not af-fect the relative deformations below and above the back-bending.

FIG. 3. Experimental $filled circles! fractional Doppler shifts forthe whole yrast SD band in 144Gd extracted from the spectra corre-sponding to the most forward and backward ring of detectors. Thesolid line represents the best fit to the data with the correspondingQ0 values above and below the backbending indicated. The limitsto the Q0 value below the backbending as obtained by a standard '2

minimization procedure are also drawn. The inset shows the two-dimensional '2 minimization surface as a function of Q0

up and Q0do .

QUADRUPOLE MOMENT OF THE YRAST . . . PHYSICAL REVIEW C 60 054302

054302-3

F τ( ) = vv 0⇒ v =F τ( )v 0

Ec θ( ) ≈E0 1+F τ( )β0 cosθ( )

F τ( ) = Ec −E0

E0β0 cosθ

Centroid shift

Krakow RFD (straggling) Method !

TRIM Monte Carlo calculation

J.F.Ziegler J.P.Biersack

Target cross time

18O + 30Si @ 68MeV

P.Bednarczyk, W.Meczynski, J.Styczen et al.

P.Bednarczyk, W.Meczynski, J.Styczen et al.

gamma–ray spectroscopy! part vi nuclear lifetimes and...

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