THE AUSTRALIAN NATIONAL* UNIVERSITY

RESEARCH SCHOOL OF PHYSICAL SCIENCES

ANU-P/948 April 1986

ELECTRIC QUADRUPOLE MOMENTS OF THE FIRST EXCITED STATES OF 19i+Pt, 296 Pt AND X 98Pt

G.J. GYAPONG, R.H. SPEAR, M.T. ESAT and M.P. FEWELL Department of Nuclear Physics, Australian National University, Canberra, ACT 2600, Australia and A.M. BAXTER and S.M. BURNETT Department of Physics and Theoretical Physics, Faculty of Science Australian National University.

INSTITUTE OF ADVANCED STUDIES ANU-P/948 April 1986

ELECTRIC QUADRUPOLE MOMENTS OF THE FIRST EXCITED STATES OF 194Pt, 196Pt AND 198Pt

G. J. GYAPONG, R M. SPEAR, M.T. ESAT and M.P. FEWELL Department of Nuclear Physics, Australian National University, Canberra, ACT 2600, Australia. and A.M. BAXTER and S.M. BURNETT Department of Physics and Theoretical Physics, Faculty of Science, Australian National University, Canberra, ACT 2600, Australia.

12 16 Abstract: Coulomb excitation of iHi96,i98Pt by «He, C and 0 projectiles has

+ been used to determine the static electric quadrupole moments Q(2t ) of the first excited states of 194« 196« 198Pt, together with values of BfpliOf^f). It is

clearly established that Q(2t+) is positive for each nucleus, having values of 0.48(14)eb and 0.66(12)eb for 194Pt and 196Pt, respectively, and 0.42(12)eb or

198 + 0.54(12)eb for Pt, depending on whether the interference term P4(22 ) is positive or negative. Results obtained for B(E2;0J+->2J+) are 1.661(1 l)e2b2,

2 2 2 2 1.382(6)e b and 1.090(7)e b for iHi96,i98Pt> respectively. The results are compared with the predictions of various nuclear models.

NUCLEAR REACTIONS 194'196-198Pt(a,a'), E =» 14.0 - 15.6 MeV, 9 = 174.8°; 196Pt(a,a'), E = 16.8 - 18.6 MeV, 9 = 90.0°;

i94,i96,i98pt(i2Cfi2C)> E = 41 0 . 45.0 MeV, 8 = 174.8°;

I94,i96(i98pt(i60i60.)t E = 55 0 . 63 0 MeV) e = i74.g=; measured

+ Coulomb excitation probabilities of first 2 states. iM,i96,i98pt deduced

+ + + B(E2;01 ->21 ) and Q(2j ). Enriched targets.

Accepted for publication in Nuclear Physics A 2

1. Introduction

The so-called "transition region" near A=190 has, for more than a decade, been a remarkably active area for nuclear spectroscopic investigations. Theoretical and experimental studies of nuclei in this region have produced major advances in our understanding of nuclear strucrore.

In 1968, Kumar and Baranger calculated1) that the nuclear shape changes from prolate to oblate in the A = 186-192 region. Their microscopic calculations involved the application of the pairing-plus-quadrupole model to Bohr's collective Hamiltonian.

+ In particular, they predicted that the static electric quadrupole moment Q(21 ) of the first excited state of even-even nuclei should change from negative (prolate charge distribution) to positive (oblate) in proceeding from the to the isotopes, and that it should remain positive for the isotopes. They calculated2) that me prolate-oblate shape transition should occur at A = 192.

Within a few these predictions were experimentally verified by Saladin and his collaborators at Pittsburgh. By studying Coulomb excitation with various

+ projectiles they found that Q(2j ) is clearly negative for 184.186,188,19O,1920S ^.efs

3 4 4 9 19 - ) and positive for i' .i 6. 8pt (refs 5,6) Subsequently, Cline and collaborators at

Rochester reported7) substantial confirmation of the Pittsburgh results; however, a detailed presentation of the Rochester data has not been published. In addition,

Coulomb excitation measurements at Canberra8'10) and at Koln11) have shown that

Q(V) is positive for »W«>.MV04Hg>

The discovery of the A = 192 prolate-to-oblate transition has triggered a very large amount of experimental work on the spectroscopy of the Os, Pt and Hg isotopes. In parallel with this, an equally large amount of related theoretical work has been published. For example, the development of the interacting boson model (IBM)

[ref. 12)] was greatly stimulated by the suggestion13) that the properties of the low-lying levels of 196Pt are in remarkably good agreement with those predicted by the 0(6) limit of the IBM, and in this context the transition region has been 3 interpreted14) in terms of a progression from the 0(6) ["/-unstable15)] limit for the heavier Pt isotopes toward the SU(3) limit (axially symmetric rotor) for the lighter Os isotopes. Other approaches to understanding the tr?nsition nuclei include interpretations in terms of boson expansion theory16,17), the rigid asymmetric-rotor model18,19), rotation-vibration models, both symmetric20) and asymmetric21), and other more complex geometric models [e.g. refs22"24)].

In all of these considerations, the value of Q(2j+) for the even-even nuclei involved plays a crucial role. For example, Q(2j+) = 0 in the strict 0(6) limit of the

IBM. Therefore, the reported positive value of Q(2j+) for 196Pt [refs.5"7)] raises complications25) for the suggestion that this nucleus is an 0(6) paradigm. However, a recent redetermination of Q(2j+) for 194Pt by the Pittsburgh group26) has produced a value consistent with zero (0.13 ± 0.17 eb), in contrast to their earlier value of 0.64 ± 0.16 eb. They attribute the discrepancy to difficulties associated with impurity subtractions owing to the lower isotopic enrichments of the targets used in the earlier work. Their published target compositions6) suggest that those problems could haw, been at least as great for 196Pt and 198Pt, which raises doubts about their results for those nuclei, and, incidentally, about the nature of the prolate-oblate transition.

Furthermore, there have been some difficulties26) in reconciling values of Q(2j+) obtained for some of the Cs and Pt isotopes using muonic X-ray techniques27*29) with those obtained from Coulomb-excitation data. It is therefore highly desirable to make new and independent measurements of Q(2j+) for the Pt isotopes. The present paper presents the results of such measurements for 194Pt, 196Pt and 198Pt. A brief report of the results for 196Pt has already been published30).

2. Experimental Procedure

The use of Coulomb excitation to determine nuclear properties such as Q(2j+)

+ + and the reduced transition probability B(E2;01 -»21 ) has been comprehensively described in several review articles31'33). The basic experimental procedures used in 4 the present work have been described in previous publications from this laboratory

[e.g. refs. 34"37)).

Although two independent measurements of the excitation probability of the 2j+

+ + + state usually suffice to determine Q(2j ) and B(E2;01 ->21 ), we have, in order to obtain substantial redundancy and increased confidence in the results, made measurements under four different experimental arrangements for 19oPt

(backscattering of 4He, 12C and 160 and scattering of 4He at 90°) and three different arrangements for 154Pt and 198Pt (backscattering of 4He, 12C and 160).

Charged-particle beams were obtained from the ANU MUD pelletron accelerator,

the beam energy having been previously calibrated38) to better than 0.1%. Targets, which consisted of isotopically enriched Pt metal evaporated onto thin foils,

had thicknesses in the range 2-15 (ig cm"2. Isotopic compositions of the enriched Pt used are listed in table 1. Backscattered particles were detected with an annular surface-barrier detector, the mean laboratory scattering angle being 174.8 ± 0.2°. Particles scattered at 90° were analysed using an Enge split-pole magnetic spectrometer

with a position-sensitive multi-electrode proprotional counter at its focal plane39). Since the Coulomb-excitation probability varies rapidly with angle at 90°, the scattering angle must be measured accurately. This was done using the kinematic

technique described by Kuehner et al.40) and resulted in a value of 90.0 ± 0.1°.

3. Analysis and Results 3.1 SPECTRUM ANALYSIS

The experimentally determined Coulomb-excitation probability PMO of the first V~ state is defined as

Thus for each spectrum obtained, the number of counts in each of the "elastic" (0j+)

and "inelastic" (2,+) peaks must be determined. Representative spectra are shown in 5 figs. 1 and 2. As is normal in this type of experiment, the 2j+ peak sits on a tail extending down in energy from the much larger elastic peak. Peak areas were extracted using well-established procedures34,35*37), with the modification that x2 was

2 40 replaced by the log-likelihood function x i p of ref. ) as a measure of goodness of fit. The elastic-scattering peak was fitted with a lineshape consisting of a skewed gaussian plus one or more exponential functions tc represent the low-energy tail of the peak. This lineshape was used to estimate the magnitude of the elastic-peak tail underneath the inelastic peak. When analysing spectra from the Enge spectrometer, allowance was made for the variation of peak shape along the focal plane. Small contributions to the spectra from Pt isotopes other than the one of primary interest ("isotopic impurities") were accounted for using the supplier's assay (table 1) and

B(E2) values from the literature25,42,43); these contributions are shown by the broken curves in figs. 1 and 2.

Values obtained for P are listed in table 2. The bombarding energies (E) given are the values obtained after applying small corrections (ranging from 1 to 15 keV) for the effects of finite target thickness. Target thicknesses were determined from Rutherford-scattering measurements. The experimental uncertainties assigned to values of P arise from statistical uncertainties, and from uncertainties involved in estimating the background beneath the 2j+ peak and in correcting for isotopic impurities.

3.2 INVESTIGATION OF TARGET CONTAMINANTS Elastic scattering from target contaminants other than Pt isotopes could distort the results by contributing to the spectrum in the region of the Pt inelastic peaks. For each experimental configuration, the masses of possible interfering nuclei were calculated, and spectra obtained at low bombarding energies were examined to set upper limits on the contributions of these contaminant nuclei to the measured excitation probabilities.

For example, in the case of i2C on 196Pt, the offending contaminants would range in mass r.umber from 185 to 191, and spectra obtained with 18-MeV 160 ions were used to set an upper limit of 0.5% on their contribution to P (at the 95% confidence level;. Other limits ranged from 0.1% for 4Heon 194Pt at 174.8° andfor4Heon

196Pt at 90°, to 0. /% for 160 on 196Pt at 174.o°. The small surplus of counts in the region between the 2j+ and 1^ peaks in fig. 1(a) is attributed to elastic scattering from isotopes of Ba; their effect on the determination of P is negligible.

3.3 DETERMINATION OF SAFE BOMBARDING ENERGIES It is essential for the valid application of Coulomb-excitation theory that the data analysed should be obtained at bombarding energies sufficiently low for

Coulomb-nuclear interference to be negligible44). In the present work the maximum safe bombarding energy was determined for each experimental configuration by

a unc on plotting the ratio Pexp/Pcoui ^ f ti of s, the distance of closest approach of the nuclear surfaces, defined by the expression

0.72 ZiZ2 An x 1 3 s(6 ) = 1 + — [l+cosec(*9 )] -l.25(.kx l* + A2 / )fm, J cm. cm. A2 where Zj,Aj and Zj^ are the atomic numbers and masses of projectile and target,

respectively, 9C m is the scattering angle in the centre-of-mass system, E is the laboratory bombarding energy in MeV, and the nuclear radius is taken to be 1.25 A1/3

fm. The quantity PCoul is the excitation probability calculated, assuming a pure

Cculomb interaction, with the de Boer-Winther multiple Coulomb-excit?tion code45).

The resulting plots are shown in figs. 3-5. In calculating PCou, it was assumed

+ f + that Q(2j ) and B(E2;0j -»21 ) have the values obtained in the present work. For

rom a each experimental configuration, the deviation of Pexp/Pcoui ^ constant value

(unity for the particular nuclear parameters used in calculating PCoul) indicates the onset of Coulomb-nuclear interference as the bombarding energy is increased. The maximum bombarding energies deemed to be safe are indicated by arrows in figs.3-5. Data obtained at energies greater than the maximum safe energy were not used in the

+ + + determination of Q(2j ) and B(E2;01 -»21 ). 7

3.4 MATRIX ELEMENTS USED IN ANALYSIS Energy levels included in the multiple-Coulomb-excitation analysis are identified in table 3. Other levels were found, using available experimental information, to make negligible contribution (<0.1%) to the Coulomb excitation of the 2 j+ state. Values adopted from the literature for the relevant matrix elements are listed in table 4.

It is usually found31,32) in the analysis of reorientation-effect experiments for the determination of Q(2j+) that interference effects from higher states are dominated by

+ + the contribution of the 22 state, which depends on the product P3(22 ) =

+ + (Of I M(E2) I 22 > {If1 M(E2) I 22 > (0^ I M(E2) 12^). Since the signs of the matrix elements are usually not known, an ambiguity arises in the value of the extracted quadrupole moment In this context it is convenient to consider the product

+ + + P4(22 ) = <2! 1 M(E2) 121+) P3(22 ), the sign of which is independent of the phase convention used in the definition of the reduced matrix elements. For Q(2j+) > 0, a

+ positive (negative) value of P4(22 ) corresponds to constructive (destructive)

+ interference. Most nuclear models predict tiiat P4(22 ) is negative for nuclei in the transition region (see, for examples, refs.52"54). However, there is strong

48,55,56 + 194 + experimental evidence ) that P4(22 ) is positive for Pt The 22 interference contribution is negligible for 196Pt because of the very small experimental upper limit on (Of1 M(E2) 122+) (table 4), and so the usual ambiguity does not arise.

+ For the nuclei studied in the present work, interference effects involving the 4t state were found to be unusually significant The relevant matrix element product is

+ + + + P3(4t ) -,. (O^ I M(E4) I 4j ) <2j I M(E2) 14, > (0^ I M(E2) I If), the sign of which is independent of phase conventions because alternative definitions of

(0j+1 M(E4) 14j*) differ only be the factor i4. It has been shown experimentally57)

that ?$(4f) is negative for iHi96,i98pt This resuit js adopted for the present

+ analysis, although the effects of assuming P3(4j )>0 are also given. Interference

+ + effects due to states other than 22 and 4j are relatively minor, and uncertainties arising from associated sign ambiguities are incorporated into the uncertainties quoted 8

+ for 0(2^) and B(E2K)1*-»21 ).

+ + + 3.5 DETERMINATION OF Q(2j ) AND B(E2;01 ^21 ) For each nucleus, values of the excitation probability were calculated using the de

+ + + Boer-Winther program, and values of Q(2j ) and B(E2;01 ->21 ) were variea to obtain the best fit to all the data obtained at safe bombarding energies. Small corrections were applied for the effects of electron screening58), vacuum polarisation59), nuclear polarisation60), and use of the semiclassical approximation, i.e. the quantal correction61). In addition, a correction for the effects of the giant-dipole resonance (GDR) was applied assuming that k = 1.0 ± 0.5, where the parameter k represents the effect of virtual excitation of states in the GDR relative to

that calculated from the hydrodynamic model [for a detailed discussion, see ref. 37)]. The net c^ect of these corrections and of corrections for the effects of target thickness

was to increase Q(2j+) by amounts ranging from 0.01 eb for 198Pt to 0.03 eb for

196 + + 2 2 196 2 2 Pt, and to increase B(E2;01 -»21 ) by from 0.001 e b for Pt to 0.003 e b for

194Pt Relativistic corrections were not applied; however, a recent calculation62), as yet unverified by experiment, suggests that effects on Q(2j+) values would be

+ + negligible, although B(E2;01 ->21 ) values could be reduced by as much as 0.03 e2b2.

+ + + + The results obtained for Q(2j ) and B(E2;01 -»21 ), assuming P4(22 )>0 (as

194 + found experimentally for Pt) and P3(4j )<0 (as found experimentally for all three nuclei) are shown in table 5. Changes which would result from the alternative choices

+ for the signs of P^*) and P3(4j ) are given in table 6. It should be noted that in

30 196 + our earlier report ) on this work for Pt, the option P3(4j )>0 was preferred

because we were not awa/e at that time of experimental evidence to the contrary57).

+ Also, the value contained in that paper for P3(41 )<0 differs slightly from the value

given in table 5 because we are now using an improved value for <0j+1 M(E4) 14j+), obtained by analysing more data than previously. The uncertainties quoted in table 5 include, in addition to statistical uncertainties and uncertainties in spectrum analysis, 9 the effects of uncertainties in the beam energy, the scattering angles, the higher-state matrix elements, and the GDR correction. In order to visualize the influence of each set of data on the determination of

+ + + Q(2j ) and B(E2;01 -*21 ), an approximate expression for the excitation probability P of the form P = fB^O^VMl +pQ(2,+)] is useful. The quantities f and p (the sensitivity parameter) are functions of experimental parameters (energy, angle, etc.) and are calculated from the de

^oer-Winther program. Fig. 6 shows plots of Pexp/f as a function of p. The fits to the data are represented by straight lines with intercepts on the vertical axis equal to

+ + + + + B(E2;01 -^21 ) and slopes of B(E2;01 -»21 ).Q(21 ).

4. Comparison with previous work

+ + 4.1 VALUES OF B(E2;01 ->21 )

+ + 63 Values of B(E2;01 -»21 ) compiled from previous work by Ramaniah et al. ) are plotted in fig.7, together with those of the present work, which are the most precise yet published. It appears that, prior to the present work, the best determined

+ + 194 value of B(E2;01 ->21 ) was that for Pt The weighted mean of the most precise previous values for that nucleus, i.e. the Coulomb-excitation results of refs.6,43,64), is 1.640 ± 0.008 eV, which is in reasonable agreement with the present value of 1.659 ±0.011 eV.

+ 4.2 VALUES OF Q(2X ) The present results for Q(2j+) are compared with those of previous work in table 7. The value of Grodzins et al.65) was obtained using the reorientation precession technique; however, the large experimental uncertainy reduces its usefulness. The results of Glenn et al.6) were obtained at Pittsburgh using Coulomb excitation by 42-MeV 160 ions (and also 6-MeV protons for 194Pt) and detecting scattered particles 10 with an Enge split-pole spectrograph. Their analysis ignored possible E4 matrix elements of higher states, and in the case of 198Pt contributions from higher states were not considered at all. The subsequent work of Chen et al.26), also at Pittsburgh, was undertaken because of concern that the relatively low enrichment of the targets used might have produced errors in the analysis of the earlier experiments. Their value

+ 194 16 of Q(21 ) for Pt was obtained by scattering 53-MeV 0 ions from more highly enriched 194Pt targets, measuring Coulomb excitation probabilities with an Enge spectrograph, and analysing the results with the assumption that B(E2;0j+—>2j+) =

1.620 e^b2, as determined from 4He scattering data by Baktash et al.43). As discussed in Sect 1 above, the concern about the effects of relatively low target enrichment also raises doubts about the earlier results of Glenn et al. for 196Pt and 198Pt

+ 194 The present value of Q(2X ) for Pt disagrees with that of Chen et al.

Although the 160 particle spectra of those authors are of excellent quality, that is not the only prerequisite for obtaining reliable results from Coulomb excitation experiments. For example, the precise determination of scattering angles becomes very important for 0 90°. Furthermore, the result obtained by Chen et al. is very

+ sensitive to their choice of B(E2;01+-»21 ).

The results obtained at Rochester by Cline and his collaborators7) using Coulomb excitation by 58Ni beams and detecting de-excitation y-rays have not been included in table 7. This is partly because they have apparently never been published, and partly because Wu and Cline66) have recently performed a more sophisticated analysis of the

194Pt data, which changed their result for 194Pt from 0.63 ± 0.06 eb to 0.45 ±0.08 eb. Presu-nably this means that the Rochester data for 196Pt and 198Pt should also be re-analysed. It seems prudent to suspend judgement on the Rochester data until their analysis is complete and the results published.

In summary, die present work has substantially clarified the situation concerning the values of Q(2j+) for 194Pt, 196Pt and 198Pt In particular, they are not consistent with zero. The positive values obtained show that the prolate-oblate transition occurs in the regiono f mass 192. Furthermore, the value obtained for 194Pt is only about one 11

standard deviation larger than the value 0.25 ± 0.17 eb stated by Chen et al.26) to be

the result obtained from muonic X-ray work by Hoehn et al.29) (the latter report docs not give any numbers). Thus, as far as can be ascertained from available publications, there seems to be no significant disagreement between Coulomb excitation and muonic X-ray results for platinum.

5. Discussion of results 5.1 SYSTEMATICS OF 0.(2^) VALUES IN THE A = 192 TRANSITION REGION

The variation of Q(2j+) as a function of mass in die transition region near A = 192 is shown in fig. 8. The values plotted are obtained from experiments involving the reorientation effect in Coulomb excitation, except for seme from muonic X-ray

work (MXR). The data are from unpublished Rochester work67), but they are the only tungsten data known to us. The Coulomb-excitation data for osmium are

from the same Rochester work, except for a recent result from Pittsburgh for 1920s

[ref. 26)]. Also shown are the MXR results for osmium reported by Hoehn °t al.28).

The value plotted for 192Pt is also from unpublished Rochester work7). The results

194 196 198 + for Pt, Pt and Pt are from the present work, assuming P4(22 )>0 and

+ 194 26 P3(41 )<0. In addition, the MXR result reported for Pt in rcf. ) is shown. The

data for mercury are ANU results8"10), as also are those for [ref.68)]. The values

198 200 202 + plotted for Hg, Hg and Hg assume that P4(22 )

The MXR result obained by Hahn et al.69) for 198Hg is also included.

Perusal of fig.8 prompts the following comments: (i) The prolate-oblate

transition near A = 192 is strikingly evident, as also is the rapid decrease in Q(2j+) a* shell closure is approached near A = 208. (ii) There is a clear need for a new

measurement for 192Pt, particularly in view of the discussion of the unpublished 12

Rochester work in Section 4.2 above. Similarly, there is a need for confirmation of the reported results for the isotopes of tungsten, (iii) There is a tendency, noted by

Baktash et al.70), for the results of muonic X-ray experiments on nuclei in this region to produce values of Q(2j+) more negative than those obtained from reorientation effect experiments. However, the differences between the results from the two techniques are barely significant, and do not in themselves provide substantial support far the suggestion70) that the analyses of existing MXR experiments may have taken inadequate account of possible axial asymmetries in nuclear charge distributions.

5.2 COMPARISON WITH MODEL PREDICTIONS There now exists a very large amount of experimental information on the spectroscopic properties of nuclei in the A = 192 transition region. A thorough comparison of this information with the predictions of the many nuclear models which have been applied in the region is beyond the scope of the present paper. Instead, discussion will be largely concentrated on the significance of the results obtained in this work. This is not as restrictive as might at first appear. For example, the value of

Q(2j+) provides a sensitive test of nuclear models in that it depends on the wave function of a single state (and the lowest excited state at that), and consequently is less subject to ^nbiguity of interpretation than are many other spectroscopic quantities which involve the wave functions of more than one state. If a model of collective behaviour is unable to account for the value of Q(2j+) it can hardly be said to have correctly predicted the state vector of the first excited state. We shall try to isolate, at least partially, those predictions which are intrinsic to a particular model from those which depend on the particular parameters chosen for the

model. A simple example is the ratio Rj = Q(2j*)/VB(E2;0, +->2X+), which the axially-symmetric rigid-rotational model predicts to equal 0.906, regardless of the values chosen for the two parameters of that model (the intrinsic quadrupole moment

and the moment of inertia). This may be compared to the values for I94,i96,i98pt obtained in the present work, which lie in the range 0.3 - 0.6. 13

Most models do not make absolute predictions of Rj, the 0(6) and SU(3) limits of the IBM being interesting exceptions, but absolute predictions can be obtained from

some if Rl is considered in conjunction with another nuclear property. There is some freedom in choosing this other quantity, but, adopting the attitude implied above that collective models should, in the first instance, be judged by their ability to predict the properties of the lowest excited states of collective nuclei, we choose to use the ratio

+ + + + 1/2 Rj = [B(E2;01 ->22 )/B(E2;01 -»21 )] . Figs. 9(a) - 9(c) are plots of Rj against Rj for the three nuclei I94.i96,i98p^ showing the experimental values (obtained from tables 4 and 5) and various theoretical predictions.

As mentioned above, the axially-symmetric rigid-rotational model (RF) predicts

Rj = 0.906; we take it to predict R2 = 0 since there is no 22+ state in this model. All three dynamical symmetries of the IBM predict Rj = 0. For the 0(6) limit, Rj is also

zero71). The SU(3) limit predicts72)

RL = y (4N+3) /2TT/(10N2+15N) ,

where N is the total number of bosons. Since the U(5) limit makes no prediction of Rj

[ref.73)], it is not plotted in fig.9. The curves in fig.9 show the predictions of those models in which Rj versus Rj may be parameterized by a single quantity. For the asymmetric rotor model (ARM), this quantity is the asymmetry angle y, which runs from 30° at the origin to 60° at the

axially symmetric value74). The curve marked CQ shows the predictions of a

simplification of the IBM known as the consistent-Q formalism75). The parameter in this case is the ratio x of the coefficients of the two terms of the quadrupole operator; X varies from zero at the origin or 0(6) limit to V35/2 at the SU(3) limit, and intermediate values of % correspond to mixing of the two limits. It is emphasized that the consistent-Q formalism represents just one path through the IBM parameter space,

albeit one which has been held to be broadly appropriate in this mass region75). The

rotation-vibration model20) (RVM) considers harmonic vibrations in both the (3 and y 14 directions about an axially symmetric equilibrium. The ratios Rj and R2 are given by two parameters; the ratios EJe and E /e of the quanta cf P and y vibrations, respectively, to the characteristic rotational energy e. The curves in fig.9 show the variation with E le, \ \ich runs from infinity at the maximum value of Rj toward zero as Rj decreases. F01 hose marked RVM-1, EJe = 90, corresponding to almost complete absence of P vibrations. To obtain the curves marked RVM-2, values of

EJe were chosen which placed the P bandhead at known excited 0+ states, the 1479.3 keV, 1402.7 keV and 1481.5 keV states of 194,196,198^ respectively, being chosen as the most likely candidates. Parts of the RVM curves are shown dashed to reflect

uncertainties of interpolation in the tables of ref.20).

Also shown in fig.9 are predictions of Rj and Rj from various more complex models. We have only shown results of those calculations for which either the relevant matrix elements have been published or sufficient information is available to

enable the required matrix elements to be calculated. For example, refs.14,76) do not

+ 77 quote values of Q(21 ), but these have been calculated using PHINT ) and the

published parameters. The values shown for refs.78,79) do not appear in these papers,

but are quoted in ref.70). The only published calculations for 198Pt are those

performed with the boson-expansion theory16,17) (BET). We have extended the

IBM-1 calculations14,76) to this nucleus using the systematics recommended in the respective papers. We have similarly extended the IBM-2 calculations of Bijker et

al.81) using the computer program NPBOS82).

For the quantities considered in fig.9, the models seem to do best for 194Pt. All have increasing difficulty as neutrons are added. Although each of the more complex models contains degrees of freedom not present in the simple models, these extra degrees of freedom do not always improve the fit to the data. For example, adding a

variable moment of inertia to the ARM [ref.79)] has no perceptible effect on the

relationship between R{ and R^ whereas adding a «iatic hexadecupole

deformation57,80) produces a change in the direction required by the data. A similar change can be obtained by abandoning the requirement that the vibrations be 15 harmonic24), although die generalized collective model (GCM) of ref.24) is so complex that it is difficult to pick any one of the additional degrees of freedom as being an important one.

Baktash et al.70) concluded from an extensive discussion of the electromagnetic properties of heavy transitional nuclei that the general experimental trends are best reproduced by the microscopic pairing-plus-quadrupole model (PPQ) of Kumar and

Baranger1,2) and the boson-expansion theory (BET) of Weeks and Tamura16,17).

While the PPQ gives satisfactory values of Rj and R2 for 194Pt, it performs poorly for

196PL The BET generally gets 1^ about right, but not R^

Generally the IBM-2 [ref.81)] predicts larger values of Rj than does the IBM-1

[refs.14-76)], but, for 194-*96Pt, still not as large as those observed. Thus, the

expectation expressed by Casten83) and others that the application of the EBM-2 would

rectify the failure of the IBM-1 to account for the Q(2j+) values of the Pt isotopes is at best only partially fulfilled. It is clear that the consistent-Q formalism is not

appropriate for I96,i98pt at least

Our result for Q(2j+) for 196Pt is of particular interest because this nucleus has

been proposed as an excellent empirical manifestation13) of the 0(6) limit of the IBM.

The non-zero value obtained for Q(2j+) is certainly inconsistent with the requirement

of the unperturbed 0(6) limit It is conceivable that, as suggested by Bolotin et al.25),

a small admixture of SU(3) to 0(6) might reproduce the observed value of Q(2j+)

simultaneously with other properties of the low-lying states of 196Pt. How* :er, we have been unable to reproduce the numerical results of Bolotin et al, with the program

PHINT77) and their published parameters. Furthermore, all of our attempts to fit Rj and R2 with some coronation of the 0(6) and SU(3) limits have failed; when we

T choose parameters to fit .v we obtain values of Rj which are much too large.

6. Conclusion

Static electric quadrupole moments of the 2,+ states of 194,196,198Pt have been 16 determined using Coulomb excitation by 4He, 12C and 160 projectiles. All known corrections were applied in the analysis; in particular, it was found that B(E4;0j+—>4j+) values are large enough to produce significant interference effects. The quadrupole moments of all three nuclei were found to be positive, thus locating the prolate-to-oblate transition at or near A = 192. Comparison with the predictions of various well-known nuclear models shows that all have difficulty in describing the systematics of the E2 properties of the first two excited states of these nuclei. Within this restricted compass, none of these three nuclei, including 196Pt, appears to be a good example of the 0(6) symmetry of the IBM. The authors are grateful to F. Todd Baker for drawing to their attention the

+ experimental evidence that P3(41 ) < 0 for the even-mass Pt nuclei.

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32. O. Hausser, in Nuclear spectroscopy and reactions, ed. J. Cerny, pan C (Academic Press, New York, 1974) p.55 33. J. de Boer, in Treatise on heavy-ion science, ed. D.A. Bromley, vol.1 (Plenum Press, New York, 1984x p.293 34 MX Esat, D.C. Kean, R.H. Spear and A.M. Baxter, Nucl. Phys. A274 (1976) 237 35. M.P. Fewell, A.M. Baxter, D.C. Kean, R.H. Spear and T.H. Zabel, Nucl. Phys. A321 (1979) 457 36. R.H. Spear and M.P. Fewell, Aust J. Phys. 33 (1980) 509 37. W.J. Vermeer, A.M. Baxter, S.M. Burnett, M.T. Esat, M.P. Fewell and R.H. Spear, Aust. J. Phys. 37 (1984) 273 38. R.H. Spear, D.C. Kean, M.T. Esat, A.M.R. Joye and M.P. Fewell, Nucl. Instr. 147 (1977) 455 39. T.R. Ophel and A. Johnston, Nucl. Instr. 157 (1978) 461 40. S. Baker and R.D. Cousins, Nucl. Instr. 221 (1984) 437 41. J.A. Kuehner, R.H. Spear, W.J. Vermeer, M.T. Esat and A.M. Baxter, Nucl. Instr. 200 (1982) 587 42. B. Harmatz, Nucl. Data Sheets 23 (1978) 607 43. C. Baktash, J.X. Saladin, J.J. O'Brien and J.G. Alessi, Phys. Rev. C18 (1978) 131 44. R.H. Spear, T.H. Zabel, D.C. Kean, A.M.R. Joye, A.M. Baxter, M.P. Fewell and S. Hinds, Phys. Lett. 76B (1978) 559 45. A. Winther and J. de Boer, A computer program for multiple Coulomb excitation, reprinted in K. Alder and A. Winther, Coulomb excitation (Academic Press, New York, 1966) p.303 46. B. Harmatz, Nucl. Data Sheets 22 (1977) 433 47. J.A. Cizewski, R.F. Casten, G.J. Smith, M.R. Macphail, M.L. Stelts, W.R. Kane, H.G. Borner and W.F. Davidson, Nucl. Phys. A323 (1979) 349 19

48. P.T. Deason, C.H. King, R.M. Ronningen, T.L. Khoo, F.M. Bemthal and J.A. Nolen, Phys. Rev. C23 (1981) 1414 49. R.L. Auble, Nucl. Data Sheets 40 (1983) 301 50. I. Berkes, R. Rougny, M. Meyer-L6vy, R. CheVy, J. Daniere, G. Lhersonneau and A. Troncy, Phys. Rev. C6 (1972) 1098 51. M.P. Fewell, G.J. Gyapong, R.H. Spear, M.T. Esat, A.M. Baxter and S.M. Burnett (to be published) 52. T. Tamura, Phys. Lett 28B (1968) 90 53. K. Kumar, Phys. Lett. 29B (1969) 25 54. V.I. Isakov and I.K. Lemberg, JETP Lett. 9 (1969) 438 55. F.T. Baker, A. Scott, T.H. Kruse, W. Hartwig, E. Ventura and W. Savin, Phys. Rev. Lett 37 (1976) 193 56. L. Hasselgren, C. Fahlander, J.E. Thun, A. Bockisch and F.J. Bergmeister, Phys. Lett 83B (1979) 169 57. F.T. Baker, Phys. Rev. Lett 43 (1979) 195 58. J.X. Saladin, J.E. Glenn and RJ. Pryor, Phys. Rev. 186 (1969) 1241 59. K. Alder and A. Winther, Electromagnetic excitation (North Holland, Amsterdam, 1975) 60. R. Beck and M. Kleber, Z. Phys. 246 (1971) 383 61. K. Alder, F. Roesel and R. Morf, Nucl. Phys. A186 (1972) 449 62. M.P. Fewell, Nucl. Phys. A425 (1985) 373 63. K.V. Ramaniah, T.W. Elze and J. Gerl, Institut fur Kernphysik Frankfurt, Internal Report KF-IBol (1983) 64. R.M. Ronningeu, R.B. Piercey, A.V. Ramayya, J.H. Hamilton, S. Raman, ?.H. Stelson and W.K. Dagenhart, Phys. Rev. C16 (1977) 571 65. L. Grodzins, B. Herskind, D.R.S. Somayajulu and B. Skaali, Phys. Rev. Lett. 30(1973)453 66. C.Y. Wu and D. Cline, University of Rochester Nuclear Structure Research Laboratory, Biennial Report (1982-1983) p. 192 20

67. P. Russo, J.K. Sprinkle, D. Cline, P.B. Void and R.P. Scharenberg, University of Rochester Nuclear Structure Research Laboratory, Annual Report (1978) p.79 68. A.M.R. Joye, A.M. Baxter, S. Hinds, D.C. Kean and R.H. Spear, Phys. Lett. 72B (1978) 307 69. A.A. Hahn, J.P. Miller, R.J. Powers, A. Zehnder, A.M. Rushton, R.W. Welsh, A.R. Kunselman and P. Roberson, Nucl. Phys. A314 (1979) 361 70. C. Baktash, J.X. Saladin, JJ. O'Brien and J.G. Alessi, Phys. Rev. C22 (1980) 2383 71. A. Arima and F. Iachello, Ann. Phys. (N.Y.) 123 (1979) 468 72. A. Arima and F. Iachello, Ann. Phys. (N.Y.) Ill (1978) 201 73. A. Arima and F. Iachello, Ann. Phys. (N.Y.) 99 (1976) 253 74. A.S. Davydov and G.F. Filipov, Nucl. Phys. 8 (1958) 237 75. D.D. Warner and R.F. Casten, Phys. Rev. C28 (1983) 1798 76. H.C. Chiang, S.T. Hsieh, M.M.K. Yen and C.S. Han, Nucl. Phys. A435 (1985) 54 77. O. Scholten, computer program PHINT, Michigan State University, East Lansing, MI (1982) 78. R. Sedlmayer, M. Sedlmayer and W. Greiner, Nucl. Phys. A232 (1974) 465 79. F. Toki and A. Faessler, Z. Phys. A276 (1976) 35 80. F.T. Baker, Nucl. Phys. A331 (1979) 39 81. R. Bijker, A.E.L. Dieperink, O. Scholten and R. Spanhoff, Nucl. Phys. A344 (1980) 207 82. T. Otsuka and O. Scholten, computer program NPBOS, Michigan State University, East Lansing, MI (1982) 83. R.F. Casten, in Contemporary research topics in Nuclear Physics, ed. D.H. Feng, M. Vallieres, M.W. Guidry and L.L. Riedinger (Plenum Press, New York, 1982) p.369 21

TABLE 1 Percentage compositions of Pt target materials as provided by the supplier (Oak Ridge National Laboratory)

Target (i.e . major ]I

196 196 194R 198ft Isotope Pt(l) Pt(2)

192ft 0.04 (1) <0.01 <0.05 0.01 (1)

194Pt 95.06 (15) 0.63 (1) 0.78 (2) 0.79 (1) IMpt 3.78 (10) 1.57 (2) 2.39 (5) 1.18(1)

196Pt 0.97 (5) 97.51 (3) 96.54(5) 2.18(2) IMpt 0.17 (2) 0.29 (1) 0.29 (2) 95.83 (5)

Targets of 196Pt were prepared using two different isotopically enriched samples. 22

TABLE 2

Measured excitation probabilities P for the 2X+ states

of 194,196,198^

P xl()2 Target Projectile 0lab E(MeV) exp

194Pt 4He 174.8° 14.199 1.887 (16) 14.399 1.944 (17) 14.599 2.022 (17) 14.799 2.185 (19) 14.999 2.230 (19) 15.199 2.363 (21) 15.599 2.532 (22)

194Pt 12C 174.8° 40.999 11.95 (ID 41.999 12.97 (10) 42.999 13.97 (14) 43.999 14.94 (13) 44.999 15.86 (10) 45.999 17.07 (11) 47.999 19.41 (19) 49.999 21.59 (22) 40.999 11.54 (15) 41.999 12.77 (12) 42.999 13.99 (14) 43.999 14.99 (15) 44.999 16.07 (14)

194Pt 160 174.8e 54.998 19.03 (28) 55.998 20.27 (28) 56.998 21.58 (29) 57.998 22.39 (44) 58.998 23.87 (41) 59.998 25.00 (37) 60.998 25.22 (41) 62.998 27.69 (44) 196Pt 4He 90.0° 16.799 0.905 (8) 16.999 0.927 (8) 17.399 0.995 (9) 17.799 1.056 (10) 17.998 M53 (21) 18.199 1.154 (10) 18.599 1.202 (12) 196Pt 4He 174.8° 14.199 1.156 (13) 14.399 1.582 (13) 14.599 1.669 (14) 14.799 1.781 (15) 14.999 1.840 (16) 15.199 1.894 (16) 15.399 2.000 (17) 15.599 2.099 (18) 23 TABLE 2 (continued) 196Pt 12C 174.8° 40.985 9.75 (12) 41.986 10.57 (12) 42.987 11.42 (13) 43.988 12.36 (13) 44.989 13.22 (14) 45.990 14.32 (14) 46.991 15.37 (14) 47.991 16.22 (14) 48.992 17.25 (15) 49.992 18.15 (15) 51.993 19.86 (16) 53.995 20.66 (17) 55.996 19.72 (21) 40.997 9.70 (10) 41.997 10.58 (10) 42.997 11.49 (11) 43.998 12.36 (10)

196pt 16Q 174>8O 54.993 15.75 (25) 55.993 16.69 (28) 56.994 17.93 (25) 57.994 18.55 (28) 58.994 20.27 (22) 59.994 20.60 (28) 60.994 22.18 (29)

198Pt 4He 174.8° 13.999 1.059 (11) 14.199 1.112 (12) 14.399 1.167 (16) 14.599 1.209 (15) 14.799 1.289 (13) 14.999 1.326 (11) 15.199 1.415 (13) 15.399 1.488 (13) 15.599 1.547 (17) 198pt 12c _gc 174 40.998 7.10 (7) 41.998 7.86 (7) 42.998 8.48 (8) 43.998 9.19 (8) 44.998 9.95 (9) 45.998 10.63 (11) 47.998 12.33 (13) 49.998 13.72 (i:) 40.998 7.22 (9) 41.998 7.88 (7) 42.998 8.47 (11)

198Pt 160 174.8° 56.997 13.55 (18) 57.998 14.41 (17) 58.998 15.07 (18) 59.998 15.87 (19) 60.998 16.67 (21) 61.998 18.00 (22) 62.998 18.33 (22) 24

TABLE 3

Excitation energies (Ex) and spin-parity values (J^) of energy levels included in multiple-Coulomb-excitation analysis

Nucleus Reference Ex(keV) Jn»

194ft 46^ 0 o,+ 328.5 V 622.0 V 811.3 V 1229.6 V

196pt 47^ 0 0i+ 355.7 V 688.7 V 876.9 V 1135.3 + o2 1293.3 V

198^ 48,49) 0 o,+ 407.4 V 774.2 V 914.4 + o2 985 4i+ 1287 V 25

TABLE 4 Magnitudes of matrix elements included in multiple-Coulomb-excitation analysis

Matrix Element 194pt 196pt 198pt

(O^IM^IV) 0.090 (2) < 0.002 0.039 (7) (O^lMO^jilV) 0.23 (8) 0.18 (7) 0.09 (9)

+ (01HlM(E4]l|42 > 0.13 (3) <0.14 <0.2

+ 1.455 (25) 1.30 (4) 1.02 (5) <21HlM(E2)j|22 >

+ + (21 ilM(E2)l|41 > 2.17 (2) 1.94 (2) 1.56 (7)

+ (21HlM(E2)||02 > 0.15 (3) 0.44 (6)

+ (21^M(E2)||42 > 0.30 (7) 0.164 (27) (ZjlMfrljlOf) 0.38 (10)

+ 2.5 (7) 1.26 (13) <22HlM(E2)||42 >

+ <4^|M(E2)||42 > 1.32 (33)

M(E2) matrix elements are given in units eb and M(E4) matrix elements in units eb2. The values are taken from refs.25'26'43-48-50-51). 26

TABLE 5

+ + + Results obtained for Q(21 ) and B(E2;01 -»21 )

+ assuming P^+X) and P3(4j )<0

+ + Q(21+) B(E2;01 -»21 ) (eb) (eV)

194Pt 0.48 (14) 1.661 (11)

196Pt 0.66 (12) 1.382 (6)

198Pt 0.42 (12) 1.090 (7) 27

TABLE 6

Changes which would be produced in the present results for Q(2j+) and

+ + + + B(E2;01 -»21 ) if the alternative signs were adopted for P4(22 ) and P3(4j )

+ ifP4(22 )<0 ifP3(V)>0

AQ(2,+) AB(E2) AQ(2,+) AB(E2) nucleus (eb) (eV) (eb) (e2b2)

194Pt +0.36 -0.001 +0.10 +0.001

196Pt 0 0 +0.09 -0.001

198Pt +0.12 0 +0.03 0 28

TABLE 7

+ 194 196 198 Published results for Q(21 ) (in eb) for Pt, Pt and Pt,

+ + assuming P4(22 )>0 and P3(4j )<0 where appropriate.

Authors 194Pt 196Pt 198Pt

Glenn et al.6) 0.64 (16) 0.51 (18) 1.22 (50)

Grodzins et al.65) 0.77 (50)

Chenetal.26) 0.13 (17) Present work 0.48 (14) 0.66 (12) 0.42 (12) 29

FIGURE CAPTIONS

Fig. 1. Representative spectra obtained with an annular counter. In each case the full curve shows a fit to the data obtained as described in the text, and the broken curve shows the calculated contribution due to scattering from Pt isotopes other than the primary isotope in the target Peaks corresponding to excited states in the target nucleus are indicated by J^ values. Pulse pile-up effects are evident on the high-energy side of the 0j+ peak in (a).

Fig. 2. Typical spectrum obtained using an Enge split-pole magnetic spectrometer. The full and broken curves are as for fig.l.

Fig. 3. Safe-energy plots for 194Pt.

Fig. 4. Safe-energy plots for 196Pt.

Fig. 5. Safe-energy plots for 198Pt.

Fig. 6. Plots of Pexp/f against the sensitivity parameter p. In each case it is assumed

+ + that P4(22 ) > 0 and P3(4j ) < 0. For simplicity of presentation, each data point shows the average of results obtained at all safe energies for the target-projectile-angle combination concerned.

+ + Fig. 7. Summary of experimental values of B(E2;01 -»21 ) taken from the compilation of ref.63). Coulomb-excitation data are shown by circles, and other data by crosses. The results indicated by G, R, B and P are due to Glenn et al.6), Ronningen et ai.64), Baktash et al.43) and the present work, respectively. 30

+ Fig. 8. Quadrupole moments of the first excited states, Q(21 ), of even-mass nucleiin the transition region near A = 192. The data are taken from experiments involving the reorientation effect in Coulomb excitation, except for those from muonic X-ray work

198 + (MXR). The value shown for Pt for the present wonc assumes P4(22 ) > 0; the

+ alternative assumption, that ¥A(2£) < 0, would increase Q(2j ) by 0.12 eb and would not change the overall picture significantly. As noted in the text, refs. 7,67> are to unpublished work.

F;g. 9. Comparison between experiment and theoretical predictions for the relationship

+ + + between the quantities Rj and Rj, where Rj = Q(21 )/VB(E2;01 ->21 ) and Rj =

+ + + + 1/2 [B(E2;01 -»22 )/B(E2;01 -»21 )] . References are indicated by the numbers in square brackets. The key to the less than obvious model acronyms is as follows: RR-axially symmetric rigid rotator; PPQ - pairing-plus-quadrupole; GCM - generalised collective model; ARM - asymmetric rotor model; ARM + VMI - asymmetric rotor

model with variable moment of inertia; ARM + p"4 - asymmetric rotor model with static hexadecupole deformation; DCM - dynamic collective model; RVM - rotation vibration model; CQ - consistent-Q formalism. The experimental value shown for I98Pt assumes

+ + that P4(22 ) > 0; the alternative assumption,that P4(22 ) < 0,would increase Rj from 0.40 to 0.52 and would not affect the conclusions. 31

•PHI60

59.0 MeV

174.8°

10'

• »•

M»4MM*I CHANNEL

P"; V I 32

S1ND00

r » <\ . x 33

JT—|—i—i—i—i—| i i i i | E(MeV)

I. A 1.0 l94 4 Pt+ He t 174.8°

0.9 7 45 50 E(MeV) T r T 1 1 1 r

I94pt + I2c 1.0 i i i \ 174.8° t O O Q- 0.9 ^. CL 55 60 _,., wl X 71—i—i—i—i—|—i—i—r E(MeV) 4>

I94pt+I60 1.0 H 11111 I I 174.8° t 0.9 i l 6 5 4 s (fm)

Fi V 2. u 34

17 18 19 E(MeV) -t—i—|—i—i—i—i—[ i i i i | i c- \'»' c » /

96Pt 4He 00 + T 90.0°

0.90 |4i • • .'p. • . .'f E(MeV)

\ LOO I- hi'i.,, ,96 4 i Pt+ He t 174.8*

090>" , • «°. E(MeV)

1.00 f ,96 ,6 -{ j I t , 1 Pt + o o \ \ cf 0.95 t 174.8°

x 45 50 55 o 1 1 1 r T 1—| 1—i—i—l—|—r E (MeV) 0- 1.00- * I * I | M i i t

96 ,2 0.90 Pt • C 174.8°

0.80

6 5 s (fm)

t' V ^ 35

T 1—i 4? i—i . • 5|° E (MeV)

,98 l2 pt+ c 1.0 -I l * i i i I 174.8° t

°**55 60 T 1—i—i—|—i—i—r E(MeV)

I98pt + I6Q

1.0 I! 174.8° e o "<\ t * 0.9 •

,98Pt + 4He 11 1.0 L '.',.., 174.8° t

0.9 5 i s (fm) F.^.r 36

C (1748°)

66F J I I L J L 1 48h

.44h

-O

\ 1.40

QT

1.36

010

F't t 57

CHRONOLOGICAL ORDER OF PUBLICATION

FiY 7 38

1 ' r 1—r T~r HfrH Sg2 *<^ H Is- h- CD 00 "c

-*-

^OOOQ-CLQ-XXQ- >-*- "** - Ox + • < > • * * O

•s,N" 1

Kji N. ^ O (Ti

J L O cvi I (Q9) (JZ)0

KIP, . 3 6 * BET(I7) * PP0[I,2J o 6CM(24J • ARM*VMI[79] » DCM[78] ° IBM-2 JBl]

4 RR » SU(3)(72] • 0(6)[71] » ARM*£4f80l • IBM-I[I4] * ;BM-l[76] 0.4 —I 1 i 1 1 1 m 1 1 ^~i 1 1 rp 1 1 r (c) /\ .. 198 /

0.3 RVM-l(20> / RVM-I[20] flVM-2feO]

cc 0.2

/

/

0.1 -

EXPT

0 49- -0.2 0 0.2 0.4 0.6 0.8 0.2 0.4 0.8 -0.2 Q2 0.4 0.6 0.8 1.0

R.