Excited states in 111Cd

2.A:3.A I

Nuclear Physics A109 (1968) 529--538; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

E X C I T E D S T A T E S I N 111Cd J. McDONALD and D. PORTER t Department of Natural Philosophy, Unicersity of Glasgow, Scotland Received 23 November 1967 Abstract: The energy levels in m Cd have been investigated by Coulomb excitation using helium ions and from the fl-decay of n~Ag. The half-life of the 246 keV level has been redetermined by the fly-delayed coincidence method. Gamma-ray energies and intensities have been measured using Ge(Li) detectors and B(E2) values deduced for levels at 246, 342 and 620 keV and for a new level at 755 keV. The energy of the 620 keV level is substantially higher than that previously accepted. Five new transitions have been found, and partial half-lives for 13 gamma rays are tabulated. Transition probabilities are discussed in terms of the core excitation and the pairing-plusquadrupole-force models.

E

RADIOACTIVITY 1nAg [from 11°Pd(n, 7)]; measured fy-delay, E~. 111Cdlevel deduced 7"+. Enriched target, Ge(Li) detector. NUCLEAR REACTIONS mCd(~, ~'y), E = 8 MeV; measured cr(E~), mCd deduced levels, B(E2), T~. Enriched target, Ge(Li) detector.

1. Introduction T h e energy levels o f 111Cd have f o r m e r l y been considered in terms o f the states available to the 63rd n e u t r o n which is in the 3s+ subshell. The g r o u n d - s t a t e spin a n d the isomeric level at 397 k e V fit in well with the single-particle description 1). T w o levels with spins z3+ a n d ~s+ are strongly p o p u l a t e d by C o u l o m b excitation 2), a n d it has been suggested t h a t they arise f r o m the w e a k c o u p l i n g o f the o d d particle to a n excited state o f the even core 3). This has been discussed with r e g a r d to betad e c a y experiments by D e l a b y e et aL 4). Kisslinger a n d Sorensen 5) have used the p a i r i n g - p l u s - q u a d r u p o l e - f o r c e m o d e l to predict the energy levels, a n d Sorensen has also studied the E2 t r a n s i t i o n rates 6). Recently Barnes et al. v) have o b t a i n e d wave functions for 1 l l C d which give better a g r e e m e n t with the results o f stripping exp e r i m e n t s t h a n those o f ref. s). This p a p e r describes a high r e s o l u t i o n study o f the g a m m a rays following C o u l o m b excitation o f ~ C d which e n a b l e d hNf-lives to be d e d u c e d for l l g a m m a rays, five o f which were n o t p r e v i o u s l y known. The wave functions o f Barnes el al. 7) were used to calculate theoretical t r a n s i t i o n rates, a n d these are c o m p a r e d with e x p e r i m e n t in sect. 4. The m e a s u r e d rate for the t r a n s i t i o n between the levels f o r m i n g the p r o p o s e d d o u b l e t o f the core excitation m o d e l is very low a n d leads to a negative value for the g y r o m a g n e t i c ratio o f the core. This is discussed in sect. 3. * Present address: AWRE, Aldermaston, Berkshire, England. 529

530

J. McDONALD

AND

D.

PORTER

2. The decay of 11tAg A source of 7.5 d t t tAg was prepared by neutron irradiation of palladium enriched to 87.5 % in 11°pd. The l t i P d decays with a half-life of 5.5 h to 11tAg, and this activity was allowed to die before measurements were made. A Ge(Li) detector system with a crystal active volume of 7 cm 3 and an energy resolution ( F W H M ) of 14 keV was used to observe the lt~Ag decay. The spectrum recorded on the Laben 512 analyser is shown in fig. 1. The decay scheme is given in fig. 2. The level energies are those determined in the present work, while the 8 - branching ratios are taken from *). t

- - - -

i

T

88 (long) "%o,.° ....'

*..

o¶

342 °'",,.. %°,°,,°,,

~.

E

"4

-

o L)

10

246.5

100

200 Energy

300

400

keV

Fig, 1. Energy spectrumof gamma rays ffomthe decay ofmAg in a 7 cm3Ge(Li) detector. 2.1. HALF-LIFE MEASUREMENT The half-life of the 246 keV first excited state in t l tCd is important in perturbed angular correlation work and has previously been measured with high accuracy 8 - 1o). These workers used t t tin sources, and the half-life was determined by the ~?-delayed coincidence method. We have re-measured this half-life using the t 1t a g source and the/~-delayed coincidence method. This approach yields better time resolution than that obtained in the previous work. Beta rays were detected in a 0.6 cm x 2.5 cm N a t o n 136 plastic scintillator and the 246 keV g a m m a ray in a 2.5 cm x 2.5 cm NaI(T1) crystal. Pulses from the anodes of the 56 AVP photomultipliers were limited by fast diodes and clipped by shorted delay cables to give voltage spikes which triggered tunnel

Xaicd EXCITED STATES

531

diode discriminators (E, G and G type TR 104S). These discriminators operated a start-stop time to pulse-height converter (type TH 200 A) operated on the 1 /is range. A single-channel analyser was set on the 246 keV photopeak in the gamma ray detector, and was used to gate the Laben 512 analyser. Since 92 % of the beta decays from 11 lAg feed the ground state of ~t ~Cd, no side channel selection was made of the 7.5d I\\

'G r-

IL

620.6

~,~

u103,_~ !

1118Cd63

L 1 102

t

L_

100

200

I

300

~ _ _

400

~L_

500

n sec

Fig. 2. Decay scheme o f m A g and fiT-delayed coincidence time spectrum for the 246 keV level. Spin values are given in table 2. TABLE I

Experimental values for the half-life of the 246 k e V level in 1]]Cd Ref.

T~r(ns )

s)

84.8-4-0.8 --0.5

9)

84.1 ~ 0 . 5

lo)

85.3~2.1

present work

85.0±0.7

beta rays to avoid counting rate effects in the slow channel. Random coincidence spectra were determined during the measurements by recording time events obtained by interchanging the start and stop inputs of the time to pulse height converter. A time spectrum with random coincidences subtracted is shown in fig. 2. The prompt

532

J. McDONALD

AND D. PORTER

part of the spectrum results from coincidences between beta rays and degraded 342 keV g a m m a rays, and has a F W H M of 6.3 ns and a slope corresponding to a halflife of 1.6 ns. Time calibration was performed with an E, G and G delay box type DB 263. P r o m p t time spectra were accumulated at intervals up to 56 ns nominal delay, allowing correction to be made for the affect of pulse attenuation. The final time calibration was the result of many measurements, all of which agreed within the error limits. The value found for the half-life of the 246 keV level is 85.0 + 0.7 ns. This is compared with the previous results in table 1.

3. Coulomb excitation of m C d

Previous Coulomb excitation measurements on ~t t Cd a, t l) used NaI(T1) gammaray detectors, and only strongly excited levels could be clearly identified because of the poor energy resolution and the g a m m a rays from other cadmium isotopes present in the targets. 1----

10~

t

iF

- - T - -

I

341.9 248.4

104L F ~_ L

.........

620 •,-617.4(~2Cd) 374.2

a~ e-

1L4 1 3 :'-" ".....:"..

l

508.5 .511

""''...i! ,, A
102

~°Cd )

i "'°"

I

I

I

"'"°

i! / .. ~ _ _ _

200

400 600 800 Energy key Fig. 3. Energy spectrum of gamma rays in the 24 cma Ge(Li) detector following Coulomb excitation of mCd with 8 MeV s-particles.

The apparatus used in the present investigation has been described in an earlier paper 12). A cadmium target enriched to 86.7 % in l i l C d was Coulomb excited by 8 MeV a-particles from the Van de Graaff at AERE, Harwell. The resulting g a m m a

11aCd EXCITEDSTATES

533

rays were detected in a 24 cm 3 Ge(Li) system which had a resolution of 4.3 keV. The spectrum is shown in fig. 3. The peaks not identified on the figure by an isotope number are interpreted as resulting from excitation of four levels in ~ C d . These levels have energies of 246.3_+0.6, 341.9_+0.6, 620.5_+ 1.0 and 754.9_+ 1.0 keV. The first two values agree with the energies 246.5_+0.8 and 342.04-0.8 keV determined from the decay of a ~l a g . The energy of the 620 keV level is substantially higher than that previously reported 2). TABLE 2 Energies and upward reduced transition probabilities for levels in 11xCd Level energy (keV)

Spin and parity

B(E2) (e2 x 10-50 cm 4)

B(E2) a)

246.3±0.6

~+

0.23±0.05 0.21Jz0.02 b)

341.94-0.6

~+

8.7 ±1.0

11.0~0.9

620.54-1.0

~+

12.6 -5=1.7

14.3±2.2

754.9~1.0

~+, ~+

4.2 ±0.8

a) Ref. 2). b) This value was obtained from the direct half-life measurement assuming c%t = 1.06.

The peak at 620 keV is composite, and in determining the value of B(E2) for the 620.5 keV level in ~l~Cd, a value 13) of 51 (units of e2× 10 -5o cm 4) was taken for B(E2) for the 617.4 keV level in 112Cd also present (6.4 ~ ) in the target. The energy assignment to the level in 111Cd is confirmed by the presence of cascade radiations with energies 374.2+0.6 and 278.8_+0.8 keV feeding the levels at 246 and 342 keV. G a m m a - r a y intensities were determined directly from the peak areas and the measured efficiency of the Ge(Li) detector. The B(E2) value deduced for the 246 keV level, after correction for the transitions from the upper levels, was much larger than that obtained from the directly measured half-life of the pure E2 transition. This suggested that there was another cascade g a m m a ray feeding the level. The peaks at 754.9 keV and 413.0 keV were attributed to a level at the former energy and a cascade g a m m a ray to the 341.9 keV level. The expected transition to the 246.3 keV level would have an energy of 508.5 keV and would therefore not be resolved from the 511 keV annihilation radiation always encountered in these measurements. The peak at 511 keV in the a~lCd spectrum was found to be broadened and had a different centroid position compared with pure 511 keV peaks obtained by bombardment of other targets and from a 22Na source. This enabled an estimate to be made of the intensity of the 508.5 keV radiation. With this extra decay mode included in the decay scheme, the B(E2) value obtained by direct excitation of the 246 keV level corresponded to a halflife of 76_+ 16 ns in reasonable agreement with the direct measurement.

(3.50±0.44) × 10-11

(1.02 :~0.14) X 10-11

(1.64___0.25)X 10-11 e)

341,9

620.6

754.9

{+

~+

{+

413.0 174

~+

½+

508.5

{+, {+ e)

~+

200.3 754.9

~+

278.8

½+

{+

½+

½+

Final state

{+

~+

{+

{+

Initial state

374.2

620.6

95.5

341.9

246.4

Transition energy (keV)

97.9 2.1

E2

12,0

56.6

31.4

2.1

3.7

24.9

69.3

M1

M1 ( + E 2 )

MI(+E2)

E2

M1 ( + E 2 )

M1 ( + E 2 )

M1 ( + E 2 )

E2

1.4

13,0

E2 MI(+E2)

85.6

100

Relative radiative intensity (~)

MI

E2

Multipolarity

6.45 x 10-9

1.36 X 10-1°

4.3 X 10-11

9,1 Xl0 -1~

1.64 x 10-11

4.68 × 10-1°

2.78 × 10-1°

4.13 × 10-11

1.48 X 10-11

2.66 × 10-9

2.78 x 10-1°

4.22 × 10-it

9.05 x 10-s

Partial radiative half-life (sec)

1/17

29

136 b)

54 b)

1/4.4

165 b)

270 b)

97 b)

1/12.9

104 b)

1/13.6

76

4.7

Hindrance factor a)

Conversion coefficients were taken from ref. 1~) and E2/MI ratios from ref. 0a) Comparison is with the Weisskopf estimates, ref. 15). b) Factors calculated assuming a pure MI transition. e) All half-lives calculated assuming spin ~ + for 755 keV levels. For a finite value of ~z these half-lives should be multiplied by 2~/3(1+?J"). ~) All data on the 420 keV level are from ref. xs).

(1.2 :~0.3) × 10-1°

(8.50!0,07) X 10-8

246.4

420,3 ~)

T½ (sec)

Level energy (keV)

TABLE 3 Half-lives, relative radiative intensities and hindrance factors for transitions in m C d

o

~"

nlcd

EXCITED STATES

535

There has been no previous report of a level at 755 keV, but a gamma ray of 720 keV has been seen in Coulomb excitation a~), and a level at 736 keV has been reported in proton scattering work 14). The values of B(E2) for the four levels in 1,1Cd seen in the present investigation are listed in table 2, which also lists the earlier results of McGowan and Stelson 2). The more accurate value of B(E2) obtained from the direct lifetime measurement is also shown in table 2. A value of 1.06 for the total conversion coefficient was used to obtain this value. We obtain a slightly smaller result for B(E2) for the 341.9 keV level than that of ref. 2), but we observed an additional transition feeding this level. '~ ~ c~

(~:~')

~

key

-

- - 7 5 4 9

620.6 :i

I~ ~1 t'~

-~Ix ~ '

_~

420.4

[--I

341.9

r 1

111 48

Cd

63

Fig. 4. The level scheme of nlCd determined by the present experiments. Intensities shown are for total transitions.

Table 3 gives half-lives, partial half-lives and the retardations with respect to Weisskopf single-particle half-life estimates 15) for each transition. The observed relative radiative intensities are also given. The decay scheme determined by the present study is given in fig. 4. The relative intensities shown on the figure are for total transitions. Internal conversion coefficients were obtained from ref. 16) and the tables of Rose ,7). For completeness, table 3 also lists information on the 420.3 keV level from the half-life measurement of Sparrman et al. is). 4, Discussion

4.1. CORE EXCITATION MODEL The identification of a group of levels in an odd nucleus as a multiplet arising from the coupling of the odd particle to an excitation of the even core is generally difficult.

536

J, M c D O N A L D A N D D . P O R T E R

When the odd particle has spin ½, however, only two levels occur in the multiplet and identification should be more precise. It was suggested by de-Shalit a) that 111Cd would be a suitable case to study, as the odd neutron is in an s~ orbit. In the Coulomb excitation experiment, the levels at 342 and 620 keV are strongly excited, and their spins are those expected for a core excitation doublet. The downward B(E2) values of 4.35 and 4.3 (units are e2x 10-5 o cm 4) are similar, in agreement with the model. The M 1 transition from the 342 keV level to the ground state is retarded by a factor of 76 with respect to the Weisskopf estimate. The transition is forbidden by the coreexcitation model, but as it is also/-forbidden on the single-particle model no conclusion can be drawn from this. In the Coulomb excitation experiment, we were able to measure the strength of the 279 keV transition between the members of the proposed doublet. If this transition is assumed to be pure M1 it is retarded by a factor of 270. Any E2 admixture would mean an even higher M1 retardation. On the basis of pure M1 the reduced transition probability is B(M1) = 6.5 x 10-3 in units (eh/2Mc) 2. Formula (9) of ref. 3) relates the strength of a proposed inter-multiplet M1 transition to gp and go, the gyromagnetic ratios of the particle and core. Using the measured value of B(M1) gives (g _gp)2 = 6.8 x 10 -2. If we assume that the ground state magnetic moment of 1~1Cd is due to the motion of the odd particle, we obtain gp --- - 1 . 1 8 . This leads to g¢ = - 0 . 9 or - 1 . 4 . Any E2 admixture in the transition would make these answers approach the value - 1.2. This raises the question of the interpretation of the core state in the de-Shalit model. In ref. 3) and in most experimental papers making use of this model agreement of B(E2)~ for members of the multiplet with the measured values for neighbouring even nuclei is taken as evidence in favour of the model. More recently de-Shalit 19) has stressed that the essential evidence for this model should be sought within the odd nucleus itself. For example in this case a measured value of the magnetic moment of the 342 or 620 keV levels would check whether the data are consistent with the above values of gc and gp. F r o m this point of view, our result for g~ merely indicates that the core in de-Shalit's model can be very unlike the neighbouring even nuclei which should have a positive g~ < Z / A [ref. 20)] for the first excited state. (The value of g has recently been measured 21) for ll4Cd, giving g = 0.44+0.06.) The predictive value of the core excitation model is greatly reduced if there is no continuity between the properties of the "core" and neighbouring even nuclei, so it is our opinion that the value of g~ from the 11~Cd experiment reveals a limitation to the usefulness of the model. 4.2. PAIRING-PLUS-QUADRUPOLE-FORCE MODEL In a recent paper by Barnes et al. 7), wave functions for 11 ~Cd are calculated as a superposition of base functions formed by the coupling of a quasi-particle in each orbit to a system including up to two phonons. Coefficients determining the proportion of each base state in the wave function for a particular level in the nucleus were found by diagonalizing the Hamiltonian of the odd-particle system. The energies

537

lllcd EXCITED STATES

chosen for the single-particle orbits differed from those of Kisslinger and Sorensen 5) by allowing a smaller occupation probability for the 3s~ neutron orbit in order to yield better agreement with the results of stripping experiments. We have used table 5 of ref. 1) to calculate theoretical values of B(E2) for transitions in 11~Cd by substitution in eq. (4.10) of the paper by Yoshida 22)t. The one-phonon transition strength was taken as the average for the 0 + ~ 2 + transitions 13) in 110, 112Cd" The small twophonon amplitudes were not considered. A comparison of the experimental results with these predictions is given in table 4. The agreement is good for the enhanced transitions to the 342 and 620 keV levels, but the wave functions fail to predict the observed retardation of the 246 keV transition. This type of retardation can occur for E2 transitions between pure quasi-particle levels corresponding to single-particle levels with energies el and ef adding to twice the Fermi energy 2. In these cases, the coupling to collective excitation modes is reduced by the presence of the factor (Ui (_If- Vi Ve)2, but it is not clear whether this is enough to give a retardation when the quasi-particle-phonon coupling is treated by matrix diagonalization. TABLE 4

Comparison of measured values of B(E2) with those calculated using the parameters of ref. 7) Transition energy (keV) 246 342 620

Experimental B(E2)~' 0.21 ±0.02 8.7 ±1.0 12.6 41.7

Theoretical B(E2)~ 6.5 6.7 11.4

A simpler approach to this problem has been made by Ikegami and Udagawa 2 3) who treat the collective coupling to low excited quasi-particle states by perturbation theory. Here the retardation is explicitly seen to be present [their eq. (13)]. Their results for the 246 keV transition in 11 iCd lead to a B(E2)~ value of 0.28, in reasonable agreement with the measured value of 0.21 _ 0.02. Sorensen 6) has obtained retardations in a matrix diagonalization treatment for cases with ei +ee ~ 22. It should be observed that as implied by the last paragraph of this reference the prediction of a retardation should really be taken as a sign that there is no collective enhancement and that a precise B(E2) value would require attention to other components of the wave function than those included in eq. (6) of ref. 6). The results of Barnes et al. correspond to ei -- 2.294 MeV, er = 0.160 MeV, 2 -- 1.685 MeV, t There is a summation over J missing from the collective part of this expression.

538

J. McDONALD AND D. PORTER

leading to a substantial collective c o n t r i b u t i o n for transitions to the d~ quasi-particle level. The wave f u n c t i o n for the 246 keV level also contains appreciable p r o p o r t i o n s o f other terms. It w o u l d be of interest to examine the t r e a t m e n t of Barnes et al. with a different choice of ei a n d ef to see how small a B(E2) value c a n be obtained, a n d whether the modifications needed to minimise this q u a n t i t y m a k e significant changes in their predictions for other properties of this nucleus. The a u t h o r s w o u l d like to t h a n k Dr. D. T. Stewart for his help a n d Professor P. I. Dee for his interest in the work. O n e o f us (J. M c D . ) is i n d e b t e d to Dr. N. MacD o n a l d for m a n y valuable discussions a b o u t the theoretical aspects of the paper. F i n a l l y we acknowledge receipt of a n e q u i p m e n t grant from the Science Research Council.

References 1) M. G. Mayer and J. D. Jensen, in Elementary theory of nuclear shell structure (John Wiley and Sons, New York, 1955) chapt. 13, p. 214 2) F. K. McGowan and P. H. Stelson, Phys. Rev. 109 (1958) 901 3) A. de-Shalit, Phys. Rev. 122 (1961) 1530 4) M. Delabye, J. P. Deutsch and P. Lipnik, Nuclear Physics 80 (1966) 385 5) L. S. Kisslinger and R. A. Sorensen, Revs. Mod. Phys. 35 (1963) 853 6) R. A. Sorensen, Phys. Rev. 133 (1964) B281 7) P. D. Barnes, J. R. Comfort and C. K. Bockelman, Phys. Rev. 155 (1967) 1319 8) P. C. Simms and R. M. Steffen, Phys. Rev. 108 (1957) 1459 9) A. Maier and K. P. Meyer, Helv. Phys. Acta 30 (1957) 611 10) Rietjens, Van den Bold and Heyligers, Physica 21 (1955) 899 11) D. G. Alkhazov, K. L. Erokhina and I. Kh. Lemberg, Izv. Akad. Nauk SSSR (ser. fiz.) 28 (1964) 1667 12) J. McDonald, D. Porter and D. T. Stewart, Nuclear Physics A104 (1967) 177 13) Nucl. Data 1 (1965) 31 14) M. Koike, report of the Institute for Nuclear Study, University of Tokyo (February 1967) 15) D. H. Wilkinson, in Nuclear spectroscopy, part B, ed. by F. Ajzenberg-Selove (Academic Press, New York, 1960) chapt. 5, p. 859 16) Nuclear Data Sheets, National Academy of Science, Washington, D.C. 17) M. E. Rose, Internal conversion coefficients (North-Holland Publ. Co., Amsterdam, 1958) 18) P. Sparrman, T. SundstrSm and J. O. Lindstrtim, Ark. Fys. 26 (1964) 479 19) A. de-Shalit, in Nuclear structure and electromagnetic interactions, ed. by N. MacDonald (Oliver and Boyd, Edinburgh, 1965) 20) W. Greiner, Nuclear Physics 80 (1966) 417 21) S. K. Bhattacherjee, J. D. Bowman and E. N. Kaufmann, Phys. Rev. Lett. 18 (1967) 223 22) S. Yoshida, Nuclear Physics 38 (1962) 380 23) H. Ikegami and T. Udagawa, Phys. Rev. 133 (1964) B1388