Measured lifetimes of states in 197Au and a critical comparison with the weak-coupling core-excitation model

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NuclearPhysics A321 (1979) 231 - 2 4 9 ; ~ ) North-HollandPublishing Co., Amsterdam

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

MEASURED LIFETIMES OF STATES IN 1 9 7 A u AND A CRITICAL COMPARISON WITH THE WEAK-COUPLING CORE-EXCITATION MODEL H. H. BOLOTIN, D. L. KENNEDY, B. J. LINARD and A. E. STUCHBERY

School of Physics, University of Melbourne, Parkville, Victoria, Australia 3052 S, H. SIE

Department of Nuclear Physics, Australian National University, Canberra, Australia and I. KATAYAMA and H. SAKAI

Research Centerfor Nuclear Physics, Osaka University, Suita, Osaka, Japan 565 Received 5 December 1978 Abstract: The lifetimes of five excited states in 197Au up to an excitation energy of 885 keV were measured by the recoil-distance method (RDM). These levels were populated by Coulomb excitation using both 90 MeV 2°Ne and 120 MeV 35C1 ion beams. The experimentally determined spectroscopy of the low-lying levels ]+ (ground state) and ½+, ]~, ~+, and 3 + at 77.3, 268.8, 278.9, and 547.5 keV excitation energy, respectively, has been critically compared with the detailed predictions of the de-Shalit weak-coupling core-excitation model. When the model is taken to represent the case of a d3/2 proton hole coupled to a 19aHg core, the model parameters obtained are in accord with the criteria implicit for weak core coupling and, at the same time, are in remarkably good agreement with virtually all measured E2 and M 1 transition rates.

NUCLEAR REACTIONS 197Au(2°Ne, 2°Ne), E = 90 MeV, 197Au(35C1, 35C1), E = 120 MeV; measured Er, RDM, particle-~ coin. 197Au levels deduced T~/2. Weak-coupling coreexcitation model calculations; predicted static moments, electromagnetic transition rates.

1. Introduction

The inherent relative simplicity, definite sum rules, and specific level spectroscopy predicted by the weak-coupling core-excitation model 1,2) make it particularly interesting to critically examine the low-lying level structures of those odd-A nuclides which appear to be a priori appropriate to be interpreted in terms of this model. This model is expected to be most appropriate 2) for an odd-A nucleus in which the single-particle energy of its lowest allowed odd-nucleon orbit in the average potential of its even-even "core" is considerably below that of the next higher available single-particle orbit in this potential and, at the same time, the latter orbital is also high compared with the excitation energy of the lowest excited core 231

232

H.H. BOLOTIN et al.

state. Under these conditions, it may be expected that the wave function of the ground state of the odd-A nucleus could be represented by the weak coupling of the odd nucleon in its lowest orbit coupled to the 0 ÷ ground state of the core, while its lowest excitation levels could be members of a multiplet of states arising from t h e various couplings of the odd nucleon in its lowest orbit to the first excited 2 + core state [i.e., (2 ÷ +j)~]. Although the spectroscopies of several odd-A nuclei (among them 63'65Cu, 99'l°lRu, l°Spd, l°7'l°9Ag, 199AB, 199Hg and 2°3'2°5T1)have been previously examined in light of this weak-coupling model, comparisons of the experimental spectroscopy of most of these nuclides with predictions of this model have, in the main, been less than completely successful 2-4). Nevertheless, some of the salient spectroscopic properties observed in a number of these nuclides [-spin, parity, enhanced E2 electromagnetic transition rates, and the center-of-gravity energy 1) of the excited multiplet states] appear to be in reasonable accord with the major predictions of this model. Perhaps, no nuclide has had the spectroscopy of its low-lying levels the subject of a greater number of detailed comparisons with the weak-coupling core-excitation model than has 197Au11s" In the past, as more detailed experimental evidence became progressively available on the static moments, reduced transition probabilities, and other characteristics of levels in 197Au, Braunstein and de-Shalit s), de-Shalit 6), and later McGowan et al. 7), Robert-Tissot et al. 8), and Powers et al. 9) examined the spectroscopy of this nuclide in considerable detail and concluded that it was rather well described by the model in terms of a d~ proton coupled to a 196pt core. However, we have noted that one of the more exhaustive of these comparisons 7) appears to contain an important calculational error, and that each of the three most recent of these studies 7-9) draws conclusions which we consider to be internally self-inconsistent to some degree. These, coupled with the absence of direct lifetime determinations reported in the literature for all but the first excited state of 197Au, have prompted us to re-examine the spectroscopy of this nuclide, both experimentally and theoretically (at least insofar as the adequacy of the core-excitation model to account for the observed spectroscopy of its low-lying excited states is concerned). To this end, we have measured directly the lifetimes of all positive parity states up to an excitation energy of 856 keV (except for that of the 77.3 keV first excited state which had been well determined by earlier workers) and utilized these findings and the experimental results of previous investigators in a detailed test of the applicability of the core-excitation model to 197Au.

2. Experimental procedure Levels in 197Au were populated by means of Coulomb excitation using beams of 90 MeV 2°Ne ions from the Osaka University AVF Cyclotron and 120 MeV 35C1 ions from the Australian National University 14 UD Pelletron tandem accelerator.

197Au

233

As the data obtained using the heavier ion beam were more detailed and complete than were those of the preliminary study using 2°Ne ions, we describe, in the main, the experimental details of the 120 MeV 35C1 investigation. A spectroscopically pure, thin gold foil target was used whose thickness, measured in a complementary a-particle Rutherford scattering experiment at the University of Melbourne 5U Pelletron accelerator, was 4.25 +0.5 mg/cm 2. Recoil-distance apparatus of standard design was employed in which the 197Au ions recoiled in vacuum and stopped in a Ta foil (10 mg/cm 2 thick) parallel to the target, through which the incident ion beams readily penetrated to stop in a much thicker (420 rng/cm 2) Ta sheet placed further downstream. A 30 cm 3 true co-axial Ge(Li) detector, placed 6.1 cm from the Au target at 0 ° to the incident beam, registered the de-excitation 7-ray transitions from forward recoiling 197Au ions in coincidence with backscattered 35C1 ions detected in the angular interval 162°-176 ° in an upstream annular particle detector. The reaction kinematics restricted by the coincidence requirement resulted in events recorded for the de-excitation of 197Au nuclei which recoiled in a forward cone of half-angle < 8 ° with an average recbil velocity measured to be v/c = (1.42+0.10)~o. Chance-coincidence event rates were small during the course of the experiment and this contribution to the recorded coincidence data was subtracted prior to analysis. A series of six target-to-stopper distances were employed ranging from 30 to 198/~m, plus an additional one at "infinite" (i.e. 1516/tm) distance. 3. Data analysis and lifetime extraction The data were analysed and corrected for relativistic detector solid angle effects, detector efficiency variations, and cascade feeding, together with assessment of perturbation of nuclear alignment during vacuum recoil, etc., very much along the lines outlined by Johnson et al. 10). The average forward velocity of the recoiling 197Au ions was evaluated experimentally 11) from the weighted average of the observed energy differences between the shifted and unshifted centroids of all transitions at each target-stopper distance. The recoil velocity was also evaluated by calculation 12) and found to agree within error with the experimental value obtained. Overall corrections to the data were minimal and the lifetimes extracted from the corrected data did not deviate in any case by more than ,-~ 3 ~ from those obtained from the raw data. A small error due to uncertainties in the specification of parameters used to assess the effect of de-orientation perturbation 13) has been added in quadrature to the statistical error, as were uncertainties in the corrections made to these data for the effects specified above.

234

H . H . BOLOTIN et al.

4. Results

The corrected ratios of the intensity of the unshifted component to that of the combined shifted and unshifted components of each transition as a function of targetto-stopper separation distance, together with the weighted least-square fit to each, are shown in fig. 1. The level and y-ray decay scheme shown in fig. 2 displays the states of interest. The J~ assignments are those of earlier workers 14) with which our results are wholly consistent. The transitions represented by bold lines are those used in the determinations of the level lifetimes. The extracted mean lives for these states, and the B(E2) values inferred from these results, are compared with those of earlier workers in table 1. The first excited state at 77 keV (½+) was not studied in the present work. The mean life of the 856 keV level [assigned J" = 59 + by Barnard et al. ~s)], though weakly populated, was measured in our investigation. Although this level was observed in previous (d, d'), (n, n') and (n, fly) studies 14), its population in earlier Coulomb excitation works had not been reported 14). Nevertheless, we are confident that the depopulating 577 keV y-ray transition is to be associated with the decay of this state as we observed it with different bombarding ions and Au foils obtained from different sources. A transition of this energy was earlier assigned to proceed 1.0,

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Fig. 1. The measured ratios, R, of the unshifted (lu) to the sum of the unshifted and shifted (Is)),-ray component intensities plotted as a function of the target-stopper distance, D, in #m, for selected transitions depopulating (see caption fig. 2) the designated levels in t97Au. The data points have been corrected for the effects discussed in the text. The solid lines represent the weighted least squares fits to these data whose slopes yielded the meanlives of the levels listed in table I.

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Fig. 2. Level and decay scheme for the low-lying positive parity states of X93Auwhich incorporates the findings of the present experimental investigation and the complementary results of earlier workers. Level and transition energies are in keV. The number above each level give the relative intensities of the designated transitions (7-rays plus internal conversion electrons) specified in ref. ~). The spin and parity assignments, with which the present results are wholly consistent, are those of previous investigators. The transitions designated by bold lines are those used in the measurement of the lifetimes of the states. between this state and the 279 keV {+ level in the report of the (n, n'7) reaction study o f B a r n a r d et al. is). However, it is s o m e w h a t surprising that M c G o w a n et al. 7) did not observe this level in their C o u l o m b excitation work, although they did report evidence for the p o p u l a t i o n of three other states at higher excitation energy (i.e., at 888, 936 and 960 keV) which we did n o t observe. This is particularly puzzling as we find n o evidence in o u r spectra of a few of the de-excitation transitions from these higher states which M c G o w a n et al. 7) show as c o m p a r a b l e in intensity to other ~-rays n o t far r e m o v e d in energy which b o t h we and they clearly observed.

236

H. H. BOLOTIN et al. TABLE 1 Measured and inferred mean lives for designated states in t97Au

Level excitation energy (keV)

j~

77.3 268.8 278.9 502.6 547.5 855.4

½* +]+ ~+ ? ~7 + (~+)

Mean lives measured directly

inferred from measured ~) B(E2~) to g.s.

2.73+0.02 ns a) 22.2 _+ 1.9 ps b) 26.8 +2.1 ps b) < 4 ps b) 9.77_+0.78 ps b) 7.3 --+3.2 ps b)

19.3 +3.8 ps 22.3 +1.3 ps 6.73 ___0.33 ps

a) Ref. 14). b) From present experiment. c) Ref. 7).

5. Application of the core-excitation model 197An 5.1. STATES C O N S I D E R E D C A N D I D A T E S F O R C O R E - E X C I T A T I O N I N T E R P R E T A T I O N

As the measured spin and parity 14) of the ground state of 197Au is 3+, representing within the context of this model the coupling of the odd proton to the 0 + ground state of its even-even core, the most likely single-particle orbital has been taken as d~ [refs. 2, 5- 9)] (more properly d~). The model prescribes the coupling of this odd nucleon (or hole) to the first excited (2~) state of the core to form a quartet of positive parity states with spins of ½, 3, ~ and ~ (i.e., both the ground and excited multiplet states have spins given by Ij-Jcl < J < (J+Jc) where j and J are, respectively, the angular momenta of the single odd d~ proton (or proton hole) and of the 197Au states, and Jc the angular momentum of the core state to which the odd particle or hole is coupled; J~ = 0 and 2 for the 197Au ground state and excited multiplet states, respectively). The quartet of states in 197Au at 77.3, 268.8, 278.9 and 547.5 keV excitation energy possess these spins in sequence and are therefore to be considered as the prime candidates of the excited multiplet in question. Intervening, at an excitation energy of 409 keV, is an ~ - state presumed to be due to single-particle h~ orbital occupation and which, for the purpose at hand, need not be discussed in the context of the core-excitation model. The weakly populated state at 502 keV, whose spin and parity remain unspecified, is presumed to be of other origin. Finally, the proposed 9+ assignment of the 856 keV level similarly removes it from contention insofar as this model is concerned. The exclusion of these three levels from active consideration in analysis of the spectroscopy of 197Au within the confines of this model is in keeping with previous treatments 2, 5-9). In general, the mean lives of the states of interest inferred from the B(E2) values measured in the earlier Coulomb excitation studies 7, a4) are in reasonably good

19"/Au

237

agreement with the lifetime results of the present work (table 1), with that for 547.5 keV 7+ the major discrepancy. 5.2. GENERAL FEATURES OF THE CORE-EXCITATION MODEL

The weak-coupling core-excitation model predicts 1, 2) that for the case of singleparticle (or hole) couplings to the core state, transitions from each member of the excited multiplet to the ground state represent the core 2~- --, 0 + de-excitation. On these grounds, M1 ground-state transitions from the multiplet states would be forbidden, while the corresponding B(E2~) of such transitions should represent, and be equal to, the B(E2; 21 --, 0~) in the core nucleus. However, intra-multiplet M1 transitions with d J = 1 would be allowed as, according to this model, they correspond to single-particle (or single-particle hole) recouplings and should proceed with single-particle speed. Lawson and Uretsky 1) have also shown that the center-of-gravity of the excitation energies of the multiplet members should coincide with the excitation energy of the 2 + state of the core. To the extent that configuration mixing is present, these simple prescriptions may be altered considerably. Nevertheless, the gross features of this weak-coupling model may be used as a guide to assess the core-excitation contributions to the low-lying levels in 197Au. It can be seen that the data (table 2) generally exhibit the overall characteristic features prescribed by the "pure" m o d e l - i.e., the B(E2~) values of transitions between the multiplet states and ground are considerably enhanced over single-particle estimates and are reasonably comparable in magnitude with each other and with the B(E2; 2 + -, 0~-) measured 16,17) for 196pt and X9SHg [e.g. 0.300_+0.010 e 2- b 2 and 0.196 + 0.015 e 2" b 2, respectively]; while all M1 transitions from the excited multiplet levels to ground are stow compared with single-particle speed. Further, in accord with the model, the center of gravity of the excited multiplet states is at an excitation energy of 364 keV, while the 2 + levels in 196pt and 198Hg are 355.7 and 411.8 keV above their ground states 16.17), respectively. While the above overall agreement serves to favor the weak-coupling coreexcitation model description of the low-lying spectroscopy of 197Au ' a more detailed and critical comparison of these data with the specific predictions of this model is required before its appropriateness and validity can be established. 5.3. DETAILED MODEL SPECIFICATIONS

Braunstein and de-Shalit s) pointed out that allowance must be taken of the possibility that the two ~*. states in 197Au (i.e., the ground and 268.8 keV ~+ states) may mix to some extent. However, if the presumption of weak coupling is valid, this admixture must be small. Following the notation of Braunstein and de-Shalit 5), the wave functions of

238

H . H . BOLOTIN et al. TABLE Summary of B(E2; J7 ~ J~) and B(MI ; J~' -~ Jf~) extracted from

Level excitation energy (keV)

Transition energy (keV); J~' ~ J~

77.3 268.8

77.4; ½+ ~ ~ 191.5; {~ --, ½+

2.73+0.2 22.2 +1.9

ns ps

268.8

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22.2 +1.9

ps

278.9 278.9 547.5 547.5 547.5

201,8; 278.9; 268,6; 278,7; 547.6;

26.8 +2.1 26.8 +2.1 9.77+0.78 9.77+0.78 9.77___0.78

ps ps ps ps ps

a) b) ¢) d) •)

B(E2~ ; j n _..}jfn) (e 2 . b 2) Level mean life ~) z

{ + - ~ ½+ ~+---, ½~ ~+ ---, i + ~+ ---, {~ ~+ ---, {~

inferred from z b)

Coul. exc. ref. 7)

0.218 ___0.0220 0.1191 +0.0200

0.137 ___0.027

0.061 ~) <> 0.10| ~) 0.0983 +0.0224 0.1789 -I-0.0317 0.00084+0.00034 0.0304 +0.0090 0.1525 +_0.0082

0.0829+0.0058 0.114 +0.021 0.209 ___0.012 0.0012+0,0005 0.047 +_0.014 0.223 +_0.011

Present work, except for 77.3 keV level whose mean life was determined by previous workers 14). Calculated using total internal conversion coefficients, branching ratios, and multipolarity mixing ratios Upper and lower limits o f B(E2~) for 268,8 keV ½~ --, ~ ~ transition obtained from measurement of mean B(E2)~.p. = 0.00681 e 2 • b 2. For comparison with single-particle speeds, B(MI)~.p I = 1.79 n.m. 2.

the five states of interest in 1 9 7 A u can be written to include this admixture as follows: 3> 1 = AI~,~>+(1 3 3 (g.s.) 13 _

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where we have included the ambiguities in the signs within the wave functions of the two 3+ states to allow for the a priori indefiniteness of the phases which have not been explicitly taken into account by earlier authors. For consistency with earlier treatments we also adopt the additional nomenclature of Braunstein and de-Shalit 5): gp is the g-factor of the odd d~ proton, go the g-factor of the 2 ~- state in the even-even core, ~p = <311fapll~>, the reduced quadrupole matrix element for the odd proton, f22o = <01192(c2)112>,the reduced quadrupole transition matrix element between the core states Jc = 0 and 2, and O52 = <211~2(2)112>, the reduced quadrupole matrix element for the 2~- core state. Although the model-specified wave functions allow for some degree of mixing of the two ~÷ levels, it can readily be anticipated that even these may not describe the five states of interest completely; admixtures of other "reasonable" configuration couplings may also play a part. Nevertheless, it is still the case that if this model is to be considered sufficiently appropriate for comparison with experiment [as

197Au

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experimental studies of designated "multiplet" levels in 197Au

B(E2 ~)/ B(E21)~.p d) inferred from z 32.0 17.5 > 8.9 < 14.9 14.4 26.3 0.123 4.46 22.4

Inferred B ( M I ) (n.m. 2) b)

Coul. ref. exc. 7)

20.1 t2.2 16.7 30.7 0.18 6.9 32.8

f r o m z e) (7.75___0.19) x 10 -3 (I . 6 0 + 0 . 2 6 ) x 10-1 4 . 4 x 10 -4 (6.06_+ 1.07) x 10 - z (1.52+0.62) x 10 -2

from Coul. exc. e) ref. 7)

(1.85 _+0.25) x 103.7× 10 -~ (7.1 + 1.5) x 10 -2 (2.08_+0.17) x 10 -2

summarized in ref. 7). life of 268.8 keV state and lower experimental limit on E2/M1 ratios 7).

held by previous authors 2, 5-9)], the amplitudes of these additional admixed configurations present in the wave functions of these states must necessarily be presumed to be particularly small. Before it can be concluded that the weak-coupling core-excitation model provides an adequate description of the spectroscopy of these low-lying levels in 197AH, it is necessary that a detailed comparison of the predictions of the model with the level spectroscopy determined experimentally satisfies certain criteria: (1) The five parameters, gp, g¢, ~'~20' ~r~22' ~¢~p'together with .4 2, should form a set which is consistent with all experimental data related to the states involved and the transitions connecting these levels. (2a) The value of A 2 derived from the fit of the model's prescription for these levels should be close to unity. Should the value of A 2 be substantially less than unity, it would serve to contradict the original underlying weak-coupling assumption of the model. [-From a survey of odd-A nuclei in this mass region, de-Shalit 6) concluded that the particle-core interaction appeared to be dominated by a dipole-dipole interaction which in first-order perturbation theory leads to A 2 ---- 1.] (2b) The values extracted for the five other parameters must be consistent with the basic presumption of the model that an odd particle is weakly coupled to a collective core, i.e., gp and f2p must be close to their single-particle d~ proton (or proton-hole) values, and the core parameters, I220, f222 and go, must be in reasonable accord with experimental findings for the 2~- ~ 0~- core transition, the measured static quadrupole moment of the 2~ core level, and the gyromagnetic ratio of the 2~- core state, respectively.

240

H . H . BOLOTIN et al.

5.4. CORE-EXCITATION MODEL INTERPRETATION OF THE DATA

The model wave functions have been used to express 2) the reduced E2 transition probabilities among the five states involved and to obtain expressions for the static moments of these levels. These expressions were employed to obtain values of 020' ~'~22and Op as a function of A 2 by fitting them to what may be considered to be the most reliable and unambiguous relevant pieces of experimental data available, i.e., the B(E2; 7 ~ _~1) and B(E2;-~ --, ½) of two pure E2 transitions which have been well studied 14), and the well-measured quadrupole moment of the ground state _ [Q (3~,) = 0.58+0.01 e" b] 1~). Due to a number of ambiguous phases in both the wave functions and B(E2]) expressions that pertain, the fitting process resulted in eight possible three-parameter sets. As the weak-coupling model for 197Au reflects either a d~ particle (proton) coupled to a 196pt core or a d~ proton-hole coupled to a 19ang core, both negative and positive values of Op are admissible, respectively. The measured quadrupole moment of the 27 state in 196pt[-Q(2?)= 0.58-t-0.18 e . b ] t6) is positive, and implies that 022 > 0 for this core nuclide. Although two independent measurements of Q(27) for 19SHg have been reported is, 19), they differ in the siffn ascribed to this quadrupole moment. While it is expected to be positive from the systematics in this mass region, we have allowed for the possibility of both positive and negative 022 values for 19SHg in our evaluation of the appropriateness of each of the solution sets for which positive f2p values pertain. Of those sets for which Op < 0 (d~ proton+196pt), all but one were rejected on the grounds that all values of 022 in a set were negative (inferring Q(2~-) < 0 for 196pt), or the values of 022 obtained implied Q(2?) values for 196pt which were at least 5 times greater than the experimental value, or the values of Op were all at least 5 times larger than the single-particle estimate for a d~ proton. Similarly, of those sets for which Op is positive (d~ proton-hole+ 19SHg), two sets yielded 022 values which inferred unreasonably high Q(2~-) values [10(27)1 >_- 2.8 e. b] for 19aHg, while a third solution set was considered unsatisfactory as no pair of 022 and Op values for any given A 2 pertained which were consistent with both the magnitude measured is, 19) for the Q(2~-) value for 19Sng and d~ single-particle estimates for the reduced quadrupole matrix element of the odd proton-hole. The two remaining solution sets (one for a 196pt core and one for a t98Hg core) are shown in fig. 3 plotted against A 2 over the range (0.8 < A 2 < 1) considered appropriate to the model. The retained solution set that corresponds to a d~ proton coupled to a 196pt core (Op is negative in this case) is shown in fig. 3. As the single-particle d~ proton estimate for Op is (Op)s.p. ~ --0.29, we have taken the range - 0 . 6 _<_Op < 0 as reasonably acceptable. On this basis, virtually all values of A 2 > 0.82 are admissible. The range of the fitted values obtained for 020 is rather insensitive to A z, and all these values of 020 infer B(E2; 2? ~ 07) in 196pt that are in reasonable agreement

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Az Fig. 3. Values o f the mode[ parameters, £/20, £/22, and ~p, plotted as a function of the mixing coefficient, A 2, of the two 3 + states in 197Au obtained from the two most acceptable fits (see text) to the measured B(E2; ~ - , ~,), B(E2; ~ ~ ½), and *9OAu ground state quadrupole m o m e n t values. The solution sets which correspond to the case of a d3/2 proton coupled to 19ept are given by the solid lines, while those for a d3j 2 proton-hole coupled to a ~gsH g core (see text) are shown dashed. The uncertainties in these fitted parameter values that reflect the experimental errors associated with these B(E2) and Q(~] ,) measurements have been omitted from this figure to preserve clarity. These parameter uncertainties are: for both ~22 sets, the uncertainties are ~ 0 . 2 b at A 2 = 0.80 rising monotonically to ~ 0.25 b at A ' = 1.0; for both ~/2o sets, ~ 0.04 b at A 2 = 0.80 decreasing monotonically to = 0.024 b at A 2 = 1.0; and for both ~p sets, ~ 0.045 b diminishing to ~ 0.015 b at A 2 = i.0.

242

H . H . B O L O T I N et al.

with the measured value. However, as displayed in fig. 3, the smallest fitted value of 022 (t222 = 2.02 at A 2 = 0.8) leads to a value for Q(2t+) for x96pt which is more than twice that found experimentally; for A 2 --- 1, f222 corresponds to a Q(2~-) value that is ~, 5 times the measured value. Certainly, from the data fit, no preferred value of A 2 is evidently defined for a d~ proton weakly coupled to a 196pt core. For the case of a d~ proton-hole coupled to 198Hg, also presented in fig. 3, again no unique value or restricted range of values of A 2 can be defined. However, f2p ranges over values not inconsistent with d~ single-particle proton-hole estimates (0 < t2v < 0.6); f220 is, over almost the entire range of A 2 shown, in keeping with the measured B(E2; 2~ --. 0~) value in 19SHg; virtually all values of ~t-~22 are in good accord with the measured magnitude is, 19) of Q(2~) for 198Hg. Other data sets were also tried in the fitting process, but none resulted in parameter values that allowed a range of A 2 to be any better defined than those fits presented in fig. 3. The above findings must be contrasted with those of McGowan et al. 7) who, using a similar fitting procedure, obtained a virtually unique value (0.969 +0.003) for A 2. We have also repeated the fit using their B(E2$) values for those transitions which were employed in their work, but, in contradistinction to their result, found no unique value of A 2. [This we have traced to a calculational error on their part in which the expression they used for B(E2; ~ ~ ~1) omitted the term dependent on fl22.] Thus, we are led to conclude that neither their data nor ours results in a narrowly prescribed value for A 2. The situation is further exacerbated for the case of a single proton coupled to a 196pt core when the fitted values of 020, ~r~22 and f~p as a function of A 2 (in fig. 3) are used to calculate the B(E2~) values prescribed by this model for all remaining E2 transitions among these five states. Fig. 4 presents these predicted values for the case of a 196pt core as a function of A 2. The cross-hatched regions shown are those defined by the range of B(E2~)+AB(E2~) values inferred from the present experimental results. It is seen that although some individual results do tend to define a limited value of A 2, the regions prescribed for A 2 are not the same - some correspond to A 2 ~ 1, some to A 2 ~ 0.8, and another to no A 2 value > 0.8. On the other hand, using the parameter values appropriate to the case of a d~ proton-hole coupled to 19aHg (fig. 3), similar comparisons of the measured and model-predicted B(E2~) values yield a higher degree of agreement and consistency for the regions of A 2 de-limited by the same six E2 transitions, as seen in fig. 5. Overall, the range of A 2 > 0.95 encompasses virtually all of the delineated overlap regions of A 2. It is also of some importance to consider the measured magnetic moments 14) of the.ground state [#(-a21) = 0.1448 n.m.] and first excited state [#(½) = 0.419 n.m.] in order to attempt to establish, from expressions s) obtained using the prescribed model wave functions, whether or not a well-defined range of A 2 can be extracted

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Fig. 4. B(E2~) values o f the designated transitions, as a function o f A 2, predicted by the model for the case o f a d3/2 p r o t o n coupled to 196pt using the model p a r a m e t e r s obtained f r o m the corresponding solution set fit ( s h o w n in fig. 3). The cross-hatched bands represent the experimentally determined [ B ( E 2 £ ) _ A B(E2~)] values in each case. Model p a r a m e t e r uncertainties reflect themselves in uncertainties in the predicted B(E2~) values (not s h o w n here for clarity o f presentation). These uncertainties are often dominated by the relative large " e r r o r s " in the p a r a m e t e r ~22. These are: (a) ,~ 5 x 10 -2 e 2 - b 2 at A 2 = 0.80 and monotonically rising to ~ 1.2x 10 -1 e 2. b 2 at A 2 = 1.0; (b) ~ 7 x 10 -3 e 2. b 2 at A 2 = 0 . 8 0 rising s m o o t h l y to ,~ 2 x 1 0 -2 e 2 . b 2 at A 2 = 1.0; (c) ~ 1 . 5 x 1 0 -2 e 2 . b 2 ( A 2 = 0 . 8 ) decreasing to ~ 8 x 10 -3 e 2 • b 2 (A 2 = 1.0); (d) ~ 10 -2 e 2 • b 2 (A 2 = 0.8) diminishing slightly to 8 x 1 0 -3 e 2 " b 2 (A 2 = 1.0); (e) ~ 3 x 1 0 -2 e 2 . b 2 ( A 2 = 0.8) to ~ 10 -1 e 2 . b 2 (A2= 1.0); (f) ~ 6 x 10 -2 e 2 • b 2 (A 2 = 0.8) decreasing monotonically to ~ 8 x 10 -3 e 2 - b 2 (A 2 = 1.0).

from these data. Fig. 6a displays the values obtained for gp and go, the gyromagnetic ratios of the odd d~ proton (or proton-hole) and 2~- core state to which it is presumed to be coupled, respectively, as a function of the mixing parameter for the two ~+ states, A 2. The single-particle estimate ofgp for the odd d~ proton is 0.083 n.m., while the 2 ~- core states of 196pt and 198Hg have measured g, values of 0.28__+0.04 n.m. [ref. 16)] and 0.55-t-0.11 n,m. [ref. 17)], respectively. From this figure, it can be seen that the single-particle estimate for gp is encompassed in the fitted range for this parameter at A 2 ~ 0.96. While no value ofg~ is represented which is less than ,~ 1.4 times larger than the measured value for the 2~ state in 196pt, the value ofg¢ for A 2 ~ 0.96 (and, indeed, over the entire range 0.8 < A 2 < 1) is consistent with the measured g-factor for the 2~ level in 198Hg. Thus, one may well either adopt A 2 ~ 0.96 or consider A 2 > 0.80 as equally acceptable. Figs. 6b-6f display the model-predicted B(MI$) values for transitions among the

H. H. BOLOTIN

244 5x10-3

et al.

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Fig. 5. P l o t s s i m i l a r to t h o s e o f fig. 4, b u t f o r t h e c a s e o f a d3/2 p r o t o n - h o l e c o u p l e d t o a 198Hg c o r e (see text). S y m b o l i c r e p r e s e n t a t i o n as p e r fig. 4 c a p t i o n . M o d e l p r e d i c t i o n u n c e r t a i n t i e s : (a) ~ 2 x 10 - 2 e 2 . b 2 (A 2 = 0.8) d e c r e a s i n g t o ~ 10 - 2 e 2" b 2 (A 2 = 1.0); (b) ~ 4 x 10 - 3 e 2 . b 2 (A 2 = 0.8) r i s i n g to ~ 1 . 3 x 1 0 - 2 e 2 ' b 2 ( A 2 = 1 . 0 ) ; ( c ) ~ 1 0 - 2 e 2 - b 2 ( A 2 = 0.8) t o ~ 8 x 1 0 - 3 e 2 " b 2 ( A 2 = 1 . 0 ) ; ( d ) 1 . 7 × 1 0 - 3 e 2 . b 2 (A 2 = 0.8) i n c r e a s i n g t o ~ 8 x 1 0 - 3 e 2 " b 2 (A 2 = 1.0); (e) ~ 2 . 7 x 10 - 2 e 2 " b 2 (A 2 = 0.8) t o ~ 4 × 10 - 2 e 2 • b 2 (A 2 = ! . 0 ) ; (f) ~ 4 × 10 - 2 e 2 • b 2 (A 2 = 0.8) d i m i n i s h i n g m o n o t o n i c ally t o ~ 8 x 1 0 - 3 e 2 . b 2 ( A 2 = 1.0).

five states of interest as a function of A 2. From the range of experimental B(MI~)-I-AB(M 11) values for each transition shown on the corresponding solution set plots, it is clear that no narrow range of A 2 is defined by the collection of M1 transitions rates. Although for A 2 ~ 0.96 there is good agreement between the measured B(M1 ;½ ~ ~1) value and that predicted, and the measured B(M1 ; ~2 --+ _321) value is consistent with A 2 ~ 1, three of these five measured B(MI~) do not agree with the model predictions for any value of A 2. 6. Discussion and conclusions

In the present case of the weak-coupling core-excitation model applied to the spectroscopy of the low-lying states in 197Au' the foregoing analysis and comparisons have shown that the extensive experimental data available (the measured level lifetimes of the present work and the large body of complementary information provided by several previous investigators) appears far more consistent with the model predictions and assumptions for the case of a d+ proton-hole coupled to a 198Hg core than for a d+ proton coupled to 196pt.

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Fig. 6. Section (a) shows the values of the gyromagnetic ratios of the single-particle d3/2 proton (or hole), gp, and the 2~- state o f its core nuclide, g¢, plotted as a function of A 2, obtained from fits to the measured magnetic m o m e n t s of the 3 + ground and ½+ first excited states in 197Au. The uncertainties in these gyromagnetic ratios that reflect the experimental errors in the measured magnetic m o m e n t s are omitted from the figure for clarity of presentation. These associated uncertainties are: for #c, ~ 5 x 10-3 n.m. independent o f A 2 ; for gp, ~ 8.7 x I 0 - 4 n.m. at A 2 = 0.8 decreasing monotonically to ~ 2.6 x 10- 4 n.m. at A 2 = 1.0. [Note the scale factor of 10 for gp in this figure.] Sections (b)-(f) display the B(M 1J,) values of the designated transitions, as a function of A 2, predicted by the model obtained using the values of gc and gp in section (a) of this figure. The cross-hatched bands represent the experimental limits of [ B ( M 1,L)-I-AB(MI ~)] in each case. The very small uncertainties in g¢ and gp are reflected in negligible uncertainties associated with all of the predicted B(MI$) values.

Contrary to the conclusions reached by the authors of earlier such analyses [McGowan et al. 7), the CERN group 8), and Powers et al. 9)-I, the detailed fits to the data of the present study using the simple wave functions for those states the model is best able to specify are not in accord with the presumption of an odd d~ proton coupled to a 196pt core; even when mixing of the two ~ ÷ states is allowed for, neither a reasonably well defined range of values for the mixing coefficient, A, is evident nor are the model parameters obtained for a 196pt core satisfactorily consistent with the fundamental weak-coupling criteria of the model. On the other hand, when the model is taken to represent the case of a d~ proton-hole coupled to 19SHg (a situation either overlooked or dismissed by previous authors), the model parameters obtained are in accord with the criteria implicit for weak core coupling and, at the same time, are in remarkably good agreement with virtually all

246

H.H. BOLOTIN

et aL

of the measured E2 transition rates and some of the experimental B(MI~) values over a restricted range of the mixing coefficient of the two -32+levels (i.e., A > 0.975). Although we differ from the conclusions reached by the earlier authors T-9) that 197Au can be well described by a d~ proton coupled to a 196pt core, it is interesting to note that the results of our analysis and certain elements of theirs are actually not inconsistent with one another. While we do not consider that the data, analysis, and model warrant or merit more definitive specification of the model parameters other than to place relatively loose limits on their values (i.e. A2>~ 0.95, 0.75b ~< ~'~22 ~ 1.1b, 0.8b < 122o ~'~ 0.9b and 0.6b < I2p < 0.8b), these ranges of values are in keeping with the proffered precision ascribed to some of these parameter values by the earlier investigators [i.e., A 2 = 0.969+0.003, ~'~22 = 0.79+0.28b, 1220 =0.970+0.049b and f2p =0.853+0.060b by McGowan et a/.7); A 2 = 0.986+0.003, ~"~22 = 0.62+0.27b, 122o = 1.025+0.022b and t2p = 0.563+0.024b by Powers et a/.9); A 2 =0.981+0.002, 1222 =0.9+0.3b, 122o = 1.06+0.05b, and 12v = 0.586+0.008b obtained by the CERN group 8)]. It should be stressed that the even-even core nucleus to which the odd d~ proton (hole) is weakly coupled is specified by the sign of the reduced quadrupole matrix element for the odd nucleon, 12p. Both we and the earlier authors 7-9) find 12p > 0 which corresponds to a proton-hole outside an even-even core. It is from our interpretation that this positive value of t2p defines a proton hole coupled to 198Hg rather than the interpretation or assumption of these earlier workers that 197Au is described in terms of a 196pt core, that the fundamental differences in our conclusions arise. To the extent that this weak-coupling core-excitation model may be considered realistic for 197Au, our conclusion that the core nucleus in this case is specified as 198Hg rather than 196pt has additional concomitant implications. The first is that if the low-lying levels in 197Au are ascribed to a d~ proton hole coupled to a 198Hg core, it implies that the d~ proton orbital in Pt and Hg is more nearly full than empty. Spectroscopic factors obtained from pickup and/or stripping reaction studies in this mass region would be extremely valuable in assessing whether or not the d~ proton orbit occupancy is in accord with this prescription. While it is unfortunate that reports in the literature of such studies are scanty, the d~ proton spectroscopic factor obtained from a x98pt(aHe, d) stripping investigation 20) is 0.116; this strongly supports the substantial fullness for this orbita! in Pt. Additional evidence that this interpretation is tenable comes from the rather extensive analysis of ground state deformations in this mass region by G6tz et al. 21). Based upon the Nilsson potential calculated with parameters of 184W, their analysis is wholly consistent with a (d l_)2 occupancy for Pt and a (d~)4 configuration for the Hg isotopes. [The slight oblate ground state deformation found for the heavier Pt and Hg nuclides is in keeping with the Nilsson orbital in question interpreted in terms of an almost pure d~ shell picture.] Secondly, although we did not a priori restrict the sign of 1222 to be positive in our

197Au

247

parameter fits, the only acceptable solution set for the case of a t9SHg core yielded a positive definite value for this parameter. The sign of 022 together with the range of values consistent with A 2 ~> 0.95 implies that Q(2~) for ~98Hg would be expected to be restricted to +0.57e- b < Q(2;) < +0.83e- b. This is in agreement (both in sign and magnitude) with that expected from the systematic trend of measured Q(2~-) values in this mass region 22) that Q(2~') for 198Hg be roughly between ~ +0.25e. b and ~ + 1.0e. b. lit must be pointed out that this range of values is also in keeping with the measured Q(2~-) for 196pt, i.e., 0.58_0.18e. b, ref. 16).] In this regard, however, the only disquieting note concerns a recently reported set of re-orientation effect measurements ~s) of the quadrupole moments of the first 2 ÷ states in the eveneven Hg isotopes; these authors find negative quadrupole moments which decrease in magnitude from 1.1e. b to ~ 0e. b in progressing from 19aHg to 2°4Hg. While the determined magnitude of Q(2~-) for 198Hg agrees with the systematic projection in this mass region, the reported sign is opposite to that expected from both these systematics and that inferred from the sign of g222 in our analysis and those of earlier authors. On the other hand, however, the slightly later reorientation effect measurement of Q(2~-) in 19aHg by Esat et al. 19), although in reasonable agreement with the magnitude of the quadrupole moment reported by Bockisch et al. is), found that the sign of Q(2~-) was positive. This result is in accord with both the systematics in this mass region and the weak-coupling model prediction. Nevertheless, in view of the difference in sign of these two Q(2~) measurements, it would be of substantial value if this important experimental point were clarified unambiguously. It is perhaps worth noting that the slightly oblate deformation measured 18, 19) for 19SHg serves to increase 21) the separation energy of the d~ and s~ proton orbitals over that expected for zero deformation. This renders the a priori prerequisite conditions more suitable for the appropriateness of this model (specified in sect. l) to the structures of the low-lying states of 197Au than would pertain for either zero or slightly prolate deformation of the core nuclide. As pointed out by Braunstein and de-Shalit s), the presence of a retarded E3 transition between the 409 keV ~ - state (presumed due to h¥ orbital occupancy) and the 279 keV I + multiplet level is consistent with a finite, but close to negligible, admixture of d~ proton orbit participation in the latter state. Although we have not explicitly considered couplings other than that of the d~ proton orbital to the core states, the surprisingly good agreement obtained with 197Au represented as a d~ proton-hole coupled to a 19aHg core supports the underlying model prescription that the contributions to these states of other "reasonable" couplings and concomitant configuration mixing would be particularly small. On this note, it is of some interest to return to those three measured M1 transition rates which were found not to correspond with model predictions for any value ofA 2 ~ 0.8. It is not particularly disquieting that the ~ ~ I and 2~2 ~ ½M1 transition rates are not in agreement with the model as, of the three, their degree of nonconcurrence with the model is slightest. Not so for the I ~ It M1 transition, however;

248

H.H. BOLOTIN et al.

at A 2 ~ 0.96, the experimental B(MI$) value for this transition is ~ 30 times larger than predicted for it. Yet, this is the single M1 transition rate which is most sensitive to even an extremely small admixture of d~ orbital contribution in the wave function of the ~+ state. We and Braunstein and de-Shalit 5) estimate that a 1-2 ~ admixture of d~ orbital participation in the ~+ state raises the model-predicted B(MI~) by roughly the amount needed to bring it into agreement with experiment for A 2 ~ 0.96 without materially affecting the predicted B(E2~) and other B(MI~) values. However, if in order to attempt to predict the experimental spectroscopy any better than our analysis has, weak couplings to even a few more single-particle orbitals are included, the model takes on many features of a detailed microscopic calculation, assumes a measure of undesirable complexity, loses much of its attractiveness, and essentially accretes to it many elements of a conventional shell model approach. In these circumstances, the model wave functions of these states would be neither unambiguous nor uncomplicated. In light of the basic nature of the model and the degree of agreement with it our analysis has displayed, such an approach seems neither justified nor profitable. From the results of the model analysis presented here for the level spectroscopy of the low-lying states of 197Au ' it appears that the predictions of the weak-cbupling core-excitation model, when interpreted in terms of a d~ proton-hole weakly coupled to a 19ang core, are in satisfactory accord with a great deal of detailed experimental data and, at the same time, are consistent with what is known about the structure of the core nuclide itself. This model possesses the inherent simplicity of weak coupling, is virtually independent of the exact nature of the core-excitation levels to which the weakcouplings are presumed, and is relatively free of microscopic detail in its specification of the wave functions of the low-lying states which should be best described by the model. It is not expected that a detailed nuclear model, even one which is considered to be particularly appropriate to the spectroscopy of a given class of nuclei or to an individual nuclide, would be found to be in complete agreement with experiment. Yet, to the extent that the weak-coupling core-excitation model is at all realistic, its basic nature leads to the higher expectation that it can do considerably better. Nonetheless, it is somewhat surprising - indeed remarkable - that this simple model, this seemingly naively simplistic model, appears to describe the low-lying level spectroscopy of t 9 7 A u a s well as it does. Note added in proof." We have recently become aware of the atomic-beam magnetic-resonance method work of Blachman et ai., Phys. Rev. 161 (1967) 60,

who obtained a value for t2p in 197Au. Their value, t2p = +0.604 b, not only agrees in sign with that appropriate to a d~ proton-hole coupled to 198Hg, but also corresponds in magnitude to that predicted by the weak-coupling core-excitation model for the value A 2 = 0.97 (see fig. 3, this paper). Coupled with the findings of the present work, this measured value of f2p makes agreement of the model with experiment even more remarkable.

197Au

249

The University of Melbourne authors express their appreciation for the courtesy and cooperation of Professor J. O. Newton and the staff of the Australian National University 14 U D Pelletron Laboratory. Two of us (D.L.K. and A.E.S.) are appreciative of the support provided by Commonwealth Post-Graduate Awards. One of us (H.H.B.) wishes to record his sincere thanks for the hospitality and unstinting support given to that facet of the present work conducted at the Research Center for Nuclear Physics, Osaka University, by Professor S. Yamabe, H. Ikegami, and M. Kondo and the AVF cyclotron research staff during the author's tenure there as visiting professor, and to the Japan Society for the Promotion of Science for its sponsorship of that visit, We also wish to acknowledge the benefit of a number of highly informative discussions with Dr. I. Morrison. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

14) 15) 16) 17) 18) 19) 20) 21) 22)

R. D. Lawson and J. L. Uretsky, Phys. Rev. 108 (1957) 1300 A. de-Shalit, Phys. Rev. 122 (1961) 1530 and references cited therein H. H. Bolotin and D. A. MeClure, Phys. Rev. C3 (1971) 797 O. C..Kistner and A. Schwarzschild, Phys. Rev. 154 (1967) 1182 and references cited therein A. Braunstein and A. de-Shalit, Phys. Lett. 1 (1962) 264 A. de-Shalit, Phys. Lett. 15 (1965) 170 F. K. McGowan, W. T. Milner, R. L. Robinson and P. H. Stelson, Ann. of Phys. 63 (1971) 549 and references cited therein B. Robert-Tissot et al., Proc. Int. Conf. on nuclear physics, Munich 1973, vol. I (North-Holland, Amsterdam, 1973) p. 315 R. J. Powers, P. Martin, G. H. Miller, R. E. Welsh and D. A. Jenkins, Nucl. Phys. A230 (1974) 413 N. R. Johnson, R. J. Sturm, E. Eichler, M. W. Guidry, G. D. O'Kelley, R. O. Sayer and D. C. Hensley, Phys. Rev. C12 (1975) 1927 J. L. Quebert, K. Nakai, R. M. Diamond and F. S. Stephens, Nucl. Phys. AIS0 (1970) 68 M. W. Guidry, P. A. Butler, P. Colombani, I. Y. Lee, D. Ward, R. M. Diamond and F. S. Stephens, Nucl. Phys. A266 (1976) 228 A. Winther and J. de Boer, in coulomb excitation, ed. K. Alder and A. Winther (Academic, New York, 1966) p. 303; D. Ward, H. R. Andrews, R. L. Graham, J. S. Geiger and N. Rud, Nucl. Phys. A234 (1974) 93 B. Harmatz, Nucl. Data Sheets 20 (1977) 73 E. Barnard, J. A. M. de Villiers, C. A. Englebreeht and D. Reitmann, Nucl. Phys. A167 (1971) 511 M. R. Schmorak, Nucl. Data Sheets 7 (1972) 395 B. Harmatz, Nucl. Data Sheets 21 (1977) 377 A. Bockisch, K. Bharuth-Ram, A. M. Kleinfeld and K. P. Lieb, Proc. Int. Conf. on nuclear structure, Tokyo 1977, contributed papers, p. 443 M. T. Esat, D. C. Kean, R. H. Spear, F. P. Fewell and A. M. Baxter, Phys. Lett. 72B (1977) 49 J. Halperin, Nucl. Data Sheets 24 (1978) 57 U. G6tz, H. C. Paul, K. Alder and K. Junker, Nucl. Phys. A192 (1972) 1 A. Christy and O. H~iusser, Nuel. Data A l l (1972) 281