Non-yrast states and shape co-existence in light Pt isotopes

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A 657 (1999) 219-250 www.elsevier.nl/locate/npe

Non-yrast states and shape co-existence in light Pt isotopes P.M. Davidson a, G.D. Dracoulis a, T. Kib6di a, A.P. Byrne a,2, S.S. Anderssen a, A.M. Baxter b, B. Fabricius a, G.J. Lane a,l , A.E. Stuchbery a a Department of Nuclear Physics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia Department of Physics and Theoretical Physics, The Faculties, The Australian National University, Canberra ACT 0200, Australia

Received 26 May 1999; accepted 30 June 1999

Abstract

Low-lying states in the even-even light platinum isotopes 176pt, 178pt, ~8°pt and ~82pt have been populated using f l + / E C decay from parent gold nuclei, created in (HI,xn) reactions. State energies, spins and parities and 7-ray branching ratios were determined using ~,-ray and electron spectroscopy. Whereas non-yrast states were observed in raPt, ~S°Pt and ~82Pt, none were seen in 176pt. The excitation energies of the observed states are analysed in terms of a band-mixing model, yielding the moments of inertia of the unperturbed bands. Branching ratios and ground-state-band quadrupole moments are calculated and compared with experimental values. The results indicate that the two lowest-lying 0 + states in each of the light Pt isotopes are formed from the mixing of two intrinsic states of different deformation, and other low-lying states can be described as admixtures of rotational states built on these intrinsic states, and on ~/-vibrational states. © 1999 Elsevier Science B.V. All rights reserved. Keywords: RADIOACTIVITY 176Au, 178Au, 18°Au, 182Au [from 144Sm(35Cl,3n), E = 173 MeV;

144Sm(37C1,3n), E = 170 MeV; 149Sm(35CI,4n), E = 170 MeV; 149Sm(37CI,4n), E = 170 MeV], measured E~,, 1~, "yyt, Ty(0); 178Au, 18°Au, 182Au [from reactions above], measured singles y and ce, e coincidences; 178pt, 18°pt, 182pt deduced levels, J, ~r, ICC, ~,-ray branching ratios; NUCLEAR STRUCTURE Shape coexistence, band-mixing

~Current address: Nuclear Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley CA94720, USA. 2 Joint appointment with Department of Physics and Theoretical Physics, The Faculties, The Australian National University. 0375-9474/99/$ - see front matter (~) 1999 Elsevier Science B.V. All rights reserved. PII S0375-9474 (99) 00340-1

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1. Introduction Shape coexistence is a well-established feature in the mercury (Z = 80) isotopes (see Ref. [1] and references therein) but, in comparison, the effect in the platinum isotopes (Z = 78) is less clear. Potential energy surface (PES) calculations [2-5] tend not to exhibit distinct minima at different deformations, instead showing softness to 7 deformation. This softness is also evident in more phenomenological collective models that have been applied to the platinum isotopes not too far from stability [6]. However, the experimental data available for the lighter isotopes have been interpreted as being indicative of shape coexistence effects. Wood et al. [7] considered the moments of inertia of the even isotopes 182pt to 186pt, as determined from the energy spacings of the low-lying states, and arrived at the conclusion that the ground states contain mixtures of strongly-deformed and less-deformed configurations. In studies of 176pt and 178pt with (HI,xn) reactions, Dracoulis et al. [8] identified the yrast sequences and reproduced them with a phenomenological model based on the interaction of two bands of significantly different deformation. A low-lying 0 + state was known in both 176pt and 178pt [9] and the strength of the mixing of the postulated bands was adjusted so that both the ground state and the excited 0 + state were given correctly. This procedure was also applied to the even isotopes from 18°pt to 184pt, and yielded the moments of inertia and bandhead energies of the u n m i x e d strongly- and weakly-deformed bands. The moments of inertia remained relatively constant from 176pt to 184pt, while the separation between the unperturbed strongly- and weakly-deformed bandhead energies showed a systematic variation with neutron number. A later study of ~74pt [10] revealed that a band crossing was also present in this isotope, and a band-mixing analysis [ 10,11 ] obtained the unmixed bandhead energies. The variation of the bandhead energy separation was parabolic with respect to neutron number, with the minimum occurring between ~S°pt and 182pt [11]. For these two isotopes, the strongly-deformed bandhead fell approximately 100 keV below the weaklydeformed bandhead, while in the bordering isotopes 178pt and 184pt the calculations resulted in roughly equal weakly- and strongly-deformed bandhead energies. For 176pt and 17apt the weakly-deformed bandhead was favoured by 280 keV and 690 keV, respectively. Such results extended the discussions of Wood et al. concerning stronglydeformed 'intruder' bands in the heavier platinum nuclei, which were expected to fall lowest in energy at the neutron mid-shell [7,12]. The shape co-existence hypothesis implies the presence of other low-spin non-yrast states in addition to the 0 + states. This paper reports the results of radioactive decay studies aimed at identifying low-spin states in 176pt, 178pt, ~8°pt, and *82pt. Our complementary studies identifying low-spin states in the neutron-deficient osmium isotopes have been reported previously [ 13,14].

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PM. Davidson et aL /Nuclear Physics A 657 (1999) 219-250

Table 1 Properties and production reactions for parent Au isotopes Decay

176Au 178Au 18°Au 182Au

~ ~ --~ ~

176pt 178pt 18°pt 182pt

Parent TI/2 a (seconds)

QEC b

1.08 (17) 2.6 (5) 8.1 (3) 21 (1)

10.5 9.6 8.6 7.8

Target

Beam

Energy (MeV)

144Sin 144Sm 149Sm 149Sm

35C1 37C1 35C1 37C1

173 170 170 170

(MeV)

a From Ref. [15]. b Values from systematics [ 15 ].

2. Experiments 2.1. Out-of-beam y - y coincidences The parent gold isotopes were produced in situ by (HI,xn) reactions induced by beams from the 14UD Pelletron at the Australian National University. The reactions are listed in Table 1, Each of the enriched samarium metallic foil targets (with thicknesses of 2.6 m g / c m 2) was backed with gold foil to stop the recoiling nuclei, The beams used were chopped with equal 'beam-on' and 'beam-off' times. For the 176pt measurement on and off times were each 2.6 s; for the 178pt measurement they were 1 s; and 4 s intervals were employed for the ~8°pt and 182pt measurements. The y - y coincidences and y-ray angular correlations from the decay products of the residual nuclei were measured during the 'beam-off' periods in the y-ray detector array CAESAR, which was configured with six Compton-suppressed HPGe detectors. Information was collected whenever a two or higher-fold coincidence event occurred, and the energies of the y-rays and their individual times of detection were recorded. The maximum energy recorded was limited to 2 MeV.

2.2. Out-of-beam electron measurements The same reactions and beam chopping times were used in experiments to measure conversion electrons. The electron-y coincidences and the conversion coefficient measurements were done simultaneously using a superconducting electron spectrometer, operated in lens mode [ 16], to transport electrons to a cooled Si(Li) detector. In this mode a baffle system limited the acceptance for a given magnetic field to a narrow momentum window. The enriched samarium targets were approximately 1.3 m g / c m 2 thick with a 1.5 m g / c m 2 gold foil backing, and targets were tilted at 40 ° from the beam axis with the electrons emerging from the back into the transport field. For the ~82pt and 18°pt measurements the spectrometer field was swept over 0.02-0.19 T, allowing electrons with energies between 120 keV and 1300 keV to be detected with full efficiency. For the 178pt measurement, where the yield was lower, the range was limited to 250-950 keV, allowing more data within this range to be collected. No measurement

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PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250

was made for lV6pt, as will be discussed in Section 4.4. Electrons and y-ray singles were collected with the Si(Li) detector mentioned above and a Compton-suppressed Ge detector, respectively. In addition, y-rays were collected in coincidence with electrons using a magnetic-field-resistant Ge detector placed close to the target, allowing an e - y coincidence rate of approximately one-sixth of the singles electron rate. 2.3. tZOAu half-life measurement

Due to some negative results in the 176pt measurement (see Section 4.4) a check was made of the half-lives in this case. The reaction used was 35C1 on 144Sm at 173 MeV, as in the y - y coincidence measurement. The beam was chopped with a period of 19.2 s, divided into 2.1 s 'beam-on' and 17.1 s 'beam-off' times. In the 'beam-off' intervals, the CAESAR array measured singles y-ray energies and times in event mode. The times were obtained by triggering a long-time-range event clock, which was reset every cycle by the beam chopping signal.

3. Analysis procedure 3.1. y - y coincidences

The data from the y - y measurements were sorted into 4096 × 4096 channel matrices, with the condition that only y-rays occurring within an interval of 170 ns of each other were included in a matrix. This relatively long interval was used to include low-energy y-rays (and X-rays), which can suffer from time walk in the HPGe detectors. The total numbers of counts in the matrices were 6.5 million, 9.2 million, 7.8 million and 6.3 million for the 182Pt, 18°pt, 178pt and ~76pt experiments, respectively. Backgroundsubtracted coincidence spectra for individual lines were then generated from the matrix and examined to construct the level scheme. 3.2. y - y angular correlations

The detectors in the CAESAR array (which are in a plane) are positioned to allow six different angular separations between pairs of detectors, with the angular differences being 14 °, 35 °, 48 °, 62 °, 70 °, and 83 °. This range allowed useful angular correlations to be formed in the cases of the most intense coincidence cascades. The function that describes the angular correlations is W ( O ) = Ao + AzePz(cosO) + A44P4(cosO) .

In instances of pure quadrupole radiation (and for attenuation coefficients close to unity) the coefficients Akk are given by Akk = Fk(2 2 10 11) F k ( 2 2 1 2 1 1 ) ,

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250

223

where the values of Fk are tabulated, for example, in Ref. [ 17] and I0, 11 and 12 are the spins of the initial, intermediate and final states, respectively. For further details of the procedure used, see Ref. [ 13]. 3.3. Internal conversion coefficients

The singles electron spectrum had much of the background removed by the momentum selection technique described in Ref. [ 16]. As only a certain range of electron energies are acceptable for a given magnetic field value, this eliminates most of the invalid events (which arise mainly from the backscattering of electrons). The intensities of the electron transitions were obtained from the momentum selected singles spectrum, while intensities of 3,-ray transitions were obtained from the spectrum of 3,-rays acquired concurrently with the singles electrons. The system was calibrated by the measurement of electrons and 3,-rays from a 152Eu radioactive source, and confirmed using known transitions in the observed decay chains. 3.4. e-3, coincidences

A two-dimensional matrix was constructed of electron energy vs y-ray energy, after momentum selection of the electron data. Background-subtracted spectra, showing 3'rays in coincidence with electrons, or vice versa, were generated from this matrix. This allowed confirmation of some transition placements made from examination of the 3"-3' data, and allowed placement of strong j~r ~ j~r transitions where the 3"-3" coincidence data were not definitive. The spectra could also be used to establish whether lines in the electron singles data were contaminated.

4. Results

Level schemes of 182pt, lS°pt and 178pt, as observed in this study, are shown in Figs. 2, 3 and 5, respectively; results for 176pt will be discussed later. The arrangement of the states on the level schemes reflects the band structures shown on prior schemes in the literature, and should not be taken as necessarily representing our interpretation of the intrinsic structures, since there remains a level of arbitrariness in such identifications given the mixing, as will be discussed in Section 5. Fig. 1 shows 3'-3" coincidence gates on the yrast 2 + --~ 0 + transitions. Platinum X-rays are clearly observed in these spectra, and the broad lines at 511 keV are the product of positron annihilation (after/3 + decay) which occurs in true coincidence. The yrast 4 + ---, 2 + transitions (at 257.3 keV, 257.5 keV and 264.7 keV) are prominent in the gates, and for 178pt, the 6 + ~ 4 + (337.9 keV) and 8 + ~ 6 + (413.4 keV) are also easily seen. As in the light osmium isotopes [ 13,14], E0 transitions are observed and are useful in establishing j~r ___,j,r assignments. The signature of such transitions is an unusually

224

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250 6000

i

I

r

I

'

I

I

'

i 3x Pt X-rays

4000

170 keV gate

(a)

257 I

338

2000

511 .j

0

\

413

.[ . . . . . .

~ . . . . . .

Pt X-rays'

'

/

:

4

~

h__

'

::3x

258

3000

~ A. . . . . . ,~k__~ .... 153 keY gate

:

(b)

511 524 2000

809

325

D i000 451 o Pt X-rays /

8000

i 3x

155 key gate

:

265

(c)

,,

6000 4000

511/513

2000 -

345 I

,

0 0

200

400

i

788

:

A:j .

.

la

_A

~

600

L

Aa

800

i000

energy [keV]

Fig. I. Coincidence gates of 2+ --~ 0~- transitions in (a) 178pt, (b) 18°pt and (c) arise from positron annihilation.

182pt.

The lines at 511 keV

large conversion coefficient, in many cases considerably stronger than the M1 value. For the special case of 0 + ~ 0 + transitions, de-excitation proceeds only by electron conversion and no corresponding y-rays should be seen.

4. l. m 2 p t

The/9-decay into 182pt has been studied previously by Calliau et al. [ 18] and Husson et al. [ 19]. Table 2 lists the y-rays observed in the current experiment and Fig. 2 shows the level scheme deduced. Conversion coefficients are given in Table 3, along with those determined by Calliau et al. [ 18 ]. This study extends the B-decay level scheme proposed in Ref. [19], in which the states at 775.2, 1152.0, 1240.2 and those above 1420 keV, were not reported. Most states have also been observed in a recent in-beam spectroscopy measurement [20], the exceptions being the states at 1152.0, 1182.2, 1311.8, 1419.5, 1473.9, 1502.5, 1521.8, 1542.5, 1684.5 and 1889.2 keV. (That is, most of the states that have not been placed into bands in Fig. 2.)

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

225

cq

02)

J

9" 697I I

6" ~9gl ...... 9 /8[I It g'gOll ,I,-,- L" 17Z8 . 1~ ' LI9 ~ 6" 666 - ~

D 66LL

~__L

~t'c~ot ~ ~

9" 9~II'

t L66

Fig. 2. The level scheme for m2pt from Z82Au decay. For the 500 keV and 456 keV transitions (marked with asterisks) only internal conversion electrons are observed.

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250

226

Table 2 Gamma-ray Energies and Intensities in 182pt E~, (keV) 154.9 264.7 326.0 344.8 355.6 356.5 363.1 366.1 383.0 386.0 436.5 439.7 465.0 513.0 523.1 531.0 572.5 614.5 617.7 644.1 667.8 682.3 701.2 751.9 762.3 787.7 812.1 820.5 834.7 856.2 879.1 886.3 997.1 999.9 1027.1 1085.2 1102.2 1122.9 1149.3 1156.6 1264.9 1387.6 1469.6

I~, 1000 (10) 443 (10) 26 (5) 124 (6) 19 (5) 26 (7) ~5 40 (20) 27 (5) ~10 34 (3) 14 (2) 10 (3) 233 (26) 25 (3) 5 (4) 17 (5) 80 (5) 15 (8) ~2 80 (10) 4 (1) 13 (3) 17 (5) 4 (1) 137 (19) 25 (6) 14 (2) 38 (8) 150 (5) 8 (3) 11 (3) 28 (2) 9 (3) 66 (7) 41 (3) 16 (5) 8 (3) 8 (3) 13 (2) 13 (3) 9 (3) 10 (3)

A22/Ao a

A44/Ao a

0,074 (25)

0.008 (29)

0.292 (63)

0,821 (68)

--0.24 (19)

--0.14 (22)

--0.130 (55)

--0.020 (63)

0.21 (23)

0.57 (26)

--0.14 (9) 0.12 (15)

0.32 (10) 0.15 (17)

0.02 (32)

--0.33 (36)

Initial State (keY) 154.9 419.6 1182.2 499.7 775.2 856.2 1306.1 1034.1 1240.2 1419.5 856.2 1473.9 1240.2 667.8 942.6 1306.1 1240.2 1034.1 1473.9 1419.5 667.8 1182.2 856.2 1419.5 1182.2 942.6 1311.8 1240.2 1502.5 856.2 1034.1 1306.1 1152.0 1419.5 1182.2 1240.2 1521.8 1542.5 1568.9 1311.8 1684.5 1542.5 1889.2

a Angular correlation coefficients in cascade with the 154.9 keV 2 + ~ 0 + transition.

PM. Davidson et aL /Nuclear Physics A 657 (1999) 219-250

227

Table 3 Conversion coefficients determined for 182pt Transition

Type

Expt.

Ref. [ 18]

(keV) 264.7 344.8 436.5 456 465.0 500 513.0

614.5 667.8 701.2 751.9 787.7 820.5 834.7 856.2 997.1 1027.1 1085.2 a b c d

C~K t~K trK OtK OtK teK tel aK aL aM aK teK aK teL teK teK teK aK ~K aK aK CtK

0.094 (8) 0.057 (13) <0.075 >0.32 <0.045 >1.0 >0.18 0.044 (6) c 0.0038 (12) 0.021 (4) 0.0096 (23) >0.27 >0.027 <0.04 0.0056 (11) 0.17 (6) <0.017 0.0080 ( 11 ) <0.014 0.0085 (16) <0.0047

0.087 (19) ~ 0.038 _> 1.7 > 6.6 > 0.165 d

~ 0.0097 0.73 (22)

0.0059 (18)

0.0066 (19) 0.0130 (40)

Theory

Multipolaritya

M1

E2

0.372 0.182 0.0969 0.0864 0.0820 0.0678 0.0109 0.0634 0.0102 0.00235 0.0398 0.0320 0.0283 0.00447 0.0237 0.0211 0.0190 0.0181 0.0170 0.0116 0.0108 0.00936

0.0840 0.0436 0.0250 0.0226 0.0217 0.0184 0.00495 0.0174 0.00454 0.00113 0.0118 0.00993 0.00899 0.00174 0.00780 0.00713 0.00657 0.00635 0.00604 0.00450 0.00426 0.00384

E2 E2 E2 E0+? E2 E0 b E0+(M1)+E2

E2 E0+MI+E2, 8 = 0 • 7+j° -0.3 (E2) (E2+M1, 8 > 5) E0+(MI )+E2 E2 (E2) (E0+MI+E2, (E2)

181 >

2.7 )

Mixing ratios /~(E2/M1 ) from angular correlations given in Table 2. X(EO/E2) = 0.014(3). Electron intensity not determined due to contamination from 182Re 510 keV L and 182pt 500 keV M lines. The ratio CtK/aL = 6.4 (13) was reported in Ref. [181. In Ref. [ 18], f o u r transitions with suggested E 0 c o m p o n e n t s w e r e o b s e r v e d with

e n e r g i e s o f 456, 500, 513 and 701 keV. A s shown in Table 3, the l o w e r limits on internal c o n v e r s i o n coefficients that we report for the 456 and 500 k e V transitions are significantly smaller than the limits reported in Ref. [ 1 8 ] , and our m e a s u r e d l o w e r limit for the 701.2 k e V transition is also s o m e w h a t smaller than the value reported in Ref. [ 18]. N o t w i t h s t a n d i n g these disparities, our limits are large e n o u g h to infer E0 c o m p o n e n t s for these transitions, and confirm the spin assignments to the levels at 499.7, 856.2 and 1311.8 keV. T h e a s s i g n m e n t o f spin zero to the 499.7 k e V level is i n d e p e n d e n t l y c o n f i r m e d by the 3 4 4 . 8 - 1 5 4 . 9 k e V y - y angular correlation, as s h o w n in Table 2, and the 2 + a s s i g n m e n t o f the level at 856.2 k e V is verified by the E2 nature o f the 856.2 k e V transition to the ground state. We also o b s e r v e an additional transition f r o m the 1311.8 k e V level to the yrast 2 + state, but no angular correlation or electron c o n v e r s i o n i n f o r m a t i o n was obtained. We m e a s u r e aK = 0 . 0 4 4 ( 6 )

for the 513.0 k e V transition, w h i c h is in d i s a g r e e m e n t

with the limit o f ~> 0.165 in Ref. [ 1 8 ] . The 513.0 k e V y - r a y overlaps the 511 k e V positron annihilation peak, m a k i n g the intensity determination difficult. In our analysis,

228

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

the positron annihilation peak was removed from the ~82pt singles spectrum by subtracting an appropriately scaled 18°pt singles spectrum. Our value is smaller than the theoretical M1 value and as aL(513.0 keV) was not measured and aM(513.0 keV) has a large uncertainty, we cannot confirm the existence of an E0 component for this transition. However, the CeK of the 667.8 keV transition to the ground state confirms an E2 assignment, and hence verifies the spin and parity of the 667.8 keV level. The state at 1240.2 keV, which was not seen in earlier measurements, is assigned 4 + because the large aK of the 820.5 keV transition to the yrast 4 + state is taken as evidence for an E0 component. Four additional decay branches are observed, to the yrast 2 + and 6 + states, to the 2 + state at 667.8 keV and to the 2 + state at 856.2 keV. The states at 942.6, 1034.1 and 1306.1 keV were assigned J~ = (3+), (4 +) and (5+), respectively, by Husson et al. [ 19]. The (3 +) assignment is consistent with our measured conversion coefficient for the 787.7 keV transition and the angular correlation of the 787.7-154.9 keV cascade, but we do not observe the 275 keV transition to the 2~state at 856.2 keV shown in Refs. [ 18,19]. The conversion coefficient for the 614.5 keV transition de-exciting the state at 1034.t keV is larger than the E2 value (indicating an MI or E0 component) and is consistent with the assignment of (4 +) to the level at 1034.1 keV. We see an additional branch from this level to the 2 + state at 667.8 keV. The assignment of (5 +) by Husson et al. to the state at 1306.1 keV was based on the observation of a de-exciting 366 keV transition to a (3 +) state and by comparison with 184pt. This tentative assignment is supported by our observation of two additional branches to the yrast 4 + and 6 + states. (We amend the energy of the transition to the (3 +) state to 363.1 keV.) Branches to the 0 + and 2 3+ states are shown in Ref. [19] for the state at 1182.2 keV. As well as these, we see transitions of 762.3 and 1027.1 keV to the 4 + and 2 + states, respectively, and assign a spin of (2) to the 1182.2 keV level based on the spins of the levels to which it decays. The level at 1419.5 keV is shown tentatively in Ref. [ 19] with a de-exciting 751 keV ( E l ) transition to the 2 + state. We observe an additional transition to the 4 + level and, tentatively, two other transitions to the 6 + and 4 + levels. We revise the assignment of ( 3 - ) made in Ref. [19] to one of (4). A single 997.1 keV transition to the yrast 2 + state de-excites the newly observed state at 1152.0 keV. The angular correlation for the 997.1-154.9 keV cascade is suggestive of a 0 ~ 2 ~ 0 cascade, although other initial spins cannot be excluded. Seven other new states, for which we do not propose any spin or parity assignments, are placed at 1473.9, 1502.5, 1521.8, 1542.5, 1568.9, 1684.5 and 1889.2 keV. 4.2. m ° P t

A comprehensive study published by de Voigt et Husson et al. [22]. In the were not reported in Ref.

of 18°pt including both in-beam and decay results has been al. [21], superseding an earlier /3-decay measurement by present decay experiments, we observe sixteen T-rays which [21] while four weak T-rays reported in Ref. [21] (184.3,

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

229

Table 4 Gamma-ray Energies and Intensities in 18°pt Er (keV)

Ir

153.2 199.7 257.5 285.8 324.7 346.3 372.0 383.3 386.7 450.6 500.3 524.1 528.2 552.2 571.7 571.9 638.3 673.7 677.4 708.1 708.9 710.4 776.7 809.4 814.0 837.4 858.1 861.4 873.1 895.8 940.5 1024.3 1033.9 1094.3 1124.0 1197.6 1234.1 1351.4 1382.0

1000 (31) 3 (2) 233 (10) 4 (3) 139 (5) 6 (2) 6 (2) 25 (5) 10 (5) 37 (5) 5 (3) 286 (6) 6 (4) 21 (4) 6 (4) ~3 24 (5) ~2 80 (30) 21 (5) 3 (2) 6 (4) 6 (2) 191 (5) 14 (7) 3 (I) 9 (5) 187 (5) 31 (4) 4 (2) 16 (4) 40 (4) 121 (5) 14 (5) 28 (3) 6 (4) 13 (4) ~20 21 (4)

A22/Ao a

An4/Ao a

0.102 (35)

-0.017 (24)

0.445 (55)

0.838 (60)

-0.015 (40)

0.244 (46)

-0.187 (61)

-0.146 (70)

0.31 (18) -0.091 (93)

0.90 (20) 0.20 (11)

Initial State (keV) 153.2 677.1 410.7 962.8 477.9 757.0 1049.1 861.3 1248.3 861.3 1177.5 677.1 1491.1 962.8 1534.7 1248.3 1049.1 1351.0 677.1 861.3 1187.1 1387.3 1187.1 962.8 1491.1 1248.3 1534.7 861.3 1351.0 1049.1 1351.0 1177.5 1187.1 1248.3 1534.7 1351.0 1387.3 1351.0 1534.7

a Angular correlation coefficients in cascade with 153.2 keV transition.

267.0, 326.2 and 388.0 keV) are not observed in our experiments. In our work, four new levels have been established at 1177.5, 1387.3, 1491.1 and 1534.7 keV. Fig. 3 shows the decay level scheme. Table 4 gives a list of all y-ray energies and Table 5 gives the conversion coefficients. In Refs. [21,22], the states at 478, 677 and 861 keV are assigned as 0 +, 2 + and 2 +, respectively. We have confirmed these assignments with measurements of conversion

230

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250

c~

r--t

c,~o

~,tLn

~

cx) t r 1 I'~l"q "e--t r--t

oor-~. ,:--Ir--I r--t ~-'l

Ln e--I r--t

O'~II~

O"

~'OIL--~

9" L611

S'096

L'EL,9 ~----~-~ L gLL ~'80L

%

IP--

c¢3

Ms) oo

co

c

["-o

t..o-4.D

tv~

t~

0 oO r-.-I

Fig. 3. The level scheme for 18°pt from 18°Au decay. The 478 keV and 490 keV transitions (marked with asterisks) occur only by electron conversion.

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

231

Table 5 Conversion coefficients determined for 18°pt Transition

Type

Expt.

(keV) 257.5 324.7 383.3 450.6 478 490 524.1

638.3 708.1 tl

ceK otK o~K O~K aK OtK otK otL trM OtK aK OtL

809.4 861.4 873. I 1024.3 1033.9

OtK OtK OtK ffK OtK

0.116 (24) b <0.11 <0.072 > 1.0 >0.30 0.057 (5) 0.010 (2) 0.005 (2) <0.06 0.21 (10) 0.034 (19) <0.012 0.0054 (12) <0.036 <0.009 0.0087 (19)

Theory

Multipolarity a

M1

E2

0.401

0.0900

0.137 0.0891 0.0763 0.0715 0.0600 0.00963 0.00222 0.0360 0.0276 0.00436 0.0193 0.0168 0.0162 0.0108 0.0106

0.0339 0.0233 0.0204 0.0193 0.0166 0.00423 0.00106 0.0109 0.00879 0.00170 0.00674 0.00598 0.00582 0.00428 0.00420

E2 E2 (E2) (E2) E0 c E0+(MI+E2) E0+E2, 6 < -11

(E2) E0+MI+E2, 8 = 2.0+_3.6 E2, ~ < --13 E2 (E2) (E2) (E0+MI+E2, I~l > 5.7 )

a Mixing ratios ~(E2/M1 ) from angular correlations given in Table 4. b Contaminated with 18°Os 318 keV K line and other unidentified contaminants. c X ( E O / E 2 ) = 0.026(2). d Electron lines unresolved from those of the 708.9 keV transition. coefficients and, for the 478 and 677 k e V states, angular correlations. T h e state at 477.9 k e V is o b s e r v e d to decay to the ground state via a strong electron transition without a c o r r e s p o n d i n g ),-ray b e i n g o b s e r v e d (indicating a 0 ÷ ~ 0 + m o n o p o l e transition) and a distinctive 0 ~

2 --* 0 correlation is o b s e r v e d for the 3 2 4 . 7 - 1 5 3 . 2 k e V cascade.

The angular correlation o f the 5 2 4 . 1 - 1 5 3 . 2 k e V cascade confirms a spin o f 2 for the 677.1 k e V level, and gives a m i x i n g ratio o f t3 < - 1 1

for the 524.1 k e V transition.

Its c o n v e r s i o n coefficients are a b o v e the E2 values (coincidentally, they agree with the theoretical M1 coefficients), so an E 0 c o m p o n e n t must be present. T h e 708.1 k e V transition b e t w e e n the states at 861.3 k e V and 153.2 k e V is also observed to have large electron c o n v e r s i o n coefficients, indicating an E 0 c o m p o n e n t and c o n f i r m i n g the 2 + a s s i g n m e n t for the 861.3 k e V level. I n d e p e n d e n t e v i d e n c e for this spin-parity a s s i g n m e n t is p r o v i d e d by the c o n v e r s i o n coefficient-based a s s i g n m e n t o f E2 multipolarity to the 861.4 k e V transition. T h e state at 962.8 k e V was assigned 3 + in Refs. [ 2 1 , 2 2 ] , although no direct meas u r e m e n t o f the parity appears to have been m a d e in either case. Our m e a s u r e m e n t o f the 8 0 9 . 4 - 1 5 3 . 2 k e V angular correlation confirms the spin but, as only an upper limit is available for the trK o f the 809.4 k e V transition, the parity cannot be determined. Tentative j , r = (4 +) a s s i g n m e n t s to the 1049 keV and 1248 k e V states are g i v e n in Ref. [ 2 1 ] . A d d i t i o n a l branches have been o b s e r v e d f r o m the 1049.1 k e V level to the 21+ state and f r o m the 1248.3 k e V level to the 2 + state.

232

I~M. Davidson et al./Nuclear Physics A 657 (1999) 219-250 r

40

~

r

T

t

~

r

T

-

-

490 key K electron gate

Pt X-rays

30

~i 8

20 511 i0

200

400

600

800

I000

energy [keV]

Fig. 4. Spectrum of y-rays in coincidence with 490 keV K conversionelectrons in 18°pt. The line at 511 keV arises from positron annihilation. The 1024.3-153.2 keV cascade has a large A 4 / A o coefficient, giving a J = 0 assignment to the newly observed state at 1177.5 keV. The limit on aK for the 1024.3 transition excludes M2 or higher multipolarity, allowing an E2 assignment to the transition, and positive parity to be assigned to the state as well. The 708.9 keV branch from the 1187.1 keV state to the 0 + state is observed for the first time. This is consistent with the spin of 2 assigned in Ref. [21]. Two additional y-rays with energies of 673.7 keV and 1351.4 keV are seen to de-excite the state at 1351.0 keV, and a 490 keV electron transition is observed in coincidence with the 861.4 keV y-ray, as shown in Fig. 4. As no 490 keV y-ray belonging to 18°pt is observed, a limit on the conversion coefficient is obtained, implying an E0 component for this transition. The previous 2 + assignment for the 1351.0 keV state was based only on the presence of particular decay branches, whereas we make this assignment definite. 4.3. 17Spt

The yrast level scheme of ~78pt has been established to spin 18h by Dracoulis et al. [8] using a (37Cl,p2n) reaction. Hagberg et al. [9], in their a-decay studies, have reported an excited (0 +) level at 421 keV. That state is observed in the current study, along with sixteen new levels (two of which, at 1815.0 and 2138.2 keV, have also been observed in-beam [ 2 3 ] ) . In the present experiment the yrast band is observed to spin 8h. Fig. 5 shows the level scheme determined from the y - y measurement. Observed y-rays are given in Table 6 and conversion coefficients in Table 7. A strong electron transition to the ground state from the state at 421.0 keV is observed with no corresponding y-ray, in agreement with the supposed E0 nature of this transition. The angular correlation coefficients of the

PM.

233

Davidson et al./Nuclear Physics A 657 (1999) 219-250

---2345.2 (8+ )

2197.6 (9)

Iil/i

I

323.2 720.2

s! 178pt

~ (6+) ~"

, ~ll

8+

•

I

I

It,l,, -~..,

m m2sT.3m 2+ 0+ ~

~

~'I'

17o.4

c~

--2028.9 -1810.3 -1747.1 -1633.5 1581.8 ~1573.4 ,4 -1426.1 %o ~-1345.3

~, 1477.1 co"

i

i,i!l,,i l /21+ t

I

~

7

/

~1815.0

1179.o i

413.4

6+

2138.2

,,

I

I

" i ~"

I

,-I~

-1001.3

m

, i~

~. i

m

,Ztie

,,,.<-7,

i,

0.0

Fig. 5. The level scheme for 178pt from 178Audecay. The 421 keV transition (marked with an asterisk) proceeds only by electron conversion. 250.6-170.4 keV cascade are also consistent with the 421.0 keV level having J = 0, so we assign a definite spin and parity. A level at 653.4 keV is observed to decay to the yrast 2 + level, to the ground state and also, via a weak transition, to the 0~- level at 421.0 keV. Our assignment of 2 + is based on the electron conversion coefficient values for the 483.0 keV transition, which indicate an E0 component. The angular correlation measurement of the 483.0-170.4 keV cascade supports this assignment. States at 1058.3, 1477.1 and 2197.6 keV are assigned (4+), (6 +) and (8+), respectively, by considering the states to which they decay. The angular correlation of the 630.6-257.3 keV cascade supports the assignment for the 1058.3 keV level. (Contamination of the K electron line of the 630.6 keV transition by a strong K electron peak from the 624 keV J~ --~ J~ transition in n8Os meant only an upper limit on the conversion coefficient could be determined.) The K conversion coefficient for the 711.5 keV transition is larger than the E2 value, indicating an M1 or E0 component,

234

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250

Table 6 Gamma-ray energies and intensities in 178pt Er (keY)

Iv

170.4 232.1 250.6 257.3 337.9 405.0 413.4 418.3 483.0 530.2 580.0 630.6 636.0 653.2 711.5 720.2 807.8 830.9 867.9 888.1 917.6 998.4 1018.3 1044.7 1049.3 1145.7 1154.1 1256.1 1263.3 1319.4 1432.0

1000 (28) ~25 62 (22) 692 (21) 326 (17) 36 (9) 135 (10) 25 (10) 146 (12) 22 (6) ~5 80 (20) 65 (11) 80 (22) 32 (8) 30 (11) 40 (8) 68 (20) 30 (15) ~40 50 (16) 16 (9) ,~10 40 (21) 34 (16) 20 (9) 33 (10) 25 (11) 40 (14) 41 ( l l ) 50 (19)

A22/Ao a

0.25 (23) 0.15 (5)

-0.01 (9)

-0.14 (13)

A44/Ao a

0.54 (23) -0.01 (5)

0.27 ( l l )

-0.20 (17)

Initial State (keV) 170.4 653.4 421.0 427.7 765.6 1058.3 1179.0 1477.l 653.4 2345.2 1345.3 1058.3 1815.0 653.4 1477.1 2197.6 1573.4 1001.3 1633.5 1058.3 1345.3 1426.1 2197.6 1810.3 1477.1 1573.4 1581.8 1426.1 2028.9 1747.1 2197.6

a Angular correlation coefficients in cascade with 170.4 keV transition. and this supports the ( 6 +) a s s i g n m e n t to the 1477.1 k e V level. A spin o f 3 for the state at 1001.3 k e V is suggested by the angular correlation o f the 8 3 0 . 9 - 1 7 0 . 4 k e V cascade. The 830,9 keV transition also has a large, but not welldetermined, c o n v e r s i o n coefficient value. It may have an M1 c o m p o n e n t ; h o w e v e r an E0 c o m p o n e n t is also possible, which w o u l d m e a n the 1001.3 k e V state's spin and parity w o u l d be 2 + . 4.4. 176pt

The analysis o f the 3'-9' c o i n c i d e n c e results for 176pt revealed no e v i d e n c e o f the population o f non-yrast states by decay. Fig. 6 shows the gate on the 264 k e V yrast 2 + ~ 0 + transition. T h e gate contains s o m e contaminants but all o f the lines o b s e r v e d can be identified with k n o w n sources, as indicated in Fig. 6. The yrast band is o b s e r v e d

235

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

Table 7 Conversion coefficients determined for 178pt Transition

Type

Expt.

Theory

Energy (keV) 421

1.0 (2) 0.18 (5) 0.11 (1) 0.010 (2) 0.0025 (4) <0.09 c <0.04 0.020 (9) 0.06 (4)

OtK O~L

483.0

O~K O~L

otM OtK ~K OtK OtK

630.6 653.2 711.5 830.9

Multipolarity a

M1

E2

0.107 0.0173 0.0743 0.0120 0.00276 0.0371 0.0339 0.0272 0.0184

0.0272 0.00871 0.0199 0.00555 0.00137 0.0112 0.00104 0.00872 0.00641

E0 b E0+(M1)+E2, 1(51> 4.2

(E0+MI+E2) (E2) (E0+MI+E2) (M1)

a Mixing ratios 8(E2/M1) from angular correlations given in Table 6. b X(EO/E2) = 0.010(4). c Electron line contaminated by I78Os transition. 2000

I

I

I

I

264 keV gate

Pt & Os X-rays

• 182p t

1500

• 1840s • 93Mo

300

120

7

t.o

342 I000

390'~ 179" ,

• Qo

685

1400

•

841

0

0

200

400

600

800

944

i000

energy [keY]

Fig. 6. Gate on 176pt yrast 2+ --~ 0+ 264 keV transition. Contaminants are marked by symbols. The position of a possible transition from the 0~" state at 443 keV to the 2+ state is marked with an arrow. As discussed in the text, no such transition is evident. up relatively h i g h - s p i n but there are no candidates for transitions f r o m non-yrast states in 176pt. In particular, although a 0 + state has been o b s e r v e d in alpha-decay w o r k (initially reported to be at 433 k e V by H a g b e r g et al. [ 9 ] , but later revised to 443 k e V by Wauters et al. [ 2 4 ] ), there is no e v i d e n c e o f a 179 k e V transition w h i c h w o u l d link a state at 443 k e V to the yrast 2 + level at 264 keV. T h e limit for such a transition is d e t e r m i n e d to be < 2 % o f the 300 k e V 4 + --~ 2 + transition. W h i l e the 0~- state m a y d e c a y m a i n l y by an E 0 electron transition and h e n c e not be o b s e r v e d in the 7 - Y data, it is unlikely that transitions f r o m any higher-spin non-yrast states w o u l d p r o c e e d o n l y by electron conversion. A c o m p a r i s o n o f the side f e e d i n g

236

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250 1.0

~I[ states ~I~ states

0.8

II{ states 0.6 5~

0.4

UI

0.2

0.0

2 4 182pt

2 4 18Opt

2

4 6 178pt

8

4

6 176pt

8

i0

Fig. 7. Approximate proportions of side feeding direct from/3-decay into even-spin, positive parity states. The proportions are estimated from intensity balances, with the values normalized to 1.0 for the total feeding into 2 + states.

observed in the four cases studied here, as estimated from intensity balances, is shown in Fig. 7. In all cases, the 2 + states are the most strongly fed, with 4 + states also having significant side feeding. For 178pt and 176pt, the 8+ states also show a considerable amount of side feeding. None of the parent states in the odd-odd gold nuclei are known; but a long-lived isomer in 184Au, linked to the ground state by a 69 keV M3 transition, has been discovered [25]. The spins suggested are I = 2, 3 for the isomer and I = 5, 6 for the ground state. These states are consistent with the observation of states in 18apt up to a spin of 8h, from the decay of m4Au. From the feeding patterns for 178pt and 176pt, it appears that 178Au and 176Au may also have more than one /3-decaying state, and that they have spins of ~ 2h and ~ 8h. It is unclear why non-yrast states in 176pt are not fed in a similar fashion to 178pt. We note that our measurements of the parent half-life for transitions in 176pt give a lifetime consistent with the published half-life of 176Au.Fig. 8 shows the observed time spectrum for the 300 keV transition; the 264 keV transition shows a similar lifetime. Due to the low absolute yield of the reaction that produces the parent nucleus, and the absence of evidence for decay to non-yrast states, conversion electron measurements were not carried out for 176pt.

237

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250 '

I

'

l

'

I

'

I

'

I

I

'

'

I

'

176pt 300 keY Zl/2 = 1.2(2) S

102

! i01

i0 0

i

I

2

,

I

4

6

8 i0 time [s]

t 12

14

16

Fig. 8. Time distribution of the 300 keV transition in 176pt in the chopped beam experiment.

5. Discussion

5.1. Phenomenological band mixing model The phenomenological model originally used by our group to analyze the observed yrast bands of 176pt and 178pt [8] represented each of two interacting bands by an expansion of the form Et = Eo + AI ( I + 1 ) + B [ I ( I + 1 ) ] 2. The second-order coefficients B were set to be the same for each band, and the interaction V between the bands was taken as constant with respect to spin. The procedure used to find the model parameters is detailed in Ref. [8]. Essentially, it was assumed that at higher spins the (unmixed) bands are sufficiently far apart that the perturbations are negligible. From the observed states with I = 8 to I = 14, the inertial parameters and bandhead energy of one band were determined. This unperturbed bandhead energy was used in conjunction with the observed (perturbed) 0 + states to determine the interaction between the bands. Finally, the inertial parameters for the second band were determined from the calculated 2 + energy, the interaction and the energy of the yrast 2 + state. This analysis determined that the moments of inertia A of the two bands differed by a factor of approximately four, a difference interpreted as a deformation difference between the intrinsic states upon which the bands are based. More sophisticated band parameterizations have subsequently been used in our studies [ 11 ], resulting in small differences to the calculated moments of inertia, but the interpretation remains the same.

5.2. Band-mixing model applied to yrast and non-yrast states The predictions in the original paper [ 8] for the energies of the (perturbed) non-yrast states are shown in Fig. 9 for 176-184pt, along with new states observed in the present

238

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

2000

"YJ

178pt

176pt

8

18Opt

0

1500 i000

5O0

i

~

182pt

i

i

•

1500 i000

5OO

i

"/j i

r

184pt

i

~

•

•

i

Spin [hi

2' Spin [h]

Spin [hi

Fig. 9. Experimentally observed even-spin levels (filled symbols) and levels predicted from the original two-band-mixing model in Ref. [8] (open, connected circles).

study. It should be noted that the predicted 2 + states for the excited bands all lie close to the observed 2 + states. However, several states of the same spin are observed in some cases and the predicted excited 4 + states lie near the 4 + in m°Pt and 182pt, and the 4 + state in m4pt. It appears that the situation in the Pt isotopes is more complicated than that in the Os isotopes, where, in many cases, both yrast and yrare states can be explained by using the two-band model [ 13,14] (excluding the s-band, which only affects states of higher spin). The exceptions are 172Os [14] and 18°Os [13], where evidence of I" = 2 + 3'vibrational states mixing with other 2 + states had been noted. The scenario described there was that the intervening isotopes, 174--178Os, did not show signs of such mixing because the 'intruder' states fall lower in these nuclei, while the T-vibration bandhead remains at a higher energy [ 13]. As the Pt isotopes are more T-soft than the Os isotopes, the T-vibrational states are expected to have lower excitation energies. Here we propose that a rotational band based upon the least energetic T-vibration mode should also be included into the band-mixing model. This is appropriate as the data for the non-yrast states allows meaningful comparisons to be made with the predictions of an extended band-mixing model. In Fig. 9 obvious candidates for the (mixed) T-vibrational states can be seen, particularly in the case of 18°pt where the 2~- and 4 + states are possibly associated with the lowest T-vibration mode. To quantify these ideas, a procedure similar to that described in Refs. [ 13,14,26,27] has been used to fit the data with a multi-band model. Three bands were incorporated;

P.M. Davidson et aL /Nuclear Physics A 657 (1999) 219-250

239

a more deformed band (called the d-band), a less deformed band (termed the g-band, as in Refs. [13,14] ), and a y-band. The unperturbed bands are characterized by the VMI [28] parameters Io and C and excitation energies E0. The g- and d-bands have K = 0 while the y-band has K = 2. The y-band was considered first. As the K = 0 bands have only even spin members, if the yrast odd-spin states are identified as being members of the y-band, it is possible to extract the parameters that describe the y-band directly, without a need to consider mixing. For each isotope, at least three odd-spin states are required. For ~82pt, we chose the states at 942.6 keV, 1306.1 keV and 1733 keV (the latter is only observed in-beam [20]), noting that none of these states have firm spin or parity assignments. Nevertheless, we assumed they are the 3 +, 5 + and 7 + members of a K = 2 rotational band. For 18°pt, the 3 + state at 962.8 keV, the 5 + state at 1315.5 keV and the 7 + state at 1727.7 keV were chosen [21]. No positive identification of odd-spin ),-band states has been made for 178pt, although the state at 1001.3 keV may be the 3 + state. The parameters for the y-band obtained from the odd spin states in ~82pt and J8°pt are given in Table 11. (For comparison, the parameters obtained for 184pt, 10 = 1.27 × 10 -2 keV -J, C = 1.13 × 106 keV 3 and E0 = 710.6 keV are very similar and show that the y-band is very stable across these isotopes.) As it was necessary to extrapolate for J78pt, we assumed that the inertial parameters Io and C do not change substantially between 18°pt and 178pt. The bandhead energy Eo for 178pt was not determined at this stage. The even-spin states were then considered. The data sets chosen consisted of the even-spin yrast states between I = 0 and 1 = 12 inclusive, and even-spin non-yrast states with I = 0, I = 2 or I = 4 (and I = 6 in 178pt). Yrast states with higher spin were not included as the s-band may perturb their energies. (In 18°pt the s-band crosses the g-band near 1 = 18h with an interaction strength of approximately 30 keV [ 2 l ] . The s-band crossing would be expected to occur at a similar spin in 178pt and 182pt.) The model space included the K = 2 y-band with fixed parameters, except for ~78pt, where the bandhead energy Eo of the y-band was allowed to vary in the fitting process. Two K = 0 bands were also included, representing the g-band and d-band as described above, and the inertial parameters I0 and C of these bands and their bandhead energies E0 were allowed to vary. In addition, three spin-independent interactions between these bands Vdg, Vd~ and Vg~ were allowed to vary, within a reasonable range. The fits yielded energies and wave functions for the mixed states. The agreement between the fitted and observed energies, compared in Tables 8, 9 and 10, is, in general, good. An illustration of the three-band mixing, showing the bands for 18°pt, is given in Fig. 10. As expected, the bandhead energies for the d- and g-bands in the present model are similar to those energies obtained from the analysis in Ref. [8], as is shown in Fig. 11. Also shown in Fig. 11 are the bandhead energies obtained for 176pt, which have been determined using a two-band model (without a T-band) to reproduce the yrast states and the 0~- state at 443 keV. It should be noted that the original band-mixing analysis for 176pt in Ref. [8] used an energy of 433 keV for the perturbed 0 + state, since this was the value originally reported [9].

240

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250 1500

i000

(D

500

I

I

I

0

2

4

I

I

6 Spin [1%]

8

Fig. 10. Graphical representation of the band-mixing results for ts°pt showing the three unperturbed bands (dotted lines) and the perturbed (mixed) bands (solid lines). The experimental states are marked. N 500

98 ,

i00 ,

102 ,

104 ,

[3

[]

106 ,

400

30O

[] O 200

v

v

i00

0

I 176

I 178

I

180 A

I

182

I

184

Fig. 11. The unperturbed bandhead energies E0 of the d-band (circles) and g-band (squares) as a function of neutron number for the platinum isotopes. Open symbols are the results from Ref. [8], filled symbols are the present results. Inspection o f the w a v e functions shows that the 0 +, 2 + and 4 + states are highly mixed, w h i c h m e a n s that, in m o s t cases, an o b s e r v e d state cannot be characterized as a m e m b e r o f the g-band, d-band or y - b a n d exclusively. F o r the non-yrast 2 + states, the w a v e functions reveal a structure that is very different f r o m the structure that has been p r e v i o u s l y a s s u m e d for the low-spin non-yrast states. As an e x a m p l e , the 2 + state in lS2pt at 667.8 k e V is often identified as the bandhead o f a T-band or quasi-T-band

241

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250 Table 8 Band mixing model results for 182pt states State

Energy (keV) Observed

Wave function amplitudes Calculated

ad

ar

ag

0+

0 499

1 499

--0.803 0.596

0.000 0.000

0.596 0.803

2+

155 668 856

151 667 860

0.872 -0.438 0.216

0.092 O.582 0.808

-0.480 -0.685 0.548

4+

420 1034 1240

422 1037 1238

-0.932 -0.274 0.235

-0.066 0.769 0.636

0.356 -0.578 0.735

6+

775

777 1470 1750

-0.961 -0.153 0.231

-0.050 0.916 0.398

0.272 -0.371 0.888

8+

1205

1204 1941 2373

--0.975 --0.093 0.201

--0.041 0.968 0.249

0.218 -0.235 0.947

Table 9 Band mixing model results for 18°pt states State

Energy (keV) Observed

Wave function amplitudes Calculated

aa

ar

ag

0+

0 478

0 478

-0.778 0.628

0.000 0.000

0.628 0.778

2+

153 677 861

151 674 868

0.867 -0.475 0.151

0.118 0.489 0.864

-0.484 -0.731 0.480

4+

411 1049 1248

414 1054 1245

-0.935 0.290 0.204

-0.090 - 0.750 0.656

0.343 0.595 0.727

6+

757

758 1480 1771

-0.964 -0.160 0.212

-0.073 0.927 0.367

0.255 -0.338 0.906

8+

1182

1i 80 1933 2417

-0.977 -0.106 0.184

-0.064 0.974 0.217

0.202 -0.200 0.959

in the literature [ 1 8 , 2 0 ] , but in our a n a l y s i s the m a k e u p o f the w a v e f u n c t i o n is 19% d - b a n d , 4 7 % g - b a n d a n d o n l y 3 4 % y - b a n d . A s a f u r t h e r e x a m p l e , the 2~- state in 182pt at 856.2 k e V has a 6 5 % y - b a n d c o m p o n e n t , in c o n t r a s t to its original identification as a m e m b e r o f a / 3 - b a n d [ 19]. Tables 8 a n d 9 also s h o w c a l c u l a t e d e n e r g i e s for n o n - y r a s t 6 + and 8 + states. F o r 182pt, the c a l c u l a t e d 6 + states are 1470 k e V a n d 1750 k e V and w e note that in Ref. [ 2 0 ] , 6 +

242

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

Table 10 Band mixing model results for J78pt states State

Energy (keV) Observed

Wave functionamplitudes Calculated

aa

a~

ag

0+

0 421

0 421

-0.744 -0.668

0.000 0.000

0.668 -0.744

2+

170 653

170 653 816

0.878 0.460 0.133

0.067 -0.392 0.917

-0.474 0.796 0.375

4+

428 1058

428 1058 1192

-0.949 -0.228 0.220

-0.045 0.783 0.620

0.313 -0.578 0.753

6+

765 1477

765 1477 1750

-0.974 -0.089 0.209

-0.033 0.966 0.257

0.224 -0.243 0.944

8+

1179

1178 1926 2423

-0.984 -0.051 O.168

-0.027 0.990 O.140

O.174 -0.133 0.976

states are reported at 1437 keV, 1649 keV and 1863 keV (although the spins of these states are not certain). A possible 8 + state is also reported at 2117 keV; the calculated 8 + states are at 1941 keV and 2373 keV. In 18°pt, a possible 6 + state is reported at 1650 keV and the calculation shows 6 + states at 1480 keV and 1771 keV. The model does not predict the non-yrast 6 + and 8 + states well. The discrepancy may be caused by the influence of yet another vibrational band at higher energy, and evidence for such a structure will be discussed in Section 5.6. Table 11 gives the parameters determined from the fits. The inertial parameters for the d-band can be seen to be roughly constant over the isotopes. The g-band exhibits a moment of inertia I0 that decreases in a regular way with decreasing neutron number. 5.3. Comparison with Os isotopes The equivalent band-mixing model has also been applied to the light osmium isotopes in our related work on low-lying non-yrast states in the nuclei 172-184Os [ 13,14]. As in the current study, the g-bands were found to have deformations quite different from the deformations of the d-bands. The inertial parameters 10 obtained for the osmium and platinum nuclei are compared in Fig. 12a, where again the values for 176pt have been determined by omitting the 3/band from the model analysis. The values of I0 for the g-bands tend to increase smoothly with neutron number in both the osmium and platinum isotopes. For the d-bands, I0 is almost constant, independent of N and Z. (Light mercury isotopes also exhibit a d-band with very similar inertial characteristics [ 11 ] ). Fig. 12b shows how the strength of the interaction between the g-band and d-band

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

243

Table 11 Phenomenological model parameters Parameters

182p1

18°pt

178pt

176pt

g-band

Io C Eo

( × 1 0 - 2 keV -1 ) ( x 106 keV 3) (keV)

0.74 3.45 322

0.64 3.59 289

0.51 3.62 233

0.17 1.6 82

d-band

Io C Eo

( x 10 - 2 keV - l ) ( × 106 keV 3) (keV)

2.77 2.46 178

3.06 3.41 189

3.08 3.13 188

3.08 2.2 361

),-band a

Io C E0

( x 10 - 2 k e V - l ) (×106 keV 3) (keV)

1.46 1.31 726

1.46 1.13 750

1.46 1.13 726

Vgd Vg~ Vat

(keV) (keY) (keV)

239 108 -7

234 ltl -28

209 71 -8

172

a K was set to 2 for the y-band.

Vgd varies with neutron number. Again there is a similarity between the Os and Pt systematics: although the interactions in the platinum isotopes are weaker, both interactions initially increase with neutron number. These comparisons are strongly suggestive of an underlying structural similarity of the intrinsic states in the platinum and osmium nuclei. It should also be noted that the trend of falling interaction energy with increasing Z continues to the even mercury nuclei [ 11 ].

5.4. y-ray branching ratios

As the model yields the wave function of each state in terms of the three intrinsic states, and the quadrupole moment of each intrinsic state can be calculated (approximately) from the inertial parameters of the associated bands, the y-ray E2 strengths between states can be determined. The general form of the expression used, as given in Ref. [ 13], is

B ( E 2 ; J/---+ Jr) =

Z 5

A A

L .i,k

jlE2[k

)]2 j

,

where j, k are summation indices over the d-, g- and y-bands. The wave function amplitudes in the initial and final states of the transitions are represented by Aji and A f. The diagonal matrix elements in the above summation are given by (dlE2[d) : V/ff/167r( Ji 2 0 0 [ Jf O)e(d[Qold) , (glE2lg) = v/-f/16~r( Ji 2 0 0 I Jf O)e(glQolg) , = v / 5 - / 1 6 ~ ( J i

2 2 0 I Jf 2)e(Ylaoly),

244

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

4.0

I

I

I

I

I

oOS la, 3.0 d-band I

.~-.-o Os

2.0 0 H

1.0

0.0

g-band

I_o//

Pt

I

I

I (b)

300 ^

,

~

-

-

~

m

Os

250

200

150

I

I

I

I

I

96

98

100 N

102

104

Fig. 12. Selected parameters of the band-mixing model, for osmium [ 13,14] and platinum nuclei. (a) The inertial parameters h~ for the g- and d-bands. (b) The interaction strength Vgd.

where the (Ji 2 K 0 t JY K) are Clebsch-Gordan coefficients. The quadrupole moments (JlQolJ) are calculated using the approximate empirical relation [28] Q0 ~ 39.5 x/~02,

( 1)

where ~o2 is the average of the moments of inertia of band j at spins zero and two, as determined from the band-mixing model. The off-diagonal matrix elements ((glQold), (g[Qol)'), (dlQ0l)'), etc.) cannot be calculated in a model independent manner. Here the off-diagonal elements are set equal to zero in the absence of better information. Experimentally, apart from some ground-state band transitions in 176pt, 178pt [8] and 18°pt [29], the absolute transition strengths are unknown. However, the ),-ray branching ratios can be obtained using the observed intensities. The calculated B(E2) values can be converted into relative ),-ray intensities by multiplying by ESt. Tables 12, 13 and 14 show observed and calculated branching ratios from non-yrast states in 182pt, 18°pt

245

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250

Table 12 Table of branching ratios for ~82pt

a

Initial st~e A

y-ray A ---* B

Fin~ st~e B

y-ray A~ C

Final state C

Expt. BR a

C~c. BR a

2~

668 (248) (168)

0{ 4{ 0~

513 513 513

2~ 2+ 2~

0.34 (6) <0.02 <0.02

0.59 0.055 0.018

2+3

856 437 357 (188)

0~ 4~ 0+ 2~

701 701 701 701

2~ 2~ 2~ 2{

4.4 (4) 2.6 (7) 0.77 (22) <0.15

0.41 2.97 1.72 0.31

4~

879 366 (178) (259)

2~ 2+2 27 6{

615 615 615 615

4~ 4~ 4~ 4~

0.10 (4) 0.50 (25) <0.06 <0.06

0.69 2.04 0.0004 0.017

4+3

1085 573 383 (206) 465

2~ 22 2+3 47 6~

821 821 821 821 821

4~ 4{ 4~ 4{ 4~

2.9 (5) 1.2 (4) 1.9 (5) <0.36 0.71 (24)

0.45 1.45 1.28 0.0045 0.29

Branching ratios are I~(A --~ B)/Ir(A --+ C).

and 178pt, respectively. Considering the sensitivity of the branching ratios to the wave functions, the agreement is good in the several cases, with some notable exceptions that will now be commented upon. For all three isotopes, each of the calculated branching ratios from the 4 + states is approximately four times larger than the observed value, suggesting that the calculated strength for the 4 + ~ 41+ transition ( o f energy 614.5 keV, 638.3 keV and 630.6 keV in ~82pt, 18°Pt and 178pt, respectively) is four times smaller than the actual value. Note that possible M1 components of J ~ J transitions have not been allowed for, and where an M 1 admixture is significant the transition probability will be greater than that expected for a pure E2 transition, as the M1 component will have a partial lifetime that is comparable to that of the E2 component. Such an M1 component may be responsible for the apparent enhancement of the 4 + ~ 4 + transition strengths. Additionally, the 2 3+ ~ 0+ transitions in 182pt and 18°pt (856.2 keV and 861.4 keV respectively) appear to have calculated strengths up to ten times smaller than observed. This is difficult to explain in terms of uncertainties in the mixing amplitudes (or phases) and more likely indicates that the wave function structure is incorrect. A possible source of an additional wave function component is a second y-vibrational band, and this will be discussed in Section 5.6. 5.5. Q u a d r u p o l e m o m e n t s in t76pt, 178pt a n d m ° P t

Lifetimes of states in the ground state bands of 176pt and 178pt have been measured by Dracoulis et al. [8], and lifetimes of ground state band states in 18°pt have been

246

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

Table 13 Table of branching ratios for 18°pt Initial sta~ A

y-ray A~ B

Final state B

y-ray A --+ C

Final state C

Expt. BR a

Calc. BR a

2~

677 (266) 200

0~ 4~ 0~

524 524 524

2~ 2~ 2~

0.28 (11) <0.02 0.010 (7)

0.52 0.073 0.030

2+3

861 451 383 (184)

0~ 4{ 0~ 2~

708 708 708 708

2~ 2J 2~ 2~

8.9 (21) 1.8 (5) 1.2 (4) <0.24

0.78 0.28 0.54 0.075

4~

896 372 (188) (292)

2~ 2~ 2+ 3 6{

638 638 638 638

4~ 4~ 4~ 4~

0.17 (9) 0.25 (10) <0.2 <0.2

0.80 1.16 0.0018 0.046

4+3

1094 572 387 (199) (491)

2{ 2~ 23+ 4~ 6~

837 837 837 837 837

4~ 4~ 4~ 4~ 4~

4.7 (23) 1.0 (8) 3.3 (20) <1.0
0.40 1.65 1.10 0.0032 0.37

a Branchingratios are I~(A --~ B)/I~,(A ---+ C). Table 14 Table of branching ratios for 178pt Initial stme A

y-my A --+ B

FinM state B

y-ray A ---+C

Final state C

Expt. BR a

Calc. BR a

2~

653 (226) 232

0~ 4~ 0~

483 483 483

2~ 2~ 2~

0.55 (16) <0.04 0.17 (12)

0.28 0.068 0.13

4f

405 631 (293)

2~ 2~ 6~

888 888 888

4~ 4~ 4{

0.5 (4) 0.45 (16) <0.2

0.54 2.29 0.057

a Branchingratios are l r ( A ~ B ) / I r ( A --~ C). measured by Noorman [29]. Transition quadrupole moments can be calculated from these values, using the expression Q, = 1 / } / / 1 . 2 2 ( 1 0 2 0 ] ( I - 2 )

0)2E~ (1 + a T ) Tin,

where Q t is in eb, E r is in MeV and z , , in ps. From our band-mixing model wave functions and moments of inertia, we can calculate the predicted values for the quadrupole moments of observed states using the empirical relation for the quadrupole moment given in the previous section. Fig. 13 compares the values calculated from the lifetimes given in Refs. [8,29] with the moments calculated by the band-mixing model. For 176pt, the y-band was not included in the band-mixing model due to a lack of data on the non-yrast states, and the calculations are based on

247

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250 - - T

T

I

I

T - -

176pt 8.0 7.0

____---o-

----0

c~

6.0 5.0

+--178pt 8.0 7.0

_------0

.0

0


6.0 5.0

----ff 18Opt 8.0 7.0

°

O~

6.0 5.0 2

4

6 Spin [h]

8

i0

Fig. 13. Transition quadrupole moments calculated from state lifetimes [81 (filled circles) and the quadrupole moments calculated from the band-mixing results (open symbols), for ground state band states in 176pt (see text), 178ptand 18°pt.

the two-band fit to the data. The calculations reproduce the experimental values roughly, with the value for the 6 + state in n8pt providing the most significant discrepancy. The calculated values are mostly larger than the experimental values, and the agreement would be better if they were all approximately 1 eb smaller, although then the 2 + in ~8°Pt state would be underpredicted. Such a global adjustment could be achieved if the constant value in Eq. (1) were reduced. (This constant is, in any case, an estimate based on evaluations which do not explicitly account for band-mixing.)

248

I~M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

5.6. Vibrational states built on g-band states

In a Letter on lS4pt, Xu et al. [30] interpret states at 1173, 1470 and 1597 keV as being members of a "y-band" built on the excited shape-coexisting structure. In the terms used in the present paper, these states arise from vibrational states built on the g-bandhead configuration. They are expected to mix with other states of the same spin, giving the observed energies. States with J~ = 2 + have also been seen at similar energies in 182pt ( 1182.2 keV) and 18°pt ( 1177.5 keV). These states also exhibit an E0 decay to the 2 + states as described for J84pt in Ref. [30]. It may be noted that a simple addition of bandhead energies (i.e. the energies of the 0 + and 2-3 states) gives 1155, 1168 and 1141 for 18°pt, 182pt and 184pt, respectively, all close to the observed energies of the states being discussed. However, it must again be emphasized that these states probably mix, possibly strongly, with lower-lying states and no unambiguous band identifications can be made. One method of generalizing our model to include such a structure would be to include another K = 2 band. In the present three-band model, the single K = 2 band has a moment of inertia that is between those of the g- and d-bands. If two y-bands were included, we would expect their moments of inertia to be different, reflecting the postulate that they are vibrational states built on intrinsic states with different deformations. The interaction between the 'vibrational g-band' and the g-band would be expected to be similar to that between the d-band and its y-band. It is plausible that there would also be a strong interaction between the two y-bands, similar to that between the g- and d-bands. Such interactions could change the extracted bandhead energies of the d-, gand y-bands and the wave functions of higher-lying states. For lVSpt, 18°pt and J82Pt, the present data are insufficient to justify inclusion of an additional band in our fit, but should further data become available, the analyses could be extended. 5. 7. Theoretical calculations

After the experimental results on I76pt were available, a number of calculations were published attempting to elucidate the shapes of light platinum nuclei at low excitation energy. Bengtsson et al. [2,3] used a Woods-Saxon potential and Strutinsky renormalisation to create potential energy surfaces which showed a clear change from a prolate deformed ground state in JS°pt to a (triaxial) less-deformed ground state in 176pt, with 178pt having a very fiat extended minimum in the area between the minima in the neighbouring nuclei. This corresponded closely to the almost equal bandhead energies for 178pt deduced from the bandmixing analysis. Total routhian surfaces [4] at low spin and dynamic deformation model [5] calculations show features similar to the PES calculations. None of these show two minima separated by a potential barrier, which is reflected by the large interaction energy between the g- and d-bands that is returned by the band mixing model. Although the applicability of the term 'shape coexistence' may be brought into question by the lack

PM. Davidson et al./Nuclear Physics A 657 (1999) 219-250

249

of a potential barrier, configuration-dependent effects not included in these calculations may have a role to play, as demonstrated by Bengtsson and Nazarewicz [31] for the lead isotopes.

6. Summary and conclusions This paper has reported on the experimental determination of the low-lying level schemes of the light even Pt isotopes from 178pt to ~82pt. We have established the spins and parities of many of the non-yrast states through internal conversion and angular correlation measurements in conjunction with y - y coincidence experiments. States in 178pt are populated relatively strongly up to a spin of 8h, while in 18°pt and 182pt the population is strong only to 4h. No transitions from non-yrast states were observed in the decay of 176Au to 176pt. A modification of the band-mixing model used successfully to describe the low-lying states of the light osmium nuclei was used to analyse the results. In addition to the g-band (less deformed) and d-band (more deformed) constituents used in previous applications of this model, it was necessary to include mixing with low-lying K = 2 vibrational states, the y-band. The inertial parameters of the three bands extracted from the model were relatively constant over the nuclei considered. The interactions also showed little variation, as expected. The bandhead energies of the g- and d-bands were almost degenerate in ~7Spt, and further apart in ~8°pt and 182pt. This corresponded to the results of an earlier analysis and is consistent with theoretical calculations. The analyses show that the d-bands appear as a very stable feature of the nuclei in this region, not only for light platinums, but also for osmium and mercury. The mixing between the various states masks this in experimental data, as the properties of the d-band can be perturbed over a large spin range. The wave functions extracted from the model shows that many states are highly mixed, and that the non-yrast 2 + states, in particular, have quite a different structure from that previously assumed. This emphasizes the importance of understanding the effects of configuration mixing before deductions are made about the systematics of intrinsic excitations. Discrepancies persist between the observed and calculated branching ratios and other moments, and to some extent the density of non-yrast states, indicating a need to extend the model space. The platinum nuclei are problematic in the respect that a number of possible excitations fall at comparable energies. Nevertheless, the model successfully demonstrates how the interplay between states of different deformation gives rise to a number of the observed properties of the light platinum nuclei. In order to understand fully the nuclei in this region, more theoretical effort is needed, particularly with regard to characterizing the microscopic nature of the states involved and their interaction, in a dynamical sense. However, in the absence of such knowledge, it is remarkable that the phenomenological description of interacting bands of different (static) deformation is able to describe such a range of nuclei quite accurately and with smoothly varying parameters.

250

P.M. Davidson et al./Nuclear Physics A 657 (1999) 219-250

Acknowledgements W e w o u l d like to t h a n k the t e c h n i c a l a n d a c a d e m i c s t a f f o f the A N U 1 4 U D P e l l e t r o n facility for t h e i r support.

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