Measured gyromagnetic ratios and the low-excitation spectroscopy of 197Au

Nuclear Physics A486 (1988) 374-396 North-Holland, Amsterdam

MEASURED THE

GYROMAGNETIC

LOW-EXCITATION A.E.

RATIOS

SPECTROSCOPY

AND OF 19’Au

STUCHBERY

Department of Nuclear Physics, Research School of Physical Sciences, Australian National University, PO Box 4, Canberra, ACT 2601, Australia L.D.

WOOD,

H.H.

BOLOTIN,

C.E. DORAN, 1. MORRISON, and G.J. LAMPARD

A.P.

BYRNE’

School of Physics, University of Melbourne, Parkville, Victoria 3052, Australia Received

13 April

1988

Transient-field precessions were measured for levels in 19’Au and ‘82.‘84*‘86W as their ions simultaneously traversed polarized Gd hosts. Gyromagnetic ratios were inferred for the positiveparity levels between, and including, the lowest 2’ and y states in 19’Au. Lifetimes of several levels were determined using the Doppler-broadened lineshape technique, and multipole mixing ratios of a number of transitions were deduced from measured particle-y-ray angular correlations. The measured static and dynamic electromagnetic moments are compared with the predictions of the weak-coupling core-excitation model and with those of the interacting boson-fermion model (IBFM), including its Spin(6) supersymmetry limit.

Abstract:

NUCLEAR REACTIONS ‘*2~‘s4~‘s6W(58Ni, ssNi’), ‘s4W(58Ni, “Ni’), ‘97Au(5sNi, “Ni’), E,, = 175,220 MeV; measured y( 0, H, T) in polarized Fe, Gd, (particle) y-coin., Coulomb excitation; deduced transient-field precessions WGd, Aug. 19’Au levels deduced g, T,,,, B(E2), B(M1). Thin-foil transient-field IMPAC technique. NUCLEAR STRUCTURE 19’Au calculated levels, g, B(Ml), excitation model, supersymmetry extensions of interacting

B(E2), weak-coupling coreboson-fermion model.

1. Introduction The spectroscopy of the low-excitation levels in 19’Au has attracted considerable interest over the past three decades, following the seminal expositive development of the weak-coupling core-excitation model by Lawson and Uretsky ‘), its later extension by de-Shalit ‘), and the seeming a priori appropriateness of the low-lying level structure of this odd-A nuclide to be accommodated in terms of this model. of 19’Au, that of Bolotin While a number of studies 3-7) have tested this description et al. ‘) provided the most extensive comparison evidence with the predictions of this model.

of the then available

’ Former National Research Fellow. Present address: Institut fiir Strahlen-und Bonn, Nussallee 14-16, D-5300 Bonn, Federal Republic Germany. 03759474/88/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

experimental

Kernphysik,

Universitiit

A.E. Stuchbery

More (IBFM)

recently,

with the development

and its supersymmetric

low-lying

positive-parity

et al. / 19’Au

375

of the interacting 8*9), interest

extensions

boson-fermion

has been refocused

levels in ‘97A~, as it has been suggested

model on the

‘o-11) that certain

experimental

data may point to the existence of a dynamical supersymmetry which links the properties of 19% and ‘97Au within a single theoretical framework. Both the weak-coupling and supersymmetry models are relatively simple, make

definite predictions for the level spectroscopies of appropriate to have been reasonably successful in describing properties

nuclides, and appear of certain levels and

selected B(E2) transition rates in 19’Au. As it is of considerable current interest to identify the appropriateness and limitations of supersymmetric descriptions of nuclei, and, as the Ml properties of nuclear levels provide particularly stringent tests of nuclear models, we report here our measurements of the magnetic moments and lifetimes of several positive-parity the y’ 1231-keV state and of the E2/Ml levels of ‘97Au up to and including multipolarity mixing ratios for a number of transitions. These experimental findings are compared, in the first instance, with the weak-coupling core-excitation model, subsequently with the IBFM in its spin(6) symmetric limit 9*‘o), and, finally, with an extensive interacting boson-fermion model calculation that allows of all relevant single-fermion orbits, which we describe here.

admixtures

During the course of the present measurements, a study by other authors of the g-factors of the lowest 2’ and 5’ states in ‘97Au was published 12) with which the present results are systematically at variance. The disparity between the present g-factor determinations of these same states and theirs has been discussed in a report 13) of the transient-field calibration aspects of the present work. Some aspects of the present measurements and nuclear structure findings were reported at the 1987 Melbourne Conference 14),

2. Experimental As there been

is no suitable

determined

(TF) strength or interpolation

precisely

excited

state in an isotope

and independently,

for Au in any ferromagnetic of the TF strength measured

The discontinuity

observed

design

between

of 79A~ whose

a calibration

g-factor

has

of the transient-field

host must rely upon the extrapolation for ions of neighbouring atomic number.

the measured

TF strengths

of 760s and 78Pt

ions traversing polarized Fe hosts with velocities -0.02~ has been discussed in earlier publications 15,16); as noted therein, the velocity dependence and magnitude of the TF strength for Au& are expected to follow that of PtFe - [with which the TF strengths of ,‘Ir and **Hg in Fe are also in accord 14*16)].In contrast with TF measurements using Fe hosts, no discontinuities in TF strength have been observed 12*17,1x) for heavy ions traversing Gd hosts. In terms of the molecular orbital (MO) model proposed 15,16) to explain the discontinuous TF behaviour observed for certain ions traversing polarized Fe, similar discontinuities might occur for

376

A. E. Stuchbery et al / “?‘Au

polarized Gd in those cases in which a ‘transient field active’ orbital of the moving ion (i.e., Is, 2s, 3s, 4s) matches the energy of the 3d orbital of the Gd host. For a polarized Gd medium, such crossings may be anticipated for ions with atomic numbers 2 - 11, 30, 54, and 88. Ions in the particular region of present interest, 74 < 2 < 80, are therefore well clear of possible MO-induced discontinuities. In a series of measurements 13,14)of which the present work is part, TF precessions were measured simultaneously for a number of excited states in 19’Au and one or as their ions traversed, in turn, both polarized Fe and Gd foils. more in 182*184*‘86W Simultaneous measurements such as these, in which the nucleus being studied (19’Au) and those used to calibrate the transient-meld strength (‘8z~‘84~~*6W) traverse the same polarized ferromagnetic foil, largely obviate possible sources of systematic error. In light of the discontinuous behaviour of the TF strength in this mass region for Fe hosts, the gyromagnetic ratios of levels in 19’Auwere inferred from precessions measured using polarized Gd hosts reported in detail here. Precession results 13.14) for AuFe, partly obtained during our study 19) of the g-factors of levels in rs6W, serve to characterize the TF behaviour of Au in Fe, or, provided a reliable calibration of the TF strength for Au& is used, corroborate the gyromagnetic ratios measured using the Gd hosts. 3. Experimental procedures As most aspects of the thin-foil transient-field experimental techniques used have been described in detail in earlier publications ‘9-22), present discussion is limited to particulars specific to the current measurements. Beams of “Ni at 17% and 220-MeV from the Australian National University 14UD Pelletron accelerator were used to Coulomb excite states of interest in 182,184,186~ and ‘97A~. In each run, four HPGe detectors were used to register de-excitation y-rays in coincidence with backscattered beam projectiles detected in a common annular silicon surface-barrier detector (146”-166”). Data were recorded in an event-by-event mode. The coincidence requirement restricted data acquisition to events associated with those W and Au ions which recoiled through the ferromagnetic foils within a forward cone of mean half-angle -8”. Beam energies, target layer thicknesses, and y-ray detector angles employed are summarized for the two bombardments in table 1. Target layer thicknesses were determined by areal-weight measurements and Rutherford scattering and energy-loss measurements using 3-MeV protons from the University of Melbourne 5U Pelletron accelerator. To provide mechanical support and improved thermal contact, the multilayered targets were pressed onto 15 pm thick Cu using an evaporated layer of In as adhesive. An electromagnet was used to apply a polarizing field of 0.07 T to the targets with Gd substrates. The Gd foils were carefully annealed prior to target preparation. TO minimize possible systematic errors, the direction of the polarizing field, applied normal to the reaction plane, was reversed at frequent intervals during the precession

A.E. Stuchbery et al. / 197A~ TABLE Experimental

particulars:

1

Beams, targets

and y-ray Target

Beam energy

175 220

Ge detector angles “)

*30°, *115” *30”, *65” *115”

Run no.

Label

I II

A B

311

detector

specifications

b,

W layer

AU Thickness

camp.

184w

1.9 (1) 2.2 (1)

““‘WO,

angles

Gd Thickness

thick. 0.42 (5) 0.54 (5)

4.4(1)d) 4.8 (1) ‘)

Backing Layer ‘)

Pb cu

“) Gamma-ray detector angles during precession measurements. “) Target layers evaporated; except ls4W which was sputtered. Thicknesses are in mg . cm-s. ‘) Backing is the non-magnetic layer in which recoiling ions come to rest. d, Cd foil rolled down from 25 pm foil supplied by Goodfellow Metals. ‘) Foil rolled from lumps of Cd metal. This target had a thin layer of Cu (0.13 mg . cmm2) evaporated on the upstream surface of the Gd foil (between layer II and Cd); see ref. ‘s).

measurements. A soft iron cone located between the target and annular detector shielded both the incident and backscattered beam ions from the fringing field of the polarizing magnet, rendering “beam-bending” effects negligible. Targets were cooled using liquid nitrogen. Typically, a target temperature of -90 K was maintained while beam was on target. Further aspects of the targets are discussed in ref. I’). Particle-y-ray angular correlations were measured for each bombardment, the most statistically precise data being taken using target B (table 1). During these measurements, the two backward-quadrant detectors were left at f 115” to serve as monitors while the forward detectors were placed pairwise, in turn, at the angles 30”, 45”, 55”, and 65” to the incident beam direction. To assess any off-set of the beam axis with respect to the optical zero-degree setting of the detector goniometer table, the detector normally in the positive quadrant was also moved to -25”. After

each measurement,

were determined

by placing

the HPGe 133Ba, “*Eu,

y-ray

detector

efficiencies

and “*Ta sources

and lineshapes

at the target position.

4. Analysis of data 4.1. TRANSIENT-FIELD

g-FACTOR

MEASUREMENTS

Procedures employed to extract g-factors from measured TF precessions, in which account is taken of the effects of cascade feeding and decay in flight corrections, have been outlined in several earlier publications *Oe2*).Although the measured g-factors 19,23,24)of the corresponding low-lying levels of the stable even 182*1847’86W isotopes are not the same, previous measurements 19,23*24)have established that the low-lying levels in the ground-band of any given one of these isotopes have identical

A.E. Stuchbery

378

g-factors target

within

experimental

was for the purpose

extract the separate strength

experienced

precessions

As the presence the TF strength,

to the observed

even W isotope

studied. directly

CORRELATIONS

AND

of these isotopes there

(fed) precessions

by W ions was inferred

[e.g., see ref. ““)I in each separate

4.2. ANGULAR

~~ltipole ray angular

uncertainties. of calibrating

contributions

gsb levels in any individual

et at. j ‘*?Au

Rather,

in the

was no need to of the individual

the time-integrated

from the observed

TF

cascade-fed

case.

MULTIPOLE

MIXING

RATIOS

mixing ratios were also inferred from the present measured particle-ycorrelations using procedures similar to those outlined in an earlier

work 26). Statistical tensors for direct population of levels in 19’Au were calculated for our geometry using a version of the Winther-de Boer code 27) which takes into account the finite dimensions of the annular particle detector and the energy loss of the beam in the target. To account for cascade feeding to the states of interest, the statistical tensors for direct population were appropriately combined using the measured transition intensities from higher excited states, which fed the states of interest, and loss-of-alignment coefficients ‘*). Apart from the 503-keV 5: level, calculated statistical tensors were not sensitive to uncertainties in the E2 matrix elements utilized in the W&her-de Boer code. In the case of the 503-keV level, the alignment depends rather sensitivity on the E2 strength connecting it with the first excited state It This strength is poorly defined experimentally, as it corresponds 21. to a weak gamma-ray branch of the order of a few percent. The resultant uncertainties in the calculated statistical tensors were included in the experimental error assigned to the mixing ratio determined Finite solid-angle attenuation

for the 503-keV transition. factors, Qkt were calculated

for the Ge detectors

using a method similar to that of Krane 29). To determine the mixing ratios for mixed multipole transitions, the angular correlation data were fitted to a standard Legendre polynomial expansion in which the dependence of the coefficients on the mixing ratio were included explicitly. Only the y-ray transition intensity and the mixing

ratio were varied

4.3. LEVEL

LIFETIMES

As a large number

in the fits.

FROM

DOPPLER-RROADENED

of events must be registered

LINESHAPES

in the full-energy

peak of a given

transition to obtain statistically meaningful results in transient field g-factor experiments, the Doppler-broadened lineshapes of these y-ray transitions de-exciting states of interest are always well defined in the course of these precession measurements. For the recoil ion velocity range typical of the present TF precession studies, the Doppler-broadened lineshape technique [ DBLS] 30) may be employed to extract the lifetimes of many of these levels having mean lives in the domain of -0.1 ps to -20 ps.

379

A. E. Stuehbery et al. / 197A~

At first sight, the main difficulties affecting DBLS analysis of lineshapes obtained in these studies might be expected to relate to complications and uncertainties associated with the multiple-layer composition of the targets employed. It is found, nevertheless, that the single greatest source of uncertainty arises from imprecise knowledge of the pertinent stopping powers. Yet, due to the unusually high statistical quality of the DBLS data obtained in the precession measurements, we are able to deduce an appropriate empirical stopping power parameterization using the extremely well defined lineshape of a transition de-exciting any given state whose mean life has already been determined to good precision using other techniques. A computer code has been developed to extract level lifetimes from Dopplerbroadened lineshapes recorded during transient field g-factor measurements, such as the present one, in which layered targets are employed. Cascade feeding, photon aberration, variations in detector efficiency, and nuclear scattering effects are taken into account. As the electronic stopping powers of Ziegler ‘I) which are used require extrapolation below -200 keV, the actual form of the low-energy electronic stopping power and the strength of the nuclear stopping power were determined by fitting the statistically well-defined lineshape of a transition depopulating a state whose lifetime has been well determined previously. In this case, the 54%keV line in 19’Au was used to parameterize the stopping powers for Au ions traversing Gd. Several lifetimes in 197Auhave been determined independently ‘,‘+“) and serve to check the present method. In addition, 19’Au level lifetimes inferred by this means from data recorded with both Gd- and Fe-backed targets [ref. ‘“)I were in excellent accord when the stopping powers for Au in Fe were related to those obtained for Au in Gd by the usual scaling rules 31). Likewise, there was good agreement between lifetimes extracted from the data recorded with different y-ray detectors positioned at different angles to the incident beam direction. A full description of the code, including an account of the sources of uncertainties, as well as lifetime results obtained from DBLS data recorded during a number of transient-field g-factor measurements of levels in other nuclides, will be published separately 32).

5. Experimental 5.1. TRANSIENT-FIELD

CALIBRATION

AND

results

g-FACTOR

RESULTS

Transient-field precession angles measured for states in 19’Au and ‘82~‘84~‘86W are summarized in table 2; it should be noted that this table presents the “raw” precession angles not yet corrected for cascade feeding effects or decays in flight. Fig. 1 shows gamma-ray spectra registered at 30” and 115” to the beam axis in coincidence with the Au region of the particle spectrum during the bombardment of target B with 220 MeV 58Ni (Run II). [Representative particle spectra have been published elsewhere ‘3*23).]Although not of critical importance, but nevertheless a convenient aspect of the recorded data, the relatively good separation of the particle groups

A.E. Stuchbery et al. / 19’Au

380

TABLE 2 Present

Run no.

Ferromagnetic host

1

II “)

111

transient-field

precession

levels in 19’Au

Target ion

Level

Gd

184W ‘97AU ‘97AU

2:,4: 3: Z+ 21

4.7 4.3 4.3

2.5 2.1 2.1

-45.7 (46) -52.1(59) -35 (10)

Gd

lSZW 184W 1B6W ‘97AU 19’AU ‘9’AU ‘9’AU 19’Atl 19’AU

4: 2134: 2:s 4: i+ 21 4: i: 5: 4: i+:

5.2 5.2 5.2 4.6 4.6 4.6 4.6 4.6 4.6

2.7 2.7 2.7 2.2 2.2 2.2 2.2 2.2 2.2

-40.3 (47) -44.6 (35) -47.8 (35) -47.0 (37) -161 (24) -36.1 (34) -65 (19) -51(17) -48 (23)

186W 19’Au

2:, 4:, 6; ;: I+ II

5.3 4.7 4.1

1.9 1.4 1.4

-34.5 (34) -28.3 (41) -19.0 (66)

2:, 4:. 6: $: Z+ 21

5.4 4.8 4.8

2.0 1.5 1.5

-34.7 (16) -29.1 (40) -23.6 (25)

Fe

19’AU IV

results of designated

Fe

186W ‘*‘AU “=Au

J:

4% “) (mrad)

vi/%"f

“) Velocities vi/ u,,( v,/ us) of ions incident upon (emergent from) the ferromagnetic foil; us = c/ 137 = Bohr velocity. not corrected for ‘) Measured transient-field precessions of states designed (i.e., “raw” precessions, feeding or decays in flight; see text). Quoted errors include uncertainties in the logarithmic derivative of the angular correlation at the detection angle. Where two or more J” values are listed, the quoted precession is the average for those levels. ‘) A reduced magnetization pertained for this Cd foil sample; see text.

backscattered from the contiguous W and Au target strata simplified the ensuing data analysis. A partiat level scheme showing the relative direct populations of the relevant levels measured in this same bombardment of target B by 220-MeV 58Ni is presented in fig. 2. While the extraction of the relative gyromagnetic ratios of levels in lQ7Au from the simultaneously measured TF precessions in any polarized ferromagnetic is rather straightforward 20-22), to obtain the u~~~~~te g-factors of the states in 197A~ from the observed precession angles requires knowledge, or determination, of the behaviour (velocity-dependent magnitude) of the TF strength for Au ions recoiling through polarized Gd hosts. As noted above (sect. 2), and in prior publicain the behaviour of the TF strength as a tions ‘2-‘4*‘7*18),no abrupt discontinuity function of atomic number is expected ‘3*‘4)or observed ‘2*17,18)for ions with atomic numbers

between

54 and 88 traversing

Gd. Measured

TF strengths

for 76W and P,P~

7/2f+3/2;

I04

103

IO’

0

200

400

600

E

energy (keV 1 of the counts accumulated at 30” and 115” to the Fig. 1. Gamma-ray spectra corresponding to -25% beam direction in coincidence with beam ions backscattered from the Au layer of target B during run II (table 1). Transitions in 19’Au are labelled by energy, in keV (upper panel), and J,“+ J; (lower panel). Several lines show Doppler-broadened lineshapes from which level lifetimes were deduced (sect. 4.3, 5.3). Due to slight overlap of particle groups backscattered from the W and Au layers of the target, weak lines from W isotopes also appear in these spectra.

ions in Gd have been found 12) to be in accord with the Chalk River parameterization 33) of the TF strength which also describes well the TF behaviour of ions of lower 17) and higher I’) atomic number traversing Gd. In light of the foregoing, the absolute values of the gyromagnetic ratios of states in 19’Au were obtained from the precessions measured in Gd hosts by scaling the TF strengths sj~~Zra~eously measured for W ions traversing the same host foil with

A.E.

382

Stuchbery

et al. / 197A~

Fig. 2. Partial level scheme of 19’Au showing the states and transitions of interest. Firm spin assignment for several levels obtained in the present work (sect. 5.2) are included. Shown at the left of each level is its relative direct population intensity (with that of the 1: state taken as 100) derived from the measured particle-y correlation data of run II. Level energies are in keV; transition branching ratios are in per cent.

virtually

the same recoil

velocities.

Small

corrections

were made

for the slightly

different velocity ranges with which the W and Au ions ion traversed the Gd foil, for the atomic number dependence of the TF strength, and for decays in flight, using the Chalk River parameterization 33). None of these corrections (all small) were sensitive

to this choice of parameterization.

As found

in our study of ‘50,152Sm

[ref. ‘*)I, any other reasonable parameterization yields very similar results. Due to the much weaker populations of the higher states (fig. 3), corrections for feeding to the states of interest were almost negligible. Gyromagnetic ratios adopted for the low-lying ground-band states in ‘84*‘86Whave been discussed in ref. 16). Like these isotopes, the lowest ground-band states in ls2W also exhibit constant g-factors *“). The calibration g-factors taken were: g( “*v(I) = 0.265 kO.007 [ref. ‘“)I; 0.289 f 0.007; g( =W) = 0.354 f 0.012. Gyromagnetic ratio results for levels in 19’Au obtained from the present ments using Gd as the polarized ferromagnetic host and our prior results in table 3. As noted in ref. 13), the present hosts 13,14), are summarized

g(ls4W) = measureusing Fe g-factors

A.E. Stuchbery et al. / l”Au I”’

1

-

383

I”“,

I.5 -

lg7Au :

- 684 lo -

11/2; -

7/2:

0.7

w(o;ka

Fig. 3. Angular correlations of de-excitation y-rays in coincidence with backscattered beam ions for E2 transitions in ‘97A~ measured during run II (data points) and calculated (solid lines). The energy (keV) and J,” + J; of each y-ray transition are designated. Only the transition intensity has been adjusted to normalize the measured correlation to that calculated.

TABLE

Measured

Measured

Level

J: 5+ 21

z: Z+ :: I2 4: 1+ 21

g-factors

target

A “)

0.30 (4) 0.21 (6)

target

B “)

0.289 (28) 1.1 (2) 0.232 (26) 0.48 (14) 0.34 (12) 0.37 (18)

3

in 19’Au

gyromagnetic

ratios

Fe host h,

adopted

0.308 (35) 1.5 (3) 0.257 (28)

0.296 (23) 1.2 (2) 0.241 (21) 0.48 (14) 0.34 (12) 0.37 (18)

“) For details of targets A and B (Gd hosts) see table 1. “) Results for Fe host from refs. 13,14).

384

A. E. Stuchbery et al. ,J ‘97Au

measured for the lowest 1’ and i’ levels in 19’Au using polarized Gd (table 3) are about 1.5 times larger than those reported by Bazzacco et al. 12)who also employed a Gd ferromagnetic foil. Comparison of our measured precession angles for target A with those of ref. I*), for which the experimental kinematics were similar, indicates that we observed significantly larger precessions in Gd for the low-lying levels of 19’Au than did they; yet, both our results and theirs for W in Gd agree. It is stressed that our g-factor measurements for levels in 19’Auwere made relative to the g-factors of states in the even tungsten isotopes as W and Au ions simultaneously traversed the same Gd host. Thus, the most likely source of systematic experimental error (e.g., diminished Gd magnetization) had no bearing on the present sjmultuneous, relative measurements. For these relative measurements of nuclear precessions in states of ‘82,184,‘86W and ‘97Au, the absolute magnitudes of the precession angles for W in Gd are not of critical importance. However, we note that the precessions measured for Wa obtained with target A are in good accord with the Chalk River parameterization 33), while those measured using target B (prepared from Gd obtained from a different source) were about 80% of the value predicted by this parameterization. This reduction is attributed ‘“) to a lower magnetization for this specific Gd sample, which again stresses the importance of performing simultaneous, relative measurements whenever possible, pa~icularly when Gd foils are employed. 5.2. ANGULAR

CORRELATIONS

AND

MULTIPOLARITY

MIXING

RATIO

RESULTS

Measured and fitted particle-gamma angular correlations for several pure and mixed multipolarity transitions in ‘97Au are displayed in figs. 3 and 4, respectively. The present multipolarity mixing ratio results are summa~zed in table 4. There are two possible mixing ratios which give good lits for the 308-keV transition from the rather weakly populated 855keV state; the larger of these mixing ratio values (S z -2) was rejected on the ground that the implied E2 strength would be unrealistically large. The mixing ratio measured for the $T + t: 279-keV transition is in good The angular correlation results, together with agreement with previous results 5Y35). the observed population intensities and lifetimes, confirm previously reported tentative spin assignments for the 2: (503 keV), 3: (737 keV), f: (855 keV), and y: (1231 keV) levels. TABLE 4 Measured E2/MI mixing ratios of ffJ:

J;

E, WV)

I+ 2,

3+

2:

?I :: >+

279 503 458 308

z; 5:

I1 ::

J; transitions in 19’Au Mixing ratio -0.39 -0.24 -0.26 -0.30

(2) (9) (3) (9)

A. E. Stuehbery et al. / “‘AU

38.5

Fig. 4. Similar to fig. 3, but showing angular correlations of E2/Ml mixed multipolarity transitions in 19’Au. The mixing ratios were varied along with the transition intensity (normalization) to obtain best fits to the data.

5.3. DBLS LIFETIME

RESULTS

Representative experimentally recorded Doppler-broadened lineshapes showing present DBLS fits are displayed in fig. 5 for selected transitions in 19’Au. The present DBLS analysis lifetime results are given in table 5, together with previously reported measured mean lives of the states of interest in ‘97Au. As can be seen from table 5, the present and earlier findings are in excellent agreement. New definitive mean lives are obtained in the present work for the 503- and 737-keV levels. 6. Theoretica 6.1. WEAK-COUPLING

calcufations and discussion

CORE-EXCITATION

MODEL

The weak-coupling core-excitation model can be applied most appropriately to the states of odd-A 19’Au below a few hundred keV excitation energy for which it can be assumed that the excitations are those of the even-even core of the nucleus rather than reflecting orbital promotion of the weakly coupled single particle. Within

A.E. Stuchbery et al. I l”Au

386

530

540

I( “‘Au

550 Energy

18

560 (keV)

I.

I

_

570

570

580

I,

I

_

590 Energy

600

610

I

lo3

57’7 keV

580

500

490

.

510 Energy

1 1 I

520 (keV)

-

I

“‘Au

620

(keV)

670

530

I

, 684

680

690

700

Energy

710

540

1 I keV

720

(keV)

Fig. 5. Measured (data points) and fitted (solid lines) Doppler-broadened y-ray lineshapes (labelled by transition energy) for several transitions in “‘Au; obtained in run II. The lifetime of the 548-keV level (548-keV transition) was fixed at its previously known value and the stopping power parameters adjusted to fit the measured lineshape (upper left panel). Lifetimes were extracted from fits to other lineshapes using this stopping power parameterization. A selection of these are shown.

this limitation, the weak-coupling model has been remarkably successful 2-7) in describing the E2 spectroscopy of the lower levels of ‘97Au. In this model, the nucleus can be considered as either a 19%‘t core to which a d3,2 proton is weakly analysis coupled, or as d3,2 proton-hole coupled to a “‘Hg core. The comprehensive by Bolotin et al. ‘) concluded that the latter characterization gave the better description of the E2 strengths in this model. Table 6 compares the measured level g-factors in 19’Au with the predictions of three alternative weak-coupling model calculations: (ii) the core (1) the core is assumed to by 19?‘t with gC= g(2 :; 19%) = 0.316+0.013, is taken to be 19*Hg with g, = g(2 :; 19’Hg) = 0.52~tO.11 [ref. 36)], and (iii) the core g-factor

is inferred

from the measured

g-factors

of the first excited

4: and ground

A.E. Stuchbery

et al. / ‘97A~

TABLE Summary

of measured

State

387

5 19’Au level lifetimes rpresent “) (PS)

Tprior (PS)

(J:) 3+ 22

8:

77 269

2:

279

2: 1+ 21

503 548

1+ ;: 2, u+ 21

737 855 1231

2760* 10 b, 22.2 f 1.9 ‘) 19.8+4.8d) 26.8k2.1 ‘) 22.8 * 4.3 d, < 4 ‘) 6.7 f 0.4 d, 6.6*0.4’) 4.4*0.5

29.4? 3.8 2.56?” 0.18 6.65?” 0 19 1.58?19 0.13 3.85+“.36 0.22 1.32?‘s0.10

‘)

1.7*0.4e)

“) Errors do not include uncertainties in the previously measured mean life of the 548 keV state used to calibrate the stopping powers; see text. b, Ref. 37), 7 from weighted average of 19’Au(y, y), Mossbauer. ‘) Ref.‘). d, Ref. 37), 7 from reported B(E2). ‘) Ref. ‘I).

TABLE 6

WC1

0.097 0.54 (3) 0.27 (1) 0.235 (8) 0.41 (2) 0.222 (7) 0.319 (13) 0.278 (11) 0.256 (9)

Comparison

of calculated

WC11

WC111

0.097 0.94 (20) 0.44 (8) 0.36 (6) 0.70 (14) 0.34 (6) 0.53 (10) 0.45 (8) 0.41 (7)

0.097 0.839 0.394 0.330 0.627 0.309 0.474 0.404 0.367

(6) (2) (2) (4) (2) (3) (2) (2)

and experimental

Spin(6)

0.154 0.566 0.294 0.263 0.316 0.251 0.250 0.300 0.275

g-factors

in 19’Au

IBFM

IBFM

(I) “)

(II) ‘)

0.146 1.874 0.811 0.305 0.893 0.352 0.652 0.372 0.430

0.027 0.855 0.308 0.294 0.433 0.291 0.385 0.395 0.364

g CXP

0.097 0.839 (6) 0.296 (23) 1.2 (2) 0.241 (21) 0.48 (14) 0.34 (12) 0.37 (18)

“) WCI: weak coupling model with g,= g(19%; 2:) = 0.316(13), g,= 0.097. WCII: weak coupling model with g, = g(19sHg; 2:) = 0.52(10), gp = 0.097. WCIII: weak couling model with g, = 0.468(3), g, = 0.097 from 19’Au lowest states. Spin(6): U(6/4) limit of IBFM with g,=O.316. IBFM: IBFM calculation with g, = 0.5. b, I denotes four-parameter fit, see text. ‘) II denotes six-parameter fit, see text.

A.E. Stuchbery et al. / L97A~

388

states.

In all three

ground

state, g, = 0.097. Similar results are obtained

cases,

the particle(hole)

is used for the d3,* proton.

Mixing

$: level has been neglected, such mixing

between

in conformity

was less than 5%. Further,

g-factor

was taken

to be that of the

if the Schmidt value, g, = 0.087,

the ground

state 2: and the first excited

with the finding

it has been assumed

of Bolotin

et al. ‘) that

for simplicity,

perhaps

naively, that the $:, g:, z:, and y: levels comprise the multiplet of states arising from the weak coupling of a d3,* proton (-hole) to the 4: excited level of the core, taking this core state to have the same g-factor as the 2: state. It can be seen from table 6 that the experimental g-factors of the lower states are less well tracked in the case of an assumed i9?t core, but that the other two weak-coupling model calculations are in reasonably good agreement with empirical findings. These results are in harmony with the conclusion of Bolotin et al. ‘) that the low excitation spectroscopy of 19’Au is remarkably well described by the weak-coupling of a d3,2 proton-hole to the excitation of a i9*Hg core. Nevertheless, the large g-factor measured for the 2: level is underestimated by these weak-coupling model calculations and, as noted by Bolotin et al. ‘), not all the measured Ml transition strengths among the lowest levels in 19’Au are particularly well reproduced by the model. This is not entirely unexpected, as these Ml observables can be very sensitive to even small configuration admixtures; indeed, the large g-factor measured of this state. for the 3: level implies a significant s,/~ admixture in the wavefunction Furthermore, any agreement between the simple weak-coupling calculations and experiment for levels above the f: state must be regarded as rather fortuitous, as this level excitation energy (548 keV) is greater than the energy separating the dX12 and s,,* proton single-particle (contravening an essential underpinning assumption of the weak-coupling

6.2. 19’Au SPECTROSCOPY

model).

AND

Although the interacting limit is more sophitisticated

THE

SPIN(6)

DYNAMICAL

SYMMETRY

boson-fermion model (IBFM) in its supersymmetric than the weak-coupling core excitation model, it still

retains

a degree of simplicity due to its use of group theoretical methods. This model partner, has been applied to ‘97Au by Vervier et al. 1o*1’).Provided the even-even in this case 19’?t, is assumed to be well described by the O(6) limit of the interacting

boson model and that the odd proton occupies only the d3,* orbital, the system of both the odd-A 19’Au nuclide and its even-even partner (‘96Pt) can be treated in the Spin (6) limit of the IBFM. In this limit, certain closed expressions are then prescribed for energies, E2 and Ml strengths, and other observables in both nuclei. Many formulae for these observables have been presented by Iachello and Kuyucak ‘); other expressions required are readily derived using their methods. Expressions for level g-factors required for our study of 19’Au, including, for completeness, those derived by Iachello and Kuyucak9), are listed in table 7. The model parameters for the Ml observables, q, and t, , are related “) to the g-factors

A.E. Stuchbery et al. / ‘97A~ TABLE

g-factor 1

g(N+f,l,f)=E

[

g(N+f,$,f)=v$

[

q,-$1,

limit.

I

1 48(N-1) 2N+4

yq,++,+p

g(N+;,;,$)=.@&

7

in the Spin(6)

4N(q, -r,) 5(2N+4)

r,+

[

formulae

389

(41-r,)

g(N+&$,+f7JiG

1 1

g(N++,$,$)=G

(2N~4)3272[q,(~N+410)-r,(:b7N-31)1

g(N+f,$,;)=d$

(2N+~)3411 [9,(854N+1244)+r,(37N+538)1

O+t,i,%=&

8q,+3r,+p

28(N-2) 9(2N+4)(q1-r1)

I

States are labelled by 1N+$, T,, J) in the notation of ref. 9), where N is the boson number, T, is the non-constant Spin(6) group label, and J is the angular momentum of the state. The parameters q, and r, are explained in the text.

of the core and the single particle, q1=

mg(2+)

respectively, and

by t, = XKOg(s.p.) .

In our calculations, the Schmidt value was taken for the single-particle g-factor and the measured g-factor of the first-excited 2+ states of 19% was used for the core, implying N = 6, q, = 1.03, and t, = 0.27. The effective charge & of ref. “) was taken to be & = 14.31 e * fm’, so that the theoretical B(E2)‘s of the 4: + t:, 2: + g:, and 7+ 2, +$: transitions are equal to the average of the experimental rates for these transitions. Comparisons between the model calculations and experiment for the g-factors are given in table 6; for transition rates in tables 8 and 9. Considering the relative simplicity of the model, the experimental g-factor trends are reproduced reasonably satisfactorily - the main discrepancy, again, being the large measured g-factor of the

390

A.E. Stuchbery et al. / 19’Au TABLE 8

19’Au B(E2) values (in ez fm”); (I) refers to the 4-parameter

IBFM fit, (II) to the 6-parameter

IBFM fit

Transition Spin(6)

J:

IBFM(1)

IBFM(I1)

Experiment

J; 2087 0 947 326 2087 1452 1626 0 480 154 2087 1327 1383 2129 296 2711

1392 718 259 3 2089 87 2429 98 175 17 2441 61 856 2466 189 3243

1063 1502 17 556 1651 373 978 532 0 13 2458 100 1545 2301 2 3315

2250 (120)* 720 (100)’ 1220 (5oy 990 (70) 1720 (150)’ n.0. “) 630 (220) 480 (40) 12 (5)* 460 (130) 2260 (loo)* n.0. “) 1450 (360)* 2600 (200) n.0. “) 3840 (550)*

l Data used in IBFM fits. “) Not observed.

TABLE 9.

19’Au B(M1)

values (in n.m.2); (I) refers to the 4-parameter

IBFM fit, (II) to the 6-parameter

IBFM fit

Transition Spin(6) JT

J”f

1+ 21 1+ ::

3+ 21 ;; :: I1 I+ 21 2+ ZL 2: z+ 21 5+

I2 5+ :: I2 2: 7+ 21 I+ :: I2 4:

TI ::

0.0107 0.0049 0 0.0050 0.0045 0 0.0098 0.0051 0.0026 0.005 1

IBFM(1)

IBFM(I1)

Experiment

0.8584 0.0466 0.0132 0.0021 0.1677 0.0032 0.0064 0.0191 0 0.0052

0.00 0.0131 0.0083 0.0093 0.0004 0.0313 0.0307 0.0068 0.0131 0.0415

0.0076 (1) 0.143 (12) <0.0003 0.061 (6) n.0. “) 0.15 (1) 0.021 (2) n.0. “) 0.31 (3) 0.059 (6)

“) Not observed.

5: state. While the predicted E2 strengths are in poor quantitative agreement with experiment (fewer than half of the calculated E2 strengths being within a factor of two of those measured), the qualitative description may be considered reasonably good in that, with few exceptions, strong (weak) transitions are predicted to be strong (weak).

A.E. Stuchbery

The limitations strengths, insufficient

of the Spin(6)

model are most clearly manifest

for which there is little agreement, flexibility

even qualitatively.

in the Ml transition As the model offers

for these through varying the parameters q, and technique the slj2 orbital is implied. The perturbation

to account

t,, symmetry-breaking

through

suggested

and Kuyucak

by Iachello

391

et al. / ‘97A~

“) to include

s,/* components

was investigated

for the t: state, resulting in g(i:) = 1.3. The experimental value lies between the perturbation result and that of the unperturbed calculated value. As a perturbation calculation for all levels would have to be performed numerically, we have, in preference, opted to perform the following more general IBFM calculation fermion.

which

6.3. INTERACTING

includes

all allowed

BOSON-FERMION

positive-parity

MODEL

orbital

admixtures

for the

CALCULATIONS

To successfully describe the electromagnetic properties of the low-excitation states of all revelant of 19’Au evidently requires a model that can include admixtures single-particle orbitals. This can be done using IBFM calculations similar to those performed earlier 37) for “‘,ro9Ag; however, complications arise in the case of 19’Au.

as will become

clear below, several extra

As in our study 37) of the g-factors of ‘07,‘09Ag, the standard quadrupole hamiltonian, when modified for Pauli blocking effects, maps into H,=C with 4 the quasiparticle hamiltonian:

energies,

T-,cQz *

v(Q)=~ ii’

.?;+J5,+

coupling

V(Q)

E, the core energies

(I) and V(Q) the (quasi)coupling

(~,~j,)‘+CA~,,,f[(d+~j,)~ x(CiaJf,)j]O,,

(2)

5’ .,,

J

where

T,, = To( ujujf - vjuj,)qjj, ,

Aid’,= -~A:,N,Pjjpj'j, and x, To, Ah are constants. Here s+(s), d’(d) are the standard IBA boson operators, at(c) are the orthogonal quasiparticle operators and the q and p are quadrupole matrices. This interaction has only two free quadrupole parameters, To and x; the other input data needed to specify the mass and isotopic dependence of the interaction are the BCS occupancies of the fermion orbits, uj and vj[ of + ~5 = 11, the quasiparticle energies 4, the number of proton(neutron) bosons, N,,,,, and the total number of

392

bosons,

A.E. Stuchbery

N. Only

interaction.

the two parameters

However,

To are x are varied

to fit the quadrupole

as the value of x can be taken from IBA parameters

for the core nucleus, In contrast

et al. / 19’Au

only the overall

with the calculations

the core (19*Hg) as being

strength

parameter

for the silver isotopes,

determined

T,, need be varied. it is not possible

in the U(5) limit of the IBA as, for example,

to treat

the first 2+

state of 19*Hg has a larger measured quadrupole moment 38) than can be accounted for in either the pure U(5) or O(6) limits. As this is one of the more important states in the model, a parameter set for the core which accounts for its quadrupole moments was used. The parameters for the 19*Hg core were taken from the analysis performed by Barfield et al. 39). For simplicity their IBA-2 parameters were converted into IBA-1 parameters

using the prescriptions

of Hatter

et al. 40), but the effective charges

and

g-factors were modified. In light of remarks made by Vervier et al. ‘I), the effective boson quadrupole charge was increased from 16.6 [ref. 39)] to 17.6 [using the notation of ref. “I)]. The resultant IBA-1 structure factors in eq. (2) were resealed for IBA-2 using projection4’). The proton effective charge was taken as 1.0 and, as in the case 37) of Ag, an effective magnetic dipole operator was required. We used the parameterization g-factors

of Maier

of shell-model

concomitant

et al. 42) which

had been

shown

to describe

well the

states in nuclei

Ml transition

near 208Pb, although it did not describe the as well, perhaps due to the simplicity of the

strengths

structure model used. As a consequence of the core not being modelled in the U(5) limit, some approximations used to derive eq. (2) are not always valid. Some of these potential sources of error can be compensated for by (i) breaking the link between the direct (To) and exchange vary independently

(A;) terms in the hamiltonian (AA # m,T,) by allowing Ah to of To and (ii) modifying the effective quasiparticle operators.

In the case of the magnetic

dipole

operator,

we modify

the Maier matrix

elements

by (allMlllb)-(allMlIIb> which allows for both the non-spherical

( LLL+,+$

V,VL,)

core and Pauli blocking

to first order. The

correction factors (s+s)/N were calculated to be 0.93, 0.75, and 0.59, respectively, for the O:, 2:, and 4: core levels. As in the case of the Ag nuclei 37), we attempted to fit experimental data by varying a set of parameters in the model. With the three-shell mixing problem for Au, the three “basic” parameters are the quasipar(s ,,2, d3,2, dS,2) appropriate title energies &,2, &I2 and the strength of the particle-core coupling, To. In the basic model, the relationship between To and Al, is fixed. In parameter set I, the ratio To/AA was allowed to vary, as discussed earlier, whilst the g-factor parameters were set at the values given by Maier et al. 42). (We also refer to this as the “four-parameter fit”.) In parameters set II, the ratio was set to the U(5) limit value

A. E. Stuchbety

of T,,/A&=a= vary

from

parameter

1, while the g-factor

the values

obtained

et al. / ‘97A~

parameters

denoted

VT were obtained

shell-model considerations. The results are shown in tables 6,8 and 9, together model.

g,, g,Y,and g, were allowed

by Maier 42). (Also

fit”.) The shell occupancies

from the Spin(6)

393

The parameters

below

from simple

with a comparison

used are shown

in table

to

as the “sixNilsson

and

with results

10. The results

show that, in general, the IBFM performs much better than the Spin(6) model in reproducing energies and g-factors, and does somewhat better for E2 and Ml “minimal” set has a quality of fit transition rates in 197A~. The four-parameter intermediate between those of the Spin (6) and six-parameter models. In this fit the d5,2 orbital is effectively decoupled, leaving a 2-shell problem consistent with the broken Spin(6) model. Since the fixed values of ge+ 6g,, g,+ Sg,, and g, given by Maier et al. 42) were obtained using a simple structure model, the more sophisticated model used here should obviate the need for any further alteration of the g-factor parameters. The gyromagnetic ratios obtained in the 6-parameter model are “unphysical” in the sense that they are strongly modified from Schmidt values (except g,). It is clear from table 8 that the main problem is in fitting the B(M1; 4: + t:). In all cases the 4: and 3: levels are difficult to model accurately. These states are those expected to have a large s,/~ component in the wavefunction.

TABLE

Parameters

IBFM(1) e3i2 e5i2 TO ‘G ge + %e & + &, g, X2

10

used in IBFM; (I) denotes the 4 parameter the IBFM, and (II) the 6 parameter fit

-0.2435 [IO481 “) 1.1118 [7038] -0.00822 [442] -0.0180 [IO81 1.09 ‘) 2.15 ‘) 4.55 ‘) 17.0

fit in

IBFM(I1) -0.2040 [615] 0.3816 [I2891 -0.00402 [ 1891 -0.00402 [ 1891 ‘) 0.128 [I521 1.023 [370] -0.221 [I4651 9.8

“) Uncertainty estimates from the fit are enclosed square brackets. b, Denotes value fixed by value of T,. ‘) Denotes fixed values (see text for details).

in the

Overall, the parameters and fits of the IBFM are satisfactory. The agreement is better than for the Spin(6) model, showing the need for greater flexibility in the parameters, particularly admixtures of other single-particle orbits, than the latter model can allow. The quality of fit is not as good as that obtained in the study of

A.E. Stuchbery

394

the Ag isotopes

reported

earlier 37). The B(M1)

than are the B(E2)‘s partly mappings particularly longer

et al. / lQ7Au

because

lead to larger corrections in a multi-shell

results

are more difficult

the higher order corrections for magnetic

basis43).

operators

This is important

to model

in the Bose-Fermi

than electric

operators,

when the U(5) limit is no

applicable.

7. Summary and conclusions Static magnetic and dynamic electromagnetic moments were determined for the low-excitation positive-parity levels in lg7Au up to the y (1231-keV) state from measurements of level g-factors, lifetimes,, and transition mixing ratios. The weak-coupling model description of ‘97Au-which assumes a dji2 proton-hole weakly coupled to a 19’Hg core-provides a remarkably good account of the low-excitation E2 spectroscopy of ‘97A~ (to the 5: level) and to track the g-factors well, although the Ml transition strengths are not so well described. This model ignores any Pauli corrections. Due to the implied relationship between the parameters To and A&, u, v, the Spin(6) model corresponds to a specific Fermi level (i.e., includes Pauli effects), but still produces many anomalous results for transition strengths due, at least in part, to the omission of the s,/:! orbit. The multi-shell IBFM can, under various fitting assumptions, produce results for energies, and B(E2) and B(M1) rates which are generally better than either of the above simpler models, although the degree of agreement with experiment is not as based on good as in our related study of ‘07,‘09Ag where the model assumptions, the U(5) limit, are valid. Complications (and consequently poorer descriptions for ‘97A~) arise in our IBFM calculations

largely because

the core nuclei in the Au region cannot

be treated

simply in a spherical limit of IBFM. This introduces uncertainties into the calculations of the occupancies of the single-particle orbitals, and results in a poorer description of the electromagnetic properties. As the expansion used in the derivation of eq. (1) is essentially

N/(j

+ 4) and, therefore,

poorest

when the sl/2 orbit is filling,

it is important to note that the fits were worse for levels which the sii2 shell dominated. In view of these complexities and consequent unce~ainties engendered in the present IBFM calculation, the overall agreement appears reasonably satisfactory. There is an obvious need for a boson-fermion applicable away from the U(5) limit.

quasiparticle

mapping

which

is

The authors wish to express their appreciation for the support and cooperation of the staff of the Australian National University 14 UD Pelletron Laboratory. The valuable technical and related support of Mr. B. Szymanski is acknowledged with thanks. One of us (C.E.D.) acknowledges the support of a University of Melbourne

A.E.

Post-Graduate wealth

Research

Post-Graduate

Australian

Research

Award;

Research Grants

Stuchbery

another Awards.

Scheme

et al. / 19’Au

two (L.D.W.

395

and G.J.L.),

This work was supported,

and Budget

Rent-a-Car

of Commonin part, by the

(Australia).

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32)

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