Nuclear structure of 192 Ir studied with direct transfer reactions

NUCLEAR PHYSICS A

Nuclear Physics A568 (1994) 445-498 North-Holland

Nuclear structure of 1921rstudied with direct transfer reactions P.E. Garrett azb ’ Dept. of Physics and

Astronomy, ~c~aster ~niversi~, Hum&on, Ontatio, L8S 4M1, Canada and b Dept. of Physics, University of Fribourg, CH-I 700 Fribourg, Switzerland

D.G. Burke Dept. of Physics and Astronomy, ~c~aster

Uni~e~i~, Hamilton, Ontario, L&S 4MI, Canada

Received 4 June 1993 (Revised 2 September 1993)

Abstract

The nuclear structure of “*Ir was investigated via the ‘931r(d, t) and “‘Itid, p) reactions, using beams of 18 and 16 MeV deuterons, respectively. The reaction products were analyzed with a magnetic spectrograph, and detected with photographic plates. The energy resolutions (FWHM) of the detected particles were typically = 5.7 keV for the (d, t) and = 8.9 keV for the (d, p) reactions. Spectra were recorded at a large number of angles (2 15). The angular distributions of cross sections were fitted with theoretical distributions from DWBA calculations, and the spectroscopic strengths were obtained. For the (d, t) reaction, the fits to the angular distributions were performed in many cases with the sum of two Z-values. Level energies, parities, spectroscopic strengths, and possible spin values were determined up to approximately 1 MeV excitation energy. Spectra were also recorded at a few select angles for the 1931r(3He,(u)19’Ir and 19’Pt(p, (u)19*Ir reactions using beams of 25.5 MeV 3He and 18 MeV protons, respectively. In order to obtain more information regarding the spins of levels in “*Ir, multidimensional scaling programs were applied to known -y-ray intensities. The method appeared to be successful, and spins were suggested for many low-lying levels. The experimental results were compared with the IBFFM and the Nilsson model. It was found that the models can only approximately reproduce the structure of “21r.

Key words: NUCLEAR

REACTIONS “‘Ir(d, p), E = 16 MeV; measured a(@, E,), ly31r(d, t), E = 18 MeV, measured ~(8, E,), ‘931r(3He, cu) E = 25.5 MeV, measured u(E,); “‘Pt(p, a), E = 18 MeV, measured o(E,). ‘921r deduced levels, f, r, L, spectroscopic strengths. Comparison with interacting boson-fermion-fe~ion model, Nifsson predictions. Enriched targets, magnetic spectrograph.

1. Introduction The A = 190 shape trans~tjonal region has recently received much attention. Some even-even nuclei, e.g. 1900s, and odd-A nuclei, such as 19’Os, have been the 0375-9474/94/$07.00

0 1994 - Elsevier Science B.V. All rights reserved

SSDZ 037.5-9474(93)E0470-S

446

P.E. Garrett, D.G. Burke / I’%

subject of detailed investigations [l-3], and some interesting effects have been observed. Only a few odd-odd nuclei in this region have been studied, and this is due to two reasons. Firstly, the high density of levels makes the experiments very difficult, since very high resolution must be achieved, and the analysis of the data is very difficult. This is evident in the exhaustive work of Kern et al. [4] on ig21r, where a collaboration of 32 people from 11 institutions performed (nth, y), (n th, e-1, average resonance capture, high resolution (d, p) and (d, t) reactions, etc., and established a level scheme composed of 120 y-rays connecting 35 levels below = 500 keV excitation energy. Secondly, more work needs to be done on the theoretical description of shape transitional odd-odd nuclei. Recently, an extension of the IBM, the interacting boson-fermion-fermion model (IBFFM) [5,6], and the symmetry limit of the extended supersymmetry (ESUSY) model [7,8] applicable in the transitional region have been investigated. These models have not been well tested, and the range of their validity is an open question. More traditional models, such as the Nilsson model and the rotation-vibration model, which have enjoyed considerable success in the well-deformed rare-earth region, are known to encounter difficulties in explaining the structure of shape transitional nuclei. In the present work, states in 1921r are studied via single-nucleon transfer reactions. The principle aims of this study were to establish the level energies and to measure angular distributions of cross sections for levels below N 1 MeV excitation energy. Nuclear structure information in the form of parities, possible spin values, and spectroscopic strengths was obtained from the fits to the angular distributions of cross sections. In the work of Kern et al. [4], Cd, p> and Cd, t) measurements were made with high resolution but only at one or two angles, thus neither spectroscopic strengths nor transferred l-values could be obtained. The data from the present study yield direct information regarding the microscopic structure of each level populated, and are used to test two nuclear models; the IBFFM, and a simple Nilsson model approach. In sects. 2 and 3, the experimental details and results are presented. In sect. 4, the multidimensional scaling technique is outlined and is used to analyze the y-intensities of Kern et al. [4]. Sect. 5 and sect. 6 contain comparisons of the data with the IBFFM and Nilsson model predictions, respectively, with $-tests of the strengths in sect. 7. 2. Experimental

and analytical details

The single-nucleon transfer experiments reported in this work were performed using the model FN tandem Van de Graaff accelerator at McMaster University. Beams of 16 MeV and 18 MeV deuterons were used to bombard targets of i911r and 1931r3 respectively. A beam energy of 18 MeV was chosen for the Cd, t) reaction since many other Cd, t> experiments performed in this mass region used this

P.E. Garrett, D.G. Burke / 1921r

447

energy, and the angular distributions of cross sections have more structure than if lower beam energies were used. The (d, p> Q-value is positive ( = 3.9 MeV), and in order to decrease the full energy width at half maximum (FWHM) of the peaks, the beam energy was reduced from that used for the (d, t) reaction. Distorted wave Born approximation (DWBA) calculations indicated that the structure in the angular distributions of cross sections would still be sufficient to allow the determination of the dominant l-transfer in each transition. All targets used in this work were produced by vacuum evaporation of metal samples, obtained from the Isotope Sales Division of the Oak Ridge National Laboratory, onto carbon foil backings approximately 30 u.g/cm* thick. Earlier (cl, p) and (cl, t> measurements used 1911r and 1931rtargets obtained from Florida State University that were approximately 30 pg/cm* thick and had enrichments, as indicated by the supplier, of 94.66% for 1911r,and 98.7% for 1931r.Some of the measurements were later repeated with newly fabricated targets which had enrichments of 96.19% 1911r,and 99.35% 1931r, and thicknesses of approximately 40 and 45 kg/cm*, respectively. The products of the reaction were analyzed by an Enge split-pole magnetic spectrograph, and detected by photographic plates placed in the focal plane. The solid angle subtended by the spectrograph was 0.76 msr. A silicon surface-barrier monitor detector was placed at an angle of 30” to the beam, and was used to measure the number of elastically scattered deuterons from the target. The solid angle subtended by an aperture placed immediately in front of the detector was 0.111 msr. The elastic-scattering cross sections, determined by DWBA calculations described below, were 4.75 b/sr (87.3% of the Rutherford value) and 6.86 b/sr (99.6% of the Rutherford value) for 18 MeV and 16 MeV deuterons, respectively. The numbers of elastic-scattered events were used to obtain normalization values by which the peak intensities on the photographic plates could be converted into absolute cross sections. The beam current on the targets was typically 1 ALA,and gave a sufficient exposure of the photographic plates after one or two hours. The exposures were usually stopped after 2 X lo6 monitor counts. Spectra were taken at 15 angles for the “‘Ir(d, p) reaction, in 2” steps from 6” to lo”, in 2.5” steps from 10” to 20”, in 5” steps from 20” to 50”, and in lo” steps from 50” to 70”. In addition to these angles, the ‘931r(d, t) experiment also had spectra recorded at 22.5” and 27.5”. The peak intensities were converted to cross sections, and angular distributions were fitted with either one or two I-value curves. The theoretical angular distributions for the transferred I-values for (d, t) and (d, p) reactions were obtained from DWBA calculations using the computer code [9] DWUCK4 and the same optical model parameters as in a single-nucleon transfer study [lo] of Pt nuclei. These parameters were chosen since the single-neutron transfer experiments on Pt nuclei, which are in the same mass region, were performed using the same beam energies as in the present work, and both the shapes of the angular distributions

P.E. Garrett, D.G. Burke / 19%

448

and the analyzing powers for various transferred angular momenta, j, were reproduced very well. The normalization value, N, was equal to 3.33 for (d, t) reactions and 1.55 for (d, p) reactions as recommended by Kunz [9]. In single-nucleon transfer from an initial state with spin Ii, more than one j-value may be transferred to a final state with spin If. From angular momentum conservation the transferred j-value is restricted to the range between 1Zj - Zf 1and Zi + If. However, usually one or two j-components will dominate the transfer, and in this work there were no angular distributions that gave reasonable evidence for more than two Z-components. The transfer of j = 3 - or j = G- is indicated by the presence of an 1 = 1 component in the angular distribution, and since the ground states of i9i1r and 1931rare t+, the final state has I” = O-, l-, 2-, or 3-. An 1= 3 component indicates the transfer of j = $ - or j = G-, and could populate final states with I” = l-, 2-, 3-, 4-, and 5-. An 1= 5 component, for transfer of j=?orj=+could populate final states with I” = 3- to 7-. If an angular distribution has &o Z-components, then clearly the spin of the state is restricted to the intersection of the possible-spin ranges of the Z-values. All of the angular distributions were first least-squares fit with one Z-value. If there appeared to be significant deviations between the data and the fit, the fit was performed with two Z-values. In order to test whether the two-parameter fit was justified, an F, test was performed. The statistic F, is defined as F = X2@ - 1) -x2(n) X x”W/(~

-

n>

and is a test of how much the additional term in the fit improves the x2. The number of degrees of freedom is JV - IZ, where .M is the number of data points and II the number of parameters. The probabilities of F, exceeding a certain value due to random fluctuations of the data are tabulated [ill. For 16 data points, a value of F, > 2.46 implies that the two-parameter fit is meaningful at the 95% confidence level, while for 17 data points, the corresponding value is 2.39. Therefore, if a value of Fx < 2.4 was observed, the one-parameter fit was favoured over the two-parameter fit. The values of the fit coefficients are equal to the spectroscopic strengths, defined as

(2) where the experimental

angular distribution is fitted with a single Z-transition, and

where it is fitted with two Z-components.

P.E. Garrett, D.G. Burke / 19%

449

To determine the errors on the fit coefficients, any systematic errors, such as uncertainties introduced by the choice of optical model parameters used in the DWBA calculations, were ignored. The uncertainties on the data points in the angular distributions, a,, were found by

(4) where aP is the statistical uncertainty in the cross section. This procedure includes an additional 10% of the cross section which is a measure of the reproducibility, i.e. when experiments are repeated trying to match the same conditions, variations in cross sections as large as 10% may be found for the some levels.

3. Experimental

results

3.1. Single-neutron transfer

The resolutions obtained for the Cd, t> spectra, an example of which is shown in Fig. 1, were very impressive, being on average 5.7 keV, with a best resolution of 4.5 keV. Due to Q-value differences, the protons from the (d, p) reaction have greater energy than the tritons from the Cd, t) reaction. Thus, even though the average peak widths for the Cd, p) spectra were only slightly greater than those for the (d, t) spectra, the FWHM in energy for the protons, 8.9 keV, was much greater than that

b E r/J si :

1000

100

d E! g

10

5 8 1 -200

0

200

400

EXCITATION

600 ENERGY

800

10001200

(keV)

Fig. 1. Spectrum obtained at an angle of B = 45” for the ‘931r(d, t) reaction with 18 MeV deuterons. Data points having a value of zero are drawn below the horizontal axis corresponding to a value of one.

450

P.E. Garrett, D.G. Burke / 1921r

b d

2

1000

1 1

ig’Ir(d,p) “‘Ir 9=45”

#

1 ’ -200

I 0

200

400

EXCITATION

600 ENERGY

800

1000

1200

(kcV)

Fig. 2. Spectrum obtained at an angle of 0 = 45” for the lglIr(d , p) reaction with 16 MeV deuterons. Peaks marked with an asterisk are due to impurities.

for the tritons. Fig. 2 shows a typical spectrum obtained in the i’lIr(d, p)‘921r reaction. The absolute calibration polynomial relating the position on the focal plane of the spectrograph to the radius of curvature of the particle trajectory was accurately known from previous calibration experiments involving a radioactive source of 212Pb. A nuclear magnetic resonance (NMR) probe was used to accurately determine the magnetic field in the spectrograph. From the positions of the triton peaks and the peak due to elastically scattered deuterons, the Q-value for the first triton peak was observed to be - 1.573 f 0.002 MeV. Assuming that the excitation energy for this state is 56.72 keV, as given in the work of Kern et al. 141, the ground-state Q-value is determined to be - 1.516 + 0.002 MeV, which is in excellent agreement with the value of - 1.515 of:0.004 MeV from the mass tables

WI. The angular distributions of cross sections from the 1931r(d, t) reaction are shown in Figs. 3a-e. The fits to the data are, in almost all cases, extremely good. There are several angular distributions that appear to be populated with pure 1 = 1 or 1 = 3 transitions, and these are well reproduced by the DWBA curves. Many of the plots have more than one curve on them, corresponding to a transfer of more than one I-value. The excitation energies, and absolute cross sections at 8 = 45”, of levels observed in the (d, t) reaction are listed in Table 1. The excitation energies were obtained by averaging the values for all angles observed. The uncertainty listed for each energy includes both the statistical error on the average as well as an estimate of the systematic error due to the calibration of the spectrograph. Since the energies listed are relative to the 56.7 keV peak, the systematic error is assumed to vary linearly from 0 keV at 56.7 keV to 1 keV at 1 MeV excitation energy. An

451

P.E. Garrett, D.G. Burke / i921r

20

40

60

80

20

xl0

MI

80

1oo-o

loo-

ANGLE

(deg)

Fig. 3a. Angular distributions of cross sections from the ‘931r(d, t) reaction. The dashed curves are the results of a DWBA calculation for the transferred I-value indicated. The solid curves are the fits to the data.

examination of the previously known energies of Kern et al. [4] listed in the table for comparison shows that this is a reasonable estimate. Also listed in the tables are the strengths and the possible spin ranges for the populated levels. The Q-values involved in (d, p) reactions are such that protons from reactions on light-mass target impurities often fall at the same position on the focal plane as protons from reactions on heavy targets and sometimes obscure a peak that is of interest, although this normally occurs only at a few angles. The proton spectrum obtained for the “‘Ir(d, p) reaction, shown in Fig. 2, contains several impurity peaks which are marked with an asterisk. However, for strongly populated levels, the presence of impurity peaks does not seriously hinder the extraction of spectroscopic strengths, although two-component fits to the data were rarely performed since the Cd, p> data were not as sensitive to the presence of additional 1= 3 or I = 5 components. The angular distributions for the “‘Ir(d, p) experiment are

452

P.E. Garrett, D.G. Burke / 19%

ANGLE

(deg)

Fig. 3b. See caption for Fig. 3a.

shown in Figs. 4a-c. As can be seen, in almost all cases a one-component fit was sufficient to describe the experimental angular distribution. Since the 1 = 1 intrinsic cross section is much greater than that for I = 3 or I= 5, it is much more difficult to detect the 1 = 3 or 5 components. In fact, no 1= 5 (d, p) angular distributions were obtained, and only a few peaks had definite 1 = 3 transitions. The excitation energies and cross sections at an angle of 0 = 45” are listed in Table 2 for the (d, p) reaction, along with the spectroscopic strengths obtained. 3.2. (p, a) and c3He, a) reactions Earlier studies [13] have shown that for nuclei in the rare-earth region, there is a good correlation between the (p, (w) cross sections and those of the (t, a> reaction leading to the same final nucleus. Therefore, in an attempt to gain information regarding the similarity of the neutron configurations in 1921rto those

P.E. Garrett, D.G. Burke / 19%

ANGLE

453

(deg)

Fig. 3c. See caption for Fig. 3a.

in ‘95Pt a (p, a) experiment was performed. Spectra were recorded at 10” and 15” for the’ ‘95Pt(p, a) reaction using an 18 MeV proton beam. The energies and relative cross sections at 10” are listed in Table 3, and the spectrum is shown in Fig. 5. The resolution (IWI-IM) of the peaks in the a-spectrum was approximately 18 keV. As can be seen, the largest peaks in the spectrum occur above 400 keV. In the low-lying portion of the spectrum, the peak intensities are small, and thus the overlaps of the wave functions of the target and those in the final states are small. Therefore, the low-lying neutron configurations in 19*Ir do not have large admixtures of the neutron configuration of the 19’Pt ground state. The ‘931r(3He, a) spectrum shown in Fig. 6, obtained earlier during a 1931r(3He9 d)194Pt experiment [14], was analyzed in the hope that it would yield some information on high-l transfers into 19*Ir. The C3He, a> reaction favours higher angular momentum transfers than the Cd, t) reaction. The cY-spectrum shown in Fig. 6 was taken at an angle of 50” with a 25.5 MeV 3He beam, and the

454

P.E. Garrett, D.G. Burke / 1921r

20

40

60

80

ANGLE

50

20

40

60

80

(deg)

Fig. 3d. See caption for Fig. 3a.

energies and cross sections are listed in Table 4. The resolution obtained was 25 keV, and the uncertainty on the absolute Q-value is perhaps as large as 30 keV. However, if the assumption is made that the main peaks in the C3He, a> spectrum are due to transitions with I = 3 or higher, there is a fairly good correspondence between strong 1 = 3 transitions in the Cd, t) spectra and the peaks in the C3He, a> spectrum. There is, however, a peak which is strongly populated in the C3He, (Y> reaction but not in the (d, t) or (d, p) reactions, at 143 keV. This may indicate the presence of an 1= 5 or perhaps an I= 6 transition, since the I = 3 component is known to be quite small. 3.3. Discussion of individual levels The level energies determined in the present study are in excellent agreement with those of Kern et al. [4], who list the energies up to approximately 500 keV.

P.E. Garrett, D.G. Burke / 19%

20

ANGLE

455

40

60

80

(deg)

Fig. 3e. See caption for Fig. 3a.

The present work has also found many new levels above 500 keV. Ground state. When this work was undertaken, the spin of the ground state was known to be 4, but the parity was unknown. Conflicting assignments had appeared in the literature, and one aim of the present work was to establish clearly the parities of many levels in 19’Ir. The ground state, which is not observed in single-neutron transfer experiments, must have its parity inferred from the multipolarities of y-transitions feeding it and the parities of the parent states. The present work confirms the assignments of Kern et al. [4] of negative parity for many excited states. Some of the negative-parity excited states decay to the ground state with y-transitions that involve parity changes, and thus the ground state has positive parity. Therefore, the results of the present work provide additional support of the assignment of Kern et al. [4] of I” = 4+ for the ground state. 62 kel/leveZ. Kern et al. [41 report the possible existence of a level at 62 keV, as observed in their Cd, t) spectra, and report a significant cross section populating

367.2(4)

390.7(4)

415.cq5) 437xX5) 444.6(5) 451.9(5) 471.3(5) 490.9(6) 508.1(5) 5 17.2(6)

389.722 392.352 >

415.039 437.3 444.1 451.250 470.6 489.435 508.989 516.3

73(13) lOS(17) 120(16) 181(22) 125(16) 144(18) 106(14)

62@)

14418)

195(23)

1,3 123 173 193 .1,3

173 193 1

173

133

193

l-3 l-3 o-3 1-3 1-3 1-3 l-3 l-3

1-3

l-3

1 1

3&2

2&2

2&l

o-3

297(38)

331.7(4)

0.066(3) 0.144(10)

2 2

o-3 1-3

120(33) 357(48)

310.5(4) 319.7(4)

0.173(5)

2&2

o-3

d,, 3 1, 3 5

133

354(39)

2 2 2 2 4, 5 = 2 4

1,3 1 1

57(9) 240(27) 205(24) 15809) 186(24) 333(50) 60(12) 14(5)

288X3)

0

o-3 l-3 o-3 o-3 l-3 o-3 l-5 l-3 3-7

1

71(13)

128.6(3) 143.5(2) 192xX2) 212.6(2) 225.7(3) 240.2(3) 256.8(2) 266.8(3) 278.2(10)

366.730 368.352 1

310.996 319.891 331.074 331.757 >

128.742 143.554 192.933 212.805 225.916 240.900 257 267.126 277.992 288.402 292.374 >

1001(110)

116.5(l)

0.015(2) 0.025(3) 0.050(2> 0.014(3) 0.042(4) 0.028(3) 0.053(5) 0.031(3)

0.046(4)

0.037(3)

0.159(5)

0.039(2) 0.010(1) 0.114(3) 0.093(3) 0.066(5) 0.089(3) ( < 0.022) 0.026(3)

0.38(2)

0.061(2) 2&3

(3),5 1

248(29) 13107) 33(10) 109(23) 0.097(7)

I=1

Transfer strength

l-3

adopted d

1, 3

possible ’

Spin

1 4 3

1,3 3

l-value

l-3 l-5 3-7 o-3

Cross section &b/x) f3= 45”

56.7 66.3t2) 83.8(3) 104.5(l)

(keW

(keV)

56.719 66.83 84.274 104.776 115.563 118.782 >

Present energy b

Previous energy a

Table 1 States in lg21r populated with (d, t) reactions

0.170(14) 0.194(21) 0.122(16) 0.089(22) 0.110(17)

0.05 l(9) 0.067(14)

0.096(19)

0.245(18)

0.098(43)

0.509(28) 0.021(12)

0.065(21)

0.027(6)

0.30(9)

0.056(31) 0.216(8) ( < 0.011)

1=3

0.34(5)

0.553(38)

1=5

:

532.5(6) 540.4(7) 582.6(6) 603.7(7) 615.5(7) 62&O(7) 646.0(6) 662-O(7) 679.0(8) 686*1(S) 702.3(9) 712.8(X) 737.6(8) 751.9(8) 766.0(9) 778.9(g) 791.1(9) 813.3(g) 825.0(9) 841.7(9) 850.3(9) 862.7(20) 874.1(17) 885.1(16) 901.1(22) 918.0(21) 938.3(16) 967.2(22) 1001.3(19) 1015.009) 1023.6(24) 1052.9(28) 1060.5(25) 1078.2(16) 1090.6(34)

50(9) 36(9) 8(4) 19(S)

66CW 24(5) 22(5) 27(7) 34(7) 65(12) 66(11)

1, 3

19W 43(7) 50(g) 137(25) 137(20) 83(15) 203(25) 71(12) 135(32) 258(30)

173 193

1, 3 133 1, 3 193

193 133

123

1, 3 193 1, 3

133

1. 3

1, 3

8002) 187(22)

24(6) 31(6) 109(22) 174(21) 108(14) 87(13) 82(13) 51(12) 183(23)

134(49) 31(17) 67(12) l-3 o-3 l-3 o-3 o-3 l-3 o-3 l-3 l-3 l-3 o-3 o-3 l-3 o-3 1-3 o-3 o-3 l-3 l-3 o-3 o-3 o-3 l-3 l-3 l-3 l-3 o-3 o-3 o-3 o-3 l-3 l-3

a Energies from ref. [4]. b An energy of 56.7 keV from the work of Kern et al. [4] has been adopted for this state, and all other include an estimate of the systematic error due to calibration of the spectrograph. ’ All states have negative parity. d Spin adopted from ref. [4] or from Table 5. ’ Spin uncertain, but believed to be either 4 or 5. See text.

530.247 543.4 581.2 603.2

energies

0.015(3) 0.022(2) 0.020(2) 0.019(l) 0.014(l) 0.013(2) O.lOl(3) 0.049(4) 0.043(2) 0.007(4) 0.042(2) 0.112(4) 0.046(4) 0.118(4) 0.012(2) 0.023( 1) 0.024(l) 0.047(4) 0.027(3) 0.054(2) 0.138(S) 0.042(2) 0.32(3) 0.055(5) 0.020(3) O.OOs(2) 0.013(l) 0.017(l) 0.015(l) 0.03 l(2) 0.031(4) 0.004(2)

are relative

to it. Errors

0.048(17) 0.067(10)

0.208(23) 0.399(33) 0.113(15) 0.047(10)

0.121(21) 0.219(18)

0.022(9>

0.051(19)

0.036(17) 0.048(13) 0.131(18)

0.20906)

0.070(12)

0.123(16)

on the energies

458

P.E. Garrett, D.G. Burke / 1921r

ANGLE

(deg)

Fig. 4a. Angular distributions of cross sections from the “‘Ir(d , p) reaction. The dashed curves are the results of DWBA calculation for the transferred I-value indicated. The solid curves are the fits to the

data.

this level. In the present work there is no evidence of this state. While the resolution obtained in the work of Kern et al. [4] is slightly better than that achieved here, the resolution obtained in the present work was such that the peak at 62 keV should have been observed. Even if the cross section were much less than the value reported, it would at least cause a shoulder on the peak due to the 56.7 keV level, contrary with experiment. It is therefore concluded that this is a spurious peak in ref. [4]. 66.3 keVleve1. The state at 66.3 keV was not observed in the average resonance capture (ARC) studies of Kern et al. [4], and since the claim of completeness for spins 0 to 3 up to 200 keV has been made for the ARC measurements, it must have spin > 3. The (d, t) angular distribution can be reproduced with a pure I = 3 component, which limits the spin to 4 or 5. A probable E5 transition has been observed to feed the ground state from an isomeric level at 161 keV, which has tentatively been assigned [15] an IT-value of 9-. If the P-value of the 66.3 keV state were 5-, an M4 transition to it from the isomer would probably be observed; since this is not observed, the spin of 4 is favoured for the 66.3 keV level.

P.E. Garrett, D.G. Burke / 1921r

10

4722 B”

50

20

40

50

50

ANGLE

(deg)

F”i’-‘: I

10

643.7 ke”

I=,

20

20

40

&I

80

ANGLE

(deg)

Fig. 4b,c. See caption for Fig. 4a.

459

460

P.E. Garrett, D.G. Burke / lg21r

Table 2 States in tg21r populated with (d, p) reactions Previous energy a

Present energy b

56.719 66.83 84.274 104.776 115.563 118.782 >

56.9(6) 66.3(12) 85.2(13) 104.5 d

128.742 143.554 192.933 212.805 225.916 240.900 257 288.402 292.374 >

128.3 d 144.8(11) 192.2(5) 212.4(5) 226.8(6) 239.9(4) 257.2(5)

c

154(18)

L3 3

288.5

25408)

1

0.175(6)

319.891

318.6(4)

194f28)

1

0.178(5)

331.757 331.074 >

331.3(4)

204f23)

1

0.164(6)

366.730 368.352 )

367.5(6)

55(9)

1

0.054(2)

389.722 392.352

390.3(5)

86(13)

173

0.024(6)

414.3(6) 438.0(6) 450.5(6) 472.2(6) 489.8(6) 507.7(6) 517.6(8) 531.3(S) 542.7(8) 582.2(8) 614.4(7) 627.6(8) 643.7(7) 660.7(8) 686.6(9) 700.7(9)

58@) 4W)

1 1

66(25) 54(13)

1,3 1

0.047(2) 0.034(2) 0.022(4) 0.050(3)

1 1 1 1 1 1 1 1 1 1 1

0.126(5) 0.066(3) 0.034(2) 0.036(2) 0.026(2) 0.035(2) 0.035(2) 0.018(l) 0.025(2) 0.021(2) 0.035(2)

415.039 437.3 451.250 470.6 489.435 508.989 516.3 530.247 543.4 581.2

a b ’ d

116.3(5)

Cross section (ub/sr) 0 = 45 68(22)

N8) c

Transferred l-value 1 3 5

Transfer strength I=1

1=3

1=5

0.058(3)
311(36)

L3

c

72@) c c

27(5) 145(21) 7007) 5000) E

c

25(4) 49(8)

26@) 236) 38(8)

1 1 1

0.224(14) < 0.03 < 0.02 0.075(3) 0.109(4) 0.041(2) 0.073(7)

0.27(7)

0.21(4) 0.431(15)

0.165(25)

0.072(17)

Energy from ref. [4]. Energy is relative to 288.5 keV peak. Peak obscured at this angle due to impurity peaks. Peak was not observed. Strength given is an upper limit.

256.8 keL’ level. The level observed at 256.8 keV was not seen in the ARC experiments by Kern et al. [4], but was observed in their (d, p) and (d, t> measurements. It appears to have an I= 3 angular distribution for both the (d, t> and (d, p>

P.E. Garrett, D.G. Burke / “‘Ir

461

Table 3 Energies and relative cross sections for states in lg21r populated by the (p, (Y)reaction Excitation energy (keV)

Relative cross section (k/u) 0 = 10”

Excitation energy (keV)

50(3) 71(3) 102(3) 127(3) 178(2) 21 l(4) 222(3) 246(3) 273(3) 291(4) 315(3) 354(4) 402(2)

7 8 4 4 14 15 24 9 20 10 15 9 95

426(2) 474(2) 493(3) 524(4) 542(3) 568(2) 604(3) 624(3) 642(3) 683(4) 697(4) 723(2)

Relative cross section (kb/sr) 0 = 10” 26 38 19 35 30 100 35 22 30 31 20 36

reactions, with perhaps a small amount of 1 = 1 present. The Cd, t) F”-value favours a two-component fit over a one-component fit. The presence of I= 1 in the angular distribution would limit the spin to be at most 3. The amount of I= 1 found by the fit is very small, and it is very sensitive to an I = 1 transition to any possible unresolved level, or to impurity peaks present in the spectra at forward angles. The 256.8 keV peak occurs in a region where the level density is fairly high, so that small, unaccounted for, impurity peaks could be present. While the energy

: d

200

B tl

100

5 8 0 -200

0

200

400

EXCITATION

600 ENERGY

800

1000

1200

(keV)

Fig. 5. Spectrum obtained at 0 = 10” from the lg31r(p, cy) reaction using a bombarding energy of 18 MeV.

P.E.Garrett, D.G. Burke / 19%

462

600

0 -200

200

0 EXCITATION

ENERGY

600

400 (kcV)

Fig. 6. Spectrum obtained at 0 = 50” from the lg31rC3He,(Y)reaction using a bombarding energy of 25.5 MeV.

of this state is greater than the limit on completeness given by Kern et al. [4], they do state that most of the spin 0 to 3 states below 400 keV would be observed. Therefore, it is assumed that the 1 = 1 component is spurious, and thus this state is probably either 4- or 5-. 367.2 keVleve1. An interesting situation occurs for the peak at 367.2 keV, where the (d, t) angular distribution required a fit with a small I = 1 strength and a large I = 3 strength, while the (d, p) angular distribution required only an I = 1 component. When a two-component fit to the (d, p) angular distribution was performed, the result fails the F’-test. However, this peak is due to an unresolved doublet at energies of 366.7 and 368.4 keV. It is suggested that one of the levels is below the Fermi surface, and is responsible for the I = 3 strength observed in the (d, t) reaction.

Table 4 Energies and relative cross sections for states in lg21r populated by (3He, (Y)reaction Excitation energy (keV)

656) 84(10) 114ClO) 143(4) 212(10) 245(Z) 281(3)

Relative cross section (pb/sr) 0 = 50”

Excitation energy (keV)

Relative cross section (kb/sr) 0 = 50”

23 9 9 19 2 20 21

298(5) 318(5) 359(3) 410(3) 482(Z) 531(3) 572(Z)

22 9 4 26 59 20 20

P.E. Garrett, D.G. Burke / ‘921r

463

4. Multidimensional scaling analysis It was suggested [16] a number of years ago that if a state of unknown spin decays to a number of lower levels with the same branching fractions as a nearby state with known spin, the spins of the two states are the same. The basis for this argument was the spin selectivity of the y-transitions. This has been put on a more quantitative basis by Cameron [17,18] using the multidimensional scaling (MDS) program [ 191 MINISSA. The basis of this method is to find the degree of similarity of the decay branching for two initial states i and j by taking the scalar product

cij= Caifajf , f

(5)

where a$ is the branching intensity from state i to final state f. In other words, a vector is formed by taking the square root of the branching intensities to all final states. The matrix of similarities, C, is then used in a multidimensional scaling program. The program compares each pair of matrix elements, for instance Cij and Clm, and if Cij < C,,,,, then dij > dr,, where dij is the distance between the points i and j in an arbitrary space, and respectively for d,,. It should be noted that the distance in the space has no physical meaning, aside from being an indication of the similarity of corresponding decay patterns. As an illustrative example, consider three states, A, B, and C, which decay to lower-lying states. Assume that states A and B have approximately the same decay pattern, and that state C has a different decay pattern, but more similar to B than to A. In the resultant similarity map, the points corresponding to state A and B will be close together, whereas that corresponding to state C will be much further away from both A and B, although it will be closer to B than to A. If a fourth state, D, which has a very similar decay pattern to C, is now considered, the resultant map will now have point D situated close to C. As the number of points increases, the positions on the map become “locked in” in the sense that it is not possible to change the position any of the points. The points on the map corresponding to states with similar decay patterns will be clustered together. As the number of selection rules increases for the y-transitions, for example K-selection, it is possible that the similarity maps will also show clustering reflecting not only the spin, but also the additional quantum numbers for the selection rules. This method has been used in the A = 20 and A = 60 regions with a great deal of success [17,181. It was found that regions of different spins on the maps are clearly delineated. An attempt has been made here to use the same method to help determine unknown spins of levels in 19’Ir. The y-branching intensities were those published by Kern et al. [41, and levels where the branching was uncertain were not considered. The maps generated by the program [19] MINISSA can be

464

P.E. Garrett, D.G. Burke / lg21r

spin1

spin2

,

I

I

I 17 1

42

22

19

I

,5

74

16 55

23fB20iz g1_11

8

,I 1 13

324

10

I I I

DISTANCE

d

Fig. 7. One-dimensional similarity plot produced by the program MINISSA. The numbers refer to levels as indicated in Table 5. States known to have spin 1 have a bar over their number, and those with spin 2 have a bar underneath. The dashed lines are suggested borders between the different spin regions. The differences between d-values are a measure of the similarity between the -y-decay patterns of the states, as described in the text.

24

'\ .I-__ ___------_______

--> 9 . .

-.

lo _6

spin2

5

_/' --__

13

15 _---

spin3

3

a

..

'._

16

7

2'0" 12

19 L

'\ 'TJ8 21 -&_3

________:<-

4 217

DISTANCE

spin1

’

d,

Fig. 8. Two-dimensional similarity plot produced by the program MINISSA. The numbers refer to levels as indicated in Table 5. States known to have spin 1 have a bar over their number, and those with spin 2 have a bar underneath. The dashed lines are suggested borders between the different spin regions. The differences between d-values are a measure of the similarity between the y-decay patterns of the states. as described in the text.

P.E. Garrett, D.G. Burke / 19%

465

Table 5 Spins for states in 19’Ir suggested by MDS maps Energy CkeV)

Level number

118.782 128.742 143.554 192.933 193.509 212.805 225.916 235.758 240.900 267.126 288.402 292.374 310.996 319.891 331.074 331.757 351.690 366.730 368.352 392.352 415.039 418.135 489.435 508.989

Spin from ref. [4]

Spin from MDS maps

24

3-

3

23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

01-, 22+ + :o:: I-, 221o-, 1-, 2(1-),2-, 31-, 21-, 2222-,(3-I 12+, 3+, 4+ 221-, 2-, 31-, 22+, 3+, 4+ 1-,2-,(3-j 1-, 2-, 3-

132 1 2 2 2 2 1 2 2 2 2 2 2 2 1 3 2 2 2 1 3 1 1

either one- or two-dimensional, and are shown in Fig. 7 and Fig. 8. The MDS method has never been applied to nuclei in this mass region, and more thorough tests need to be made. For instance, as the number of selection rules increases, the “spin” clusters will likely break down into a number of smaller clusters such that the maps could have an almost uniform density, resulting in a loss of information. Tests need to be performed so that the range of applicability, and the sensitivity to additional quantum numbers, of the MDS method can be investigated. In the present case, the known spins appear to be separated from one another. Boundaries on the maps suggest spins for the unknown states, and it should be noted that the spins and y-multipolarities in the work of Kern et al. [4] are consistent with those suggested by the similarity maps, except for one O- state at 128.7 keV, which appears in the spin 1 or 2 region. The outcome of the program is very sensitive to the placement of the y-rays, and if more spins could be included the maps would probably be clearer. The suggested spins are listed in Table 5. It should be pointed out that in ref. [41 the transitions were placed according to the Ritz principle so that spurious assignments are likely to occur especially for transitions of lower

466

P.E. Garrett, D.G. Burke / 1921r

precision or of higher energy, where there are possible unresolved doublets. This introduces a bias into the results of the similarity maps.

5. Interpretation in terms of the IBFF’M 5.1. IBFFM calculations

Results of calculations performed by Paar and Brant [20] within the context of the interacting boson-fermion-fermion model (IBFFM) have been obtained. The IBFFM hamiltonian is written [21,22] as H IBFFM

-H,,,(r) -

+HIBFM(~)

-HIBM+HRE~(Tv)~

(6)

where H,,,,(T) and H,,, (v) denote the IBFM hamiltonian [23,24] for the neighbouring odd-proton and odd-neutron nuclei, respectively, and H,,, denotes the IBM hamiltonian [25,26]. The calculations were performed [4] with the computer code IBFFM, which has been described in the literature [27-291. The parameters for the IBM hamiltonian were determined [4] from the boson core, 194Pt fitted in the SO(6) limit, which is applicable to the Os-Pt region. The number of bosons in the core, however, was truncated to N = 4 from the actual number N = 7 in order to reduce the length of the computations. This was justified on the basis of the renormalizability of the SO(6) symmetry since similar results can be obtained for the energies, EM transition strengths, etc., for a smaller boson number if the parameters are renormalized. Problems are likely to appear, however, with the single-particle transfer strengths since these depend on the details of the microscopic wave functions, and the degree of fragmentation cannot be reproduced by renormalization of the SO(6) parameters. The HrurM(rTT)and HrurM (v) parameters were found by fitting the experimental properties of 1931rand 1930s, respectively. The HIBFM(r) calculation included the ~sr,~, rd3,z, rd,,,, and rhi1,2 quasiparticles. The H,,,,(v) calculation included the ~pi,~, vp3,z, vf5,2, Vh9,2, and yi,3,2 quasiparticles. The only symmetry limit used in the calculations was the SO(6) limit of the core. By requiring that the IBFFM calculation reproduce the ground-state quadrupole and magnetic moments, spin and parity, as well as the first excited state spin and parity, the H&TV) hamiltonian parameters were determined [4]. Details of the calculations, and the values of the parameters used, can be found in the work of Kern et al. [4]. The IBFFM calculation makes predictions for both the wave functions and energies of excited states. The wave functions determine the specific properties of the levels, such as the transfer strengths, electromagnetic (EM) transition rates, etc. Cizewski et al. [30] pointed out that the IBFM calculations had difficulty in predicting both the EM transition rates and the spectroscopic strengths simultane-

P.E. Garrett, D.G. Burke / 19%

461

ously. Therefore, it might be expected that the IBFFM will also have these difficulties, even if the boson core were not truncated. The wave functions obtained from the calculation are very configuration mixed, often with four or five components with amplitudes of 0.4 or more. Examples of the wave functions for 19*Ir were presented in the work of Kern et al. [4]. The proper normalization for the spectroscopic strengths for pickup reactions, defined as in Eq. 3, requires that for a particular j-transfer, the sum of Sj over all possible final spins is (2j + l>I$*, for each j-value. The strengths calculated from the Nilsson model have the proper normalization. The spectroscopic strengths obtained from the IBFFM calculations of Paar and Brant 1201,on the other hand, are normalized such that for each angular momentum value Zf of the final nucleus, the sum of strengths is (2j + l>y.’ for pickup reactions. Therefore the IBFFM strengths must be renormalized so that the sum over all final spin values Zr of the pickup strength is (2j + l>q;.“. Once the renormalization is achieved, the experimental values of the strength can be directly compared to the calculated values. The renormalization procedure is somewhat arbitrary, since in general each j-component for each final spin Zf can have a different normalization. Unfortunately, this introduces 14 parameters (only 10 of which are independent) into the strength calculations that are not predicted by the model. The procedure chosen to determine the parameters was the following: for each final angular momentum Zf, a normalization R, was found by examining the experimental Cd, t> strength distribution, and then matching, as closely as possible, the theoretical distribution for each j-component subject to the constraint of the sum of the strengths. For some spin values, such as O-, there was only one experimental state known in 19*Ir, and therefore the renormalization value used was such that the Cd, t> strength to that state was reproduced. For other spins, especially l- and 2-, many experimental states were known, and the renormalization values chosen were those that best reproduced the experimental strengths. Where possible, the same renormalization value was used for the same j-component for different spins. The stripping strengths obtained from Paar and Brant [20] must also be renormalized with the same parameters. If a value different from that used for the (d, t> reactions was employed, this would effectively change the Z.$*-values. Since the (d, t) strength data are more reliable and in many cases yield values for more than one j-transfer to a single state, the renormalization constants were found from these data, and then applied to the Cd, p) strengths. The renormalization values used are shown in Table 6. One of the main advantages of the present work is that the absolute spectroscopic factors, rather than relative values, can be compared with predictions. In previous works involving comparisons with the IBFFM, the experimental angular distributions were either not obtained, or the absolute values of the cross sections were not known. Thus, the comparisons with the IBFFM predictions have concentrated on the relative spectroscopic strengths or cross sections between levels for

P.E. Garrett, D.G. Burke / 1921r

468

Table 6 Renormalization

constants

Final Spin 0123456-

for spectroscopic

strengths

A/2

j3/2

0.5 0.5

0.024 0.2 0.55 0.1

k/2

i9/2

0.15 0.15 0.15 0.6

0.1 0.15 0.32 0.32

each j-transfer to each final spin If. In the present work, for the first time, the absolute values of the spectroscopic strengths can be compared with the IBFFM predictions. These comparisons can determine if the model can accurately reproduce the structure of the low-lying states, and provide a much more sensitive test for the theory. The calculated low-lying negative-parity states below 500 keV for i9’Ir are shown in Fig. 9. As can be seen, there is a large number of 2- states predicted, whereas the numbers of O- and 4- states are relatively small. This agrees with the experimental situation also shown in Fig. 9. There are three l- states that are predicted below 150 keV, and these are observed in the experiments (see Table 5). Above 150 keV the l- states that are observed become separated in energy more

--

th.

exp.

th.

wvvvw

Spin

O- Spin

exp.

th.

1‘ Spin

exp. th.

2- Spin

exp.

th.

3- Spin

exp.

4-

Fig. 9. Predictions from the IBFFM for low-lying states and experimentally observed levels in l’*Ir. Only the negative-parity states with spin < 4 are shown. Levels with dashed lines correspond to levels for which the spin is uncertain. The lines connecting levels are the assignments made in the present work.

P.E. Garrett, D.G. Burke / 19’Ir

469

500 400

+

IBFFM

0

Observed

-

0

’

I

012

I

Prediction

+

t

4

5

I

3

Spin Fig.

10. E versus I(1 + 1) plot for yrast states predicted with the IBFFM and observed in 1921r.

than predicted. The 2- states are somewhat closer in energy than predicted, but several of these have spin assignments based on the similarity maps. If some of the states that are suggested to be 2- are actually l-, the overall agreement would improve. There are, however, other more serious discrepancies. The calculated energies of the 3- and 4- states appear to be much greater than observed. For instance, the first 3- state is predicted at 257 keV whereas experimentally it is observed at 83.8 keV. The situation is even more exaggerated for the first 4- state (predicted at 412 keV but assigned at 66.3 keV). Fig. 10, which plots E versus I(I+ 1) for the yrast levels, illuminates this difficulty. As can be seen, the theoretical values increase approximately linearly with spin, whereas the experimental results show a very different behaviour. Table 7 presents the results of the IBFFM spectroscopic strengths for 19’Ir calculated by Paar and Brant [20]. The values given in the table were renormalized using the values listed in Table 6. In Fig. 11, the predicted and experimental strength distributions for I= 1 and I = 3 transfer with the (d, t) reaction are shown. The predicted I= 1 strength to some of the low-lying l- states is much greater than observed, especially for the first and third l- levels. The lowest 2- state has a predicted I = 1 strength that is consistent with the observed value to the doublet 116.5 keV, but the predictions for the next four 2- states are a factor of approximately 2 too great. In fact, there is a general trend that the predicted 1 = 1 strength to the low-lying states is much greater than observed, and this is best illustrated in Fig. 12, which shows the sum of the 1 = 1 and I= 3 strength versus energy. Above 130 keV, the predicted I= 1 strength sum grows at a rate approximately 60% greater than the observed I= 1 strength. The major discrepancies for the I= 3 strength occur for the 4- state at 66.3 and the 4- or 5 state at 256.8

P.E. Garrett, D.G. Burke / 1921r

470 Table 7 IBFFM Prediction for “*IT Energy

Spin

CkeV) 57 112 128 131 1.51 192 208 233 257 261 263 269 277 288 306 329 340 347 360 367 383 389 391 396 399 400 402 405 412 431 434 438 439 477 484 490 494 497

1012112031231320211212252233411421226273-

(d, t) Strength I=1

I=3

0.253 0.039 0.064 0.334 0.193 0.013 0.283 0.00009 0.009 0.049 0.146 0.010 0.161 0.114 0.227 0.008 0.241 0.009 0.005 0.050 0.038 0.007 0.012

0.029

Cd, p) Strength I=5

0.104 0.048 0.016 0.042 0.012 0.047 0.004 0.015 0.137 0.0004 0.00006 0.146

0.020

0.008 0.010

0.030 0.022 0.027 0.006 0.044 0.001 0.006

I=1

1=3

0.095 0.001 0.020 0.171 0.021 0.003 0.115 0.000003 0.002 0.018 0.029 0.003 0.029 0.032 0.057 0.0002 0.050 0.003 0.0006 0.014 0.010 0.004 0.004

0.002

0.0005 0.010 0.029 0.020 0.403

0.082

0.227 0.066

0.027

0.002

0.002 0.0005 0.0039

0.009 0.0001 0.002 0.022 0.00007 0.0002 0.017

0.055

0.00005 212.6 0.0002 0.0002

331.8 118.8 225.7 240.2

266.8 415.0 292.4 310.5 0.0003

0.041 0.002 0.0005 0.002

0.00008 0.0012 0.006 0.003 0.065

0.026

0.037 0.007

0.009

0.0002

0.076

0.016

143.5 192.6

0.002 0.001 0.001 0.0001 0.003 0.0002 0.001

0.0001

0.008

56.7 128.6 104.5 115.6

0.007 0.007 0.0008 0.001 0.0005

0.017 0.192 0.007 0.002 0.008

1=5

Experimental level

288.4 331.1 0.000004 0.000004 0.0007 0.00016

256.7 66.3 319.7

0.000001

0.002

0.007

0.00007

keV, which have large I = 3 strengths, and are predicted in the IBFFM to have an energy greater than 400 keV. The predicted and observed sum of 1= 3 strength shown in Fig. 12 are approximately equal at an energy of 450 keV. While the IBFFM cannot correctly predict the energy of states with large 1= 3 strengths, it reproduces the correct magnitude of total 1= 3 strength to low-lying levels.

P.E. Garrett, D. G. Burke / 1921r

471

0.15

Spin s

E

0.04

0

0.02

;

0.01

1 1

0.10

0.03

g

Spin

E Q B

P

F *

0.0s

m

a

0.00

0.00 0

0.30 x

,

Spin

0.25

t; !z o.20

II :I

Spin 9

10.20

400

500

2

-

F? P

4

-

l-&n-

b m 0.10

300

o.40 I

1

E 0.30

20.,5

200

100

t;

0

0.03

0

0.00 0

200

100

300

400

0.40

0

I

t

Spin

J

X

I

500

2

o.40

X

100

300

200

I

400

Spin

500

3

I

-DI j!iILLll---J $0.30

g 0.30

-

I

6 & 0.20

Ei rr; 0.20

D

s

t;

P

0

_ 0.10 I

“y

Db

,

0

0.40

100

200

300

400

,

I

I

z

Spin

0

500

100

I

,

0.00

200

300

400

300

400

300

0.60

3

QOZIz 8 m 0.13

-

II

100

EXCITATION

ENEkGY

200

(keV)

Fig. 11. Predicted strengths from the IBFFM (bars) and experimental strengths (dots) for negative-parity states populated in the lg31r(d, t)1921rreaction.

The predicted and observed strength distributions for the (d, p) reaction are shown in Fig. 13 for both 1 = 1 and I = 3 transfer for final states with P-values Oto 4-. As can be seen, there are serious discrepancies for the 1 = 3 strength, with

472

P.E. Garrett, D.G. Burke / 19%

1=1

IBFFM

0

100

200

EXCITATION

400

500

ENERGY

(keV)

300

600

Fig. 12. Sum of 2 = 1 and 1= 3 strength predicted by the IBFFM and observed for the lg31r(d, t)lg21r reaction. The predicted I = 1 strength grows at a rate approximately 60% greater than observed, and the discrepancies between the predicted and observed I= 3 strength sum arise mainly from the low-lying 4- states.

some very strong states observed but not predicted. This is best illustrated in Fig. 14, which plots the sum of strengths for the (d, p) reaction for both experimental and predicted 1 = 1 and 1= 3 transfer. The predicted 1= 1 strength is also underestimated, but not as seriously as the 1 = 3 strength. The observed values for the 1 = 3 strengths for most low-lying levels show that the (d, t> I = 3 strengths are approximately the same as those for the (d, p) reaction. The notable exceptions are the levels at 66.3 keV, which has a much larger (d, t) I= 3 strength than (d, p) I = 3 strength (only an upper limit to the (d, p) I = 3 strength could be given), and 240 keV, which had a much larger (d, p) 1= 3 strength than (d, t) I= 3 strength. Assuming that the target wave functions for the (d, p) and (d, t) reactions do not differ significantly, the V*-value for transfer to the 66.3 keV level must be much greater than the U*-value. Since the f 5,2 neutron orbital is expected to lie relatively close to the Fermi surface, the lJ*and V*-factors should be approximately equal. One possibility is that the wave function for the 66.3 keV level has a significant f7,* neutron component, which is expected to lie well below the Fermi surface, and hence have a much larger V*-value. The f7,* states were observed with significant strength in both (d, t) and (d, p) transfer studies on the Pt nuclei [lo]. The agreement between the experimental and predicted magnitude at 450 keV of the sum of (d, t) I = 3 strength would appear to indicate that the exclusion of the f,,* neutron orbital from the calculations is not too serious. However, the possibility exists that with the inclusion of the f,,* orbital, the f5,* strength would be redistributed such that there would be better agreement between the IBFFM calculation and experiment.

P.E. Garrett, D.G. Burke / 1921r 0.04

0.20 Spin

E 0.03 : 10.02

Spin

0

I

10.10 ii

-

;

0.05

n

0.00 0

300

-

400

-

500

1

0

’ 100

n 200

300

1

400

Spin

500

2

9

a 6 d0.10

-

0.00 200

100

Spin $0.15

I

i4

-

0.01

1

$O.lS

-

6

;

473

-

ii ; 0.05

-

E

* rln,

0.00 0

100

nn. 200

300

.A 400

500

0

0.30

100

200

300

400

0.30

Spin 2 rJ 0.20

I

B E VI 0.10 ;

0.00 0

-I 100

3

E cj 0.20 B f z 0.10 I

4-l

0.00 200

300

400

500

0

0.30

100

200

300

400

500

0.50

Spin

3

$ * 0.20

Spin

P

,& 0.40

4

s 2 0.30

6 &

500

!A g 0.20

0.10

0

;

_I 0.10

n.

0.00 0

100

200

300

3

nrl

0.00

400

500

ENE”RG7;00(ke2t)

300

400

500

EXCITATION Fig.13. Predicted strengths from the IBFFM (bars) and experimental strengths (dots) for negative-parity states populated in the lglIr(d, p)“‘Ir reaction.

The very small values for the predicted 1 = 3 strength for the (d, p> reaction suggest that the U2-values for the f5,2 orbital should be greatly increased in the calculations from the present value of U 2 = 0.38. The inclusion of the f2,7 neutron

P.E. Garrett, D.G. Burke / 19%

414

IBFFM --------

Observed

I=’ \?,_J __-’ __-__-,-----’ #’ ,’ ______r..._

s

0

100

200

EXCITATION

/

300

400

ENERGY

1=3

500

I

1

600

(keV)

Fig. 14. Sum of 1= 1 and I = 3 strength predicted by the IBFFM and observed for the lglIr(d, p)1921r reaction. The observed I = 1 strength grows at a rate approximately 60% greater than predicted, and the predicted I= 3 strength is seriously underestimated.

orbital, along with a decrease of the k”-parameter for the f5,2 orbital, may improve the fit to the I= 3 strengths. The discrepancies between the predicted strengths and the calculated strengths are not due to the choice of renormalization parameters. The renormalization parameters are applied to both the predicted (d, t) and (d, p) strengths. For instance, if the parameters for the 1= 1 strength were reduced so that the predictions were in agreement with the experimental results for (d, t) reactions, the agreement with the (d, p) results would become much worse, and vice versa if the parameters were increased. As well, a change in the renormalization parameters would have little effect on the predicted strengths since the proper sum of all strengths must be maintained. A decrease in the renormalization parameter for a particular j-transfer for one final spin must be accompanied by an increase in a renormalization parameter for another spin, thereby effectively cancelling the change in overall strength. Therefore, the discrepancies come from the model calculations themselves, and not from the renormalization. This may also be seen by comparing the relative strengths for some particular levels. For instance, the spin 0 states must be populated with j = 3 transfer. The predictions listed in Table 7, and shown in Fig. 11, for (d, t) transfer show that the lowest-lying O- state, predicted at 112 keV, will have at least five times more strength than other Ostates. This is consistent with the experimental results since only one known Ostate was populated. The spin 3 states which are populated with I = 1 must also have j = 5 transfer. Again, only one 3- state is predicted to have a strong 1= 1 population relative to other spin 3 states, which is consistent with the experimental results. However, the spin 3 states have serious discrepancies with the relative

P.E. Garrett, D.G. Burke / 19’Ir

47.5

1= 5 strengths, since the lowest-lying 3- state should have only 50% more I= 5 strength than some higher-lying 3- states. This is not consistent with the experimental results. The spin 1 levels populated with 1= 3 must involve j = $ transfer, and should be within the model space. An examination of the relative strengths for this case also shows that there is a poor correspondence between predictions and theory. Thus, even with a less stringent test, problems appear with the ability of the IBFFM to reproduce the spectroscopic strengths. 5.2. Discussion of individual leveb In order to obtain good agreement between the theoretical and experimental strengths, the predicted energy and relative position of the states in the IBFFM calculation must be disregarded in some cases. For example, the first 4- state at 66.3 keV has a spectroscopic strength that matches the second 4- state in the IBFFM, whereas the state at 256.8 keV, if it is a 4- state, would be a better match to the strength predicted for the first 4- state in the IBFFM. The assignments of predicted levels to observed ones made in this work are based primarily on the (d, p) and (d, t) strengths. However, in making assignments the relative positions of the predicted states are disregarded only in cases where it is clear that doing so results in a significantly improved agreement. In the following, only states that require special attention, such as those where the relative positions of the predicted states must change, or are of special interest, are discussed. Ground state. The ground state in 1921r has been determined [4] to have spin and parity 4+, and was not populated in the (d, t) or Cd, p) reactions. The IBFFM parameters were adjusted [41 so that the calculation reproduces the ground-state spin, and predicts that it should have vanishing cross section, since it involves d5,2 proton components, and the target primarily has d3,2 proton configuration. 66.3 keVleve1. The first 4- state predicted in the IBFFM comes at an energy of 412 keV, approximately 346 keV higher than the first observed 4- state at 66.3 keV. The next 4- state is predicted at 434 keV and has a better strength match to the observed level at 66.3 keV, and therefore this assignment is adopted. It should be noted, however, that this match occurs for the strength values predicted when the state is at 434 keV and not at 66 keV. If the parameters in the calculation were adjusted so that this state were brought down in energy, it is probable that the wave function would change significantly, thereby changing the predicted strengths considerably. As pointed out above, an examination of the (d, t) and Cd, p) strengths to this level indicates that the V2-parameter must be much greater than the U2-parameter. This would be more in line for an f7,2 transfer rather than f5,2 transfer, as the f7,2 neutron orbital is expected to lie well below the Fermi surface. 84.3 keV level. An interesting situation occurs with the 84.3 keV 3- state. Even though the transfer of j = $, 5, 3, and g would satisfy the angular momentum coupling rules, the Cd, t> cross section to this state appears to be essentially a pure

476

P.E. Garrett, D.G. Burke / 19%

I = 5. The IBFFM calculations for 3- states have essentially no I= 5 strength, and thus no match can be found for the state at 84.3 keV. This is clearly an inadequacy in the calculations. 116.5 keV doublet. The most intense peaks observed in the (d, t) and (d, p) reactions are due to an unresolved doublet of the 115.6 and 118.8 keV levels. The state at 115.6 keV is either l- or 2-, while the one at 118.8 keV is known to be 3-. In the work of Kern et al. [41, the two states were resolved in the (d, p) and (d, t) spectra. At an angle of 45”, the lower member of the doublet was measured to have a Cd, t> cross section approximately 61% greater, and a (d, p) cross section 54% greater, than the upper member of the doublet. Kern et al. [4] favour the assignment of spin 2 for the level at 115.6 keV. The best match to the total strengths for the peak is obtained by assigning the first 2- state predicted at 131 keV to the 115.6 keV level, and the third 3- level predicted at 288 keV to the level at 118.8 keV. With this assignment, the lower member of the doublet is predicted to have approximately three times the (d, t), and five times the (d, p), cross section of the upper member of the doublet. This does not reproduce the observations of Kern et al. [4] for the cross section ratios for these states, and the combined 1= 3 strength is not reproduced. 143.5 keVleue1. The state at 143.5 keV was populated in the (d, t) reaction, but was not observed in the (d, p) reaction. Its (d, t) strength was S, = 0.010 + 0.001 and S, = 0.027 + 0.006. The similarity plots of the -y-ray intensities from this state, in one and two dimensions, favours a spin of 1 (see Figs. 7 and 8). Adopting this, the best match in the IBFFM would be the state predicted at 192 keV, which has Cd, t> strengths of S, = 0.013 and S, = 0.042. The third l- state predicted at 151 keV is predicted to have a large (d, t) 1 = 1 strength, and is therefore not a good candidate. 278.0 keVleve1. Kern et al. [4] reported a level at 278.0 keV having an I”-value of 3- or 4-. In the (d, t) spectra, there is evidence for a weak peak at this energy with an angular distribution that would be consistent with an I = 5 transition with S, = 0.34 + 0.05. Since there are no 3- states in the IBFFM with significant 1 = 5 strength, the model favours a spin of 4 for this state. However, a spin of 3 cannot be ruled out on this basis since the model failed to reproduce the observed 1 = 5 strength to the level at 84.3 keV. 288.5 kevdoublet. The peak observed at an energy of 288.5 keV in the spectra is due to an unresolved doublet of states at energies of 288.4 keV and 292.4 keV. However, the observed energy of the peak suggests that the lower member of the doublet dominates the cross section, and this is supported by the Cd, t) spectrum shown in the work of Kern et al. [4]. Both members of the doublet have either I” = l- or 2-. The similarity plots for the 288.4 keV level favour spin 2. The most appropriate candidate in the IBFFM is the state predicted at 399 keV, with Cd, t) strengths that are in excellent agreement with the observed value, but the Cd, pl strength is seriously underestimated.

P.E. Garrett, D.G. Burke / 1921r

471

319.7 kel/ level. The state observed at 319.7 keV in both the (d, p) and (d, t) reactions has I” = 2-. The angular distribution for this peak in the (d, t) reaction had to be fitted with both I= 1 and 1= 3 curves, yielding strengths of S, = 0.144 f 0.010, and S, = 0.098 + 0.043. The (d, p> angular distribution appeared to be a pure I = 1 with strength S, = 0.178 k 0.005. The IBFFM predicts a 2- state at 438 keV with S, = 0.082, S, = 0.066 for the (d, t> strengths and S, = 0.026, S, = 0.007 for the (d, p) strengths. This is a very poor match to the observed strengths, but there are no unassigned 2- states in the IBFFM that would give a better agreement. 331.7 keV doublet. The peak at 331.7 keV, which was observed in both the (d, p) and (d, t) spectra, is due to an unresolved doublet of levels at 331.1 and 331.8 keV, with I”-values of 2- or 3-, and l-, respectively. Kern et al. [4l favour the assignment of spin 2 for the former state, and the similarity plots also favour this. The (d, t) angular distribution for this peak was fitted with a pure 1= 1 DWBA curve, yielding a strength value of S, = 0.159 + 0.005. The (d, p) angular distribution also resembled that of a pure I= 1 with S, = 0.164 5 0.006. Since the two levels lie so close together, the amount of strength to each is not known, and it is not possible to make firm assignments with states in the IBFFM. However, there is the restriction that the sums of the predicted strengths match the observed strengths for the peak, and that they have only 1 = 1 strength. Since there is no 2level left unassigned that predicts significant 1 = 1 strength, it is implied that in order to match the observed strength, most of it would have to come from the spin l- level. The only candidate that meets this requirement and lies relatively close in energy is the l- level predicted at 277 keV, which gives S, = 0.161, S, = 0.0004 for the (d, 0, and S, = 0.029, S, = 0.00007 for the (d, p> reaction. For the 2- level, the best candidate is the one closest in energy to the observed state, at 400 keV, which has Si = 0.007, S, = 0.010, and S, = 0.002, S, = 0.001 for (d, t) and (d, p) reactions, respectively. While this result agrees with the observed (d, t) strength, it seriously underestimates the (d, p) strength. However, there are no other unassigned states remaining that would give better agreement with the (d, p> strength. 367.2 keVdoublet. The peak observed at 367.2 keV is due to unresolved levels at 366.7 and 368.4 keV, both of which have spin 2-. The (d, t) angular distribution appeared to be mainly I= 3, with strength S, = 0.245 & 0.018, and a small amount of I= 1, with S, = 0.037 & 0.003. The (d, p) angular distribution appears to be that of an I= 1 transition, with S, = 0.054 + 0.002. There are no candidates in the IBFFM for 2- states that would match the observed (d, t) 1 = 3 strength. A plot of both the experimental and theoretical energies is shown in Fig. 9 where the connecting lines are based on the above assignments. Figs. 15 and 16 show the experimental and theoretical (d, t) strengths for I= 1 and 1 = 3 transitions, and Figs. 17 and 18 show the (d, p) I= 1 and I= 3 strengths, respectively, based on the above assignments. It is clear that the IBFFM does not give a complete description of 1921r* , it can , however, approximately reproduce the struc-

478

P.E. Garrett, D.G. Burke / 1921r

Excitation

Energy

(keV)

Fig. 15. Predicted strengths from the IBFFM (bars) and experimental strengths (dots) for negative-parity states populated with I= 1 transfer in the 1931r(d,t)‘921r reaction based on the assignments in Fig. 9. In the abscissa are reported the experimental excitation energies.

tures for some of the low-lying states. The discrepancies of the model with the Cd, p) strengths are greater than those with the (d, t> strengths, which may indicate the need to adjust the v/-parameters used in the calculation. The calculations also suffer from the neglect of the f7,2 neutron orbital. In 193Pt, the pickup strength for j = s is greater than that for j = : transfer [lo], and so it is expected that there is also significant f 7,2 transfer strength into 1921r.

0.60 0.50 i!

0.40

biz

0.30

m nr

0.20

2

0.10 0.00

Excitation

Energy

(keV)

Fig. 16. Predicted strengths from the IBFFM (bars) and experimental strengths (dots) for negative-parity states populated with I = 3 transfer in the 1931r(d,t)19’Ir reaction based on the assignments in Fig. 9.

P.E. Garrett, D. G. Burke / lp21r

Excitation

Energy

(keV)

Fig. 17. Predicted strengths from the IBFFM (bars) and experimental strengths (dots) for negative-parity states populated with 2 = 1 transfer in the “‘Ir(d, p)1921rreaction based on the assignments in Fig. 9. In the abscissa are reported the experimental excitation energies.

Another problem with the IBFFM calculations for 1921r, as pointed out by Cizewski [31], is that the number of bosons in the core, N, is severely truncated. Typically, the wave functions for the SO(6) core states have components with different numbers of d-bosons, ad, due to the terms in the h~iitonian that change fzd by + 2. For example, Of states may have components with Q = 0, 2, 4,. . . , N - 1

0.50

1

,

6_L 1p11r(d.p~p21r

E 0

0.40

2

0.30

-

t; m il

0.20

-

-

0.10

-

/

z

0.00

Excitation

Energy

(keV)

Fig. 18. Predicted strengths from the IBFFM (bars) and experimental strengths (dots) for negative-parity states populated with I = 3 transfer in the “‘Ir(d p)‘921r reaction based on the assignments in Fig. 9. ’

480

P.E. Garrett, D.G. Burke / 19%

or N. When a single fermion is coupled to the core, the boson-fermion interaction, which can change IZ~by f 1, will cause the wave functions to have components with values of nd possibly ranging from 0 to N. Therefore, there will be a great degree of fragmentation of the single-particle strength. By truncating the number of bosons in the core, the number of components in the wave functions are truncated, and thus the degree of fragmentation may be reduced. The wave functions written in Kern et al. [4] for some low-lying states in 1921rshow that all but one of the allowed n,-values (from 0 to 4) are present as main components in the wave function. The energies of the levels predicted and also the electromagnetic properties of the core may be reproduced by renormalization of the parameters, but the fragmentation of the single-particle strength cannot. It would be interesting to compare the results of the present experimental work with a full IBFFM calculation that did not truncate the number of core bosons.

6. Interpretation in terms of the Nilsson model 6.1. Nihon

model calculations

The Nilsson model has been one of the most successful models developed for nuclear structure. It can describe a wide variety of nuclear phenomena, and is relatively easy to use. It has been applied to many of the rare-earth nuclei which have a well-defined deformed shape. In the A = 190 transitional region, it has been applied to the OS, Ir, and Pt nuclei with varying degrees of success. Single-neutron transfer studies [32-341 showed that the Nilsson model worked reasonably well for some of the states in 189,191,1930s,although there are some discrepancies, but had only limited success [35,36] in 195,197Pt. Single-proton transfer studies [37] of 191,1931r showed that the Nilsson model was able to describe the low-lying proton states in these nuclei. One of the difficulties that the Nilsson model cannot overcome is a proper description of the core. The large number of states observed in nuclei in this region may be related to the effects of y-soft cores and triaxiality [38,39]. For instance, in 1910s there is a total of 22 $ - and : - states found [l] below 1300 keV. The Nilsson orbitals plus the various couplings of yand p-vibrations can account for nine states. It is possible that the introduction of other degrees of freedom in the core may explain these states. Not including these degrees of freedom puts a limitation on the model, but the inclusion of effects such as -y-softness introduces [40] a great deal of complication and takes away from the simplicity of the model. The Nilsson model calculations performed in this work used values of K and /-L equal to 0.0637, 0.600, respectively, for the protons and 0.0636, 0.392, respectively, for the neutrons. The quadrupole deformation, S,, was taken as 0.18 for all states. It is possible that some of the states observed are based on different deformations,

P.E. Garrett, D. G. Burke / ‘921r

481

but at the present time there are no data indicating what the deformations are for individual levels, and therefore 6, is not used as a free parameter. In many studies of odd-odd nuclei with single-nucleon transfer reactions, the Coriolis matrix elements are calculated only between configurations involving the target orbital, which is assumed to be a pure Nilsson state. The assumption is also made that the nucleon in the odd-A target acts only as a spectator in the reaction. These assumptions are not strictly true. There can occur Coriolis mixings in the target ground state and also in the final state between different proton, and neutron, orbitals. In the present work, all low-lying configurations that have been identified were included in the Coriolis and particle-particle coupling calculations. This has very important consequences since configurations not involving the dominant target orbital can, in some cases, have significant mixings with those involving the target orbital. Thus, states which in a first approximation would not be populated, can have significant transfer strength as a result of the admixed amplitude in the final state. The Coriolis and particle-particle matrix elements of ref. [41] were used, where the Cl?-coefficients were determined in the Nilsson calculation outlined above. The Coriolis attenuation factor, p, was set to 0.65, and the unperturbed energies of the Nilsson orbitals and their rotational parameters, @/2x, were taken as free parameters. For each spin, I, a matrix was set up using the Nilsson wave functions as a basis, the unperturbed energies along the diagonal, and the various coupling matrix elements off-diagonal. This matrix was diagonalized, and the resulting eigenvalues and eigenvectors represented the energies and wave functions of the states. Included in the calculations were the $‘[402], & i-[510],, $‘[402], +‘[400], f +-[512],, and the - ;‘[402], + 5 -]5121,, +‘[400],, f i-[510],, + ;-[5051,, ;+ [402], + $ -[503],, s +[402], + g -[503], configurations. The effect of a mixed target ground-state configuration was also included, as outlined in ref. [421. The spectroscopic strength is calculated using the equation

+

VW - 1)h-1’2(zi- Krin[zfK)])2+jl.

(7)

The factor (lr7,) is the parity of the target and Pvn is the pairing factor which is U,, for stripping reactions and V,, for pickup reactions. The factor at,, is the amplitude of the two-quasiparticle configuration present in the wave function, and a( is the amplitude of the Nilsson configuration in the target wave function. For the spectroscopic strength calculations performed in this work, the target groundstate wave function was taken as -0.125(~+[400],) + 0.992($+[402],) for 191*1931r,

482

P.E. Garrett, D.G. Burke / 1921r

10000 b $ g : d

1000

100

B E

10

E 1 0

100

200

300

EXCITATION

ENERGY

400

500

(ksV)

Fig. 19. Low-energy portion of the 1931r(d,t)19*Ir spectrum obtained at 45” with a beam energy of 18 MeV. The peaks are labelled with their dominant Nilsson configurations where A = :‘[402],, B = ~‘[400],, C = $-[510],, D = z-[512],, E = q-[505],, F = z-[503],, and G = G-[503],.

as determined by Coriolis coupling calculations that reproduce the low-lying energy spectrum for these nuclei. Kern et al. [4] have interpreted some of the levels in terms of the Nilsson model. These interpretations were based mainly on selection rules applied to the y-rays connecting states and on transfer cross sections. The results of the single-nucleon transfer study of the present work give data complementary to those of Kern et al. [4], and provide evidence for the main components in the wave functions. The low-energy portion of the 1931r(d t)19*Ir spectrum is shown in Fig. 19, where the peaks are labelled with their dominant Nilsson configurations assigned in the present work. The Nilsson assignments are also shown in Fig. 20, where a “rating” of (Y or p is given on the assignments for particular levels. The a-rating is for levels where the assignments are reliable, the P-rating for levels where the assignments are tentative. In making assignments with the Nilsson model, the similarities of population strengths to states in different nuclei were taken advantage of. For instance, information regarding the configurations in i9’Ir obtained from single-proton transfer [42,43] could also be applied to states in i9*Ir that had similar (d, t> strengths to those in 19’Ir. As an example, the three lowest states in “*Ir (at 56.7, 66.3, and 84.3 keV) were populated with 1 = 1 and 3, 1 = 3, and I= 5 transitions in the (d, t) reaction, and have I”-values of l-, 4-, and 3-, respectively. In 19’Ir, the three lowest levels populated in the (d, t) reaction [441 have 1 = 3, I = 1, and 1 = 5

P.E. Garrett, D. G. Burke / 19%

$ [4021n

; [40217T

*;

; WI,,

[512] y

o-.3

t"z

389.7

483

; [4001fl $

[5051"

B

l-2 ,g 3-.4 278.2

O-.2 240.2 p 2-.2

a

l-2 ,-.I

4+

292.4

@

~

B

192.9

115.6

[512] y

a3-.3 116.8 -o-.1

O-.0

128.7 104.5

a

2-.2 225.7

l-.2 143.6

c( a

3-.3

84.3

o(

56.7

ff

lg21r +

;

[4021,

y

[6151

I/

Fig. 20. Interpretation of levels in 1921r in the Nilsson model as suggested in the present work. The a-ratings are for levels where the assignments are definite, the P-ratings are for tentative assignments.

transitions of similar strengths to those in 19*Ir, and have been assigned I” = 4-, l-, and 3-, respectively. Of the three lowest levels in 19’Ir, only the l- state was populated in the c3He, d) and (a, t) reactions. The cross section in the single-proton transfer to the l- state was small compared with the largest peaks in the spectrum, which have as their dominant neutron the i-[512], orbital (the target wave function is approximately 0.95($ -[512]) + 0.3(+-[510]), and a logical assignment is the : +[4021, - i -[510], band head. This is consistent with the assignment of Kern et al. [4] for the corresponding l- state at 56.7 keV in 19*Ir. The lowest-lying 3- and 4- states in lWIr which are not populated in single-proton transfer, do not involve the +-[512] 6r the i-[510] neutron orbitals. Consistent with this, the presently adopted assignments for the lowest 3- and 4- levels in “‘Ir 1 discussed below, do not involve the $-[512] or the i-[5101 neutrons. 6.2. The ground state The ground state in 19*Ir has been previously assigned as having I” = 4+, and was not populated in the (d, t) or (d, p) reactions. The only neutron orbital that can give a 4+ band head when coupled with the $ +[402] proton is the 9 +[6151, orbital. In single-neutron transfer, this would be populated by an I= 6 transition, which has it maximum cross section near 50” in the (d, t) reaction. An upper limit on the ground-state (d, t) cross section of 1 kb/sr can be given at this angle, which

484

P.E. Garrett, D.G. Burke / “‘lr

yields an upper limit on the strength of S, < 0.02. This is well above the calculated value of S, = 0.001 for this configuration. In the work of Kern et al. [4], the ground state is assigned as a mixture of the 9 -[505], - t -[512], and - 5 +[402], + $+[6151, configurations based on the analysis of the magnetic moment. Therefore, as with the IBFFM calculation, in order to explain the static properties of the ground state, configurations must be mixed for which the coupling matrix elements usually considered, i.e. the Coriolis or particle-particle coupling matrix elements, vanish. The K = 4 rotational band built on the - 5’[402], + $+[615], configuration should have the Z = 5, 6, and 7 members populated via 1 = 6 transitions with strengths of N 0.36, 0.16, and 0.04, respectively. While these would be extremely difficult to detect with the (d, t) or (d, p) reactions since the intrinsic 1= 6 cross section is very small relative to the 1 = 1 or 1= 3 cross section, in the C3He, cy) reaction the 1= 6 intrinsic cross section is much larger. Therefore, peaks which are strongly populated in the C3He, a) reaction but weakly (or not observed) in the Cd, t) reaction probably involve 1 = 6 transitions to the +‘[402], f ?[615], configuration. The spin 5 member of the ground-state band would be expected to lie between 200 and 300 keV (assuming a rotational parameter between 20 and 30 keV). Assigning the peak observed at 143 keV, which was strongly populated in the C3He, a> reaction but only weakly in the (d, t) reaction, to the spin 5 member yields a rotational parameter of only 14 keV, which is much lower than would be expected. As well, a spin 5 state at this energy would probably lie in the decay path of the 9- isomer since an 18 keV M4 transition would compete favourably with the 161 keV E5 transition to the ground state, and thus a 143 keV transition from the 5+ state to the 4+ ground state should have been observed with the half-life of the isomer. Therefore, it is unlikely that the peak observed at 143 keV in the C3He, a) reaction is a spin 5 state, and thus the spin 5 member of the ground-state band is probably one of the peaks observed between 200 and 300 keV. However, there are several candidates for this level, such as the peaks observed at 245, 281, and 298 keV, and it is not possible at the present time to make an assignment. The spin 8 member of the K = 7 band based on the $‘[402], + +‘[615],, configuration should be one of the largest peaks in the (3He, a) spectrum since its 1= 6 strength is calculated to be N 0.53. Therefore, the peak at 482 keV, which is the largest peak in the (3He, (u) spectrum, is tentatively assigned as the spin 8 member of the K = 7 band. 6.3. The $+[402/,

f f -[.510],, configurations

The 3-[510] neutron orbital forms [45] the ground state in “‘Hf, is3W, and and 189,191,1930s. It is 185,1870s,and also occurs at low energies in 183Hf 185,187~, therefore expected to be present at low energied in 1921r. It can couple to the %‘[4021, orbital to form K” = l- and 2- bands, with the K” = l- band head

485

P.E. Garrett, D.G. Burke / 19%

Table 8 Experimental model

and predicted

spectroscopic

Nilsson configuration

$+[402],+

;-[510],

K”

I

l-

1 2 3 4 2 3 4 3 4 0 1 2 3 4 1 2 3 4 2 3 4 1 2 3 4 0 1 2 3 4 4 5

2-

;+[402],+

;-[512],

3o-

; +[4001, f ; -]5121,

1-

;+]400],&

2-

;-[512],

f +[4001, + f -[5101,

1-

o-

5 +[402], f ; -[503], ;+[402],+ ;-[503],

45-

Energy (IreV)

(d, t) strength for states in 19’Ir assigned in the Nilsson

I = 3 Strength

I = 1 Strength observed

predicted

56.7 115.6

0.097(7) - 0.24 a

0.081 0.106 0.042

192.9

0.114(3)

0.113 0.111

-

observed

predicted

0.056(31) - 0.18 =

0.013 0.095 0.151 0.081 0.020 0.030 0.095 0.140 0.049

- 0.12 a

118.8

- 0.14 a

0.110

128.6 104.5 240.2 389.7

0.039(2) 0.061(2) 0.089(3) < 0.046 ’

0.029 0.054 0.012 0.030

143.5 292.4

0.010(l) < 0.173 c

0.002 0.013 0.002

0.027(6)

225.7

0.066(5)

0.055 0.000

0.065(21)

(235.8)

< 0.04 b < 0.096 ’

0.002 0.023 0.007 0.001 0.000 0.000 0.000

66.3 256.7

0.216(g) 0.509(28)

0.043 0.055 0.163 0.005 0.000 0.032 0.000 0.017 0.002 0.000 0.010 0.0005 0.005 0.008 0.020 0.001 0.003 0.000 0.003 0.558 0.472

I= 5 Strength Observed ;+[402],+

;-[505],

3-

3 4

83.8 278.2

a Strength estimated from cross-section ratio of two states in the doublet. b Upper limit to strength from fit to angular distribution. ’ Total strength for unresolved doublet given.

0.553(38) 0.34(5)

Predicted 0.488 0.188

486

P.E. Garrett, D.G. Burke / 19’Ir

expected to lie lower in energy from the Gallagher-Moszkowski [46] rule. With a deformation of 6, = 0.18, the wave function for the $-[510] neutron orbital contains j = 3 and j = 3 components with amplitudes of 0.67 and 0.61, respec-

Table 9 Experimental model

and predicted

spectroscopic

Nilsson configuration K” ;+[4021,+

$-[510],

l-

2-

;+[402],+

3-[512],

30-

++[400],+

; f[4001,

+-[512],

* 3 -[5121,

l-

2-

I

Cd, p) strength

Energy

I= 1 Strength

CkeV)

observed

1-

0-

;+[402],+ ; +[402],

;-[503], + ; -[503],

;-[505],

predicted

0.057 0.028 0.028 0.060 0.074

< 0.27 a

0.050 0.101 0.054 0.011 0.030 0.062

< 0.27 =

0.093

56.7

< 0.224 a

192.9

0.075(3)

3 4 0 1 2 3 4

118.8

< 0.224 a

0.073

128.6 104.5 240.2 389.7

< 0.03 b < 0.04 b 0.073(7) < 0.046 a

0.019 0.036 0.009 0.020

0.011

0.073

0.031

0.21(4) < 0.096 a

0.020 0.028 0.109 0.003

1

143.5

< 0.02 b

0.001

0.000

2 3 4

292.4

< 0.175 a

0.008 0.000

0.015 0.000 0.011

2

225.7

0.041(2)

0.029

0.001

0.000

0.000 0.005

1 2 3 4 0 1 2 3 4

(235.8)

0.001

0.000

0.013 0.005

0.002 0.005 0.013

0.000 0.000 0.000 0.000

4-

4

66.3

5-

5

257.6

3-

in the Nilsson

observed

115.6

$+[402],*

predicted

1

0.0580)

in 19’Ir assigned

I= 3 Strength

2 3 4 2 3 4

3 4 f +c[4001, + ; -[5101,

for states

3

a Total strength for unresolved doublet b Estimated upper limit to strength.

83.8 given.

0.001 0.002 0.000 0.002
b

0.372

0.43105) 0.202 I = 5 Strength observed

predicted

< 0.25 b

0.262

P.E. Garrett, D.G. Burke / “‘Ir

A-C

487

CALCULATED

A+D

0

1=1

1=3

P T i T

s i

0.25

A+C

-B+D

A-D

2

1

0

1

2

2

B+D

3

Li 3 a”

Fig. 21. Strengths observed in the ‘931r(d, t)1921r reaction (dots) compared with Nilsson-model predictions (bars) taking into account Gxiolis coupling and effects of mixed target ground states. The states are labelled with their dominant Nilsson configuration, with A = 3’[402],, B = ~‘[400],, C = f -[510],, and D=:-[512],. Data points with arrows are upper limits, and those with no error bars have an uncertainty smaller than the size of the data point. The theoretical strengths shown for the doublet at 116.5 keV are the sums of the strengths predicted to each member.

tively. Therefore, the spectroscopic strength to rotational-band members based on this neutron configuration should have both I = 1 and 1 = 3 components. The l- state at 56.7 keV was assigned by Kern et al. [4] as the 3 +[4021, - i-[510], band head, with the 2- member at 115.6 keV. The assignment of the 2- member was based on the strong Ml + E2 y-decay to the l- band head, and also on its large single-neutron transfer cross section. This assignment is adopted in the present work. The results of the calculations described above are presented in Table 8 and Table 9, where the experimental strengths are listed along with the theoretical ones, and shown in Fig. 21 and Fig. 22 for the (d, t) and (d, p) reactions, respectively. Both the (d, t) and (d, p) strengths to the l- member of the K” = l- band are well reproduced. The 2- band member is predicted to have almost equal amounts of 1 = 1 and I= 3 strength. Unfortunately, it is part of an unresolved doublet, and thus the strengths to each level were not determined. However, when an attempt was made to deconvolve the doublet in the (d, t) spectra, the results indicated that the lower member had N 70% more cross section than the upper member. This is consistent with the results of Kern et al. [4] where the two levels were resolved. If the assumption is made that the 1= 1 strength is divided between the two unresolved members in the same ratio as the cross sections, the resulting strengths are S, = 0.24 for the 2- state and S, = 0.14

P.E. Garrett, D. G. Burke / 1921r

488

A-C 0.50

CALCULATED

A+D 3

0 A-D

EXCITATION

ENERGY

1

1=1 1=3

(keV)

Fig. 22. Strengths observed in the “‘Irfd p)19’Ir reaction (dots) compared with Nilsson-model predictions (dars). See caption to Fig. 21.

for the upper member of the doublet. The strength predicted to the 2- state is far less than the value obtained from the deconvolution of the doublet. The 3- member of the K” = l- band would be expected to lie below 300 keV but there are no obvious candidates. The state at 257 keV was not populated in the ARC measurements, and is probably a 4- or 5- state. The state at 267.1 keV could have a spin of 3; however, the similarity plots favour a spin of 2 and its cross section is much too small for it to be a reasonable candidate for the 3- member of the band. Therefore, the higher spin members of the band are not assigned. The K = 2 band was not identified in the work of Kern et al. [4], and it is suggested in the present work that the 2- state at 192.9 keV is the band head. This state was populated with a strong I = 1 transition, and also has a very strong Ml y-transition to the l- state at 56.7 keV, and a weaker y-transition to the 2- state at 115.6 keV. The K” = 2- band head is expected to be populated with a strong 1 = 1 transition (the 1 = 3 component is much smaller) in both the (d, t) and (d, p) reactions. The level at 192.9 keV has (d, t) and (d, p) 1 = 1 strengths that match the predicted strengths extremely well. The levels observed at 212.6 and 240.2 keV also would be appropriate matches to the predicted (d, t) strengths, but are poorer matches for the predicted (d, p) strengths. The higher-spin members of this band were not identified. 6.4. The : +[402], f $-(5121,

configurations

The i-[512] neutron orbital forms [45] the ground state of ls3Hf, 185P187W, and 189,1930s, and therefore should lie low in energy in 19’Ir. It can couple to the

P.E. Garrett, D.G. Burke / 19%

489

$‘[402] proton orbital to form both a K = 3 and a K = 0 band, with the K = 3 band expected to lie lower in energy from the Gallagher-Moszkowski rule. With the value of S, used in this work, the $-15121 neutron orbital is calculated to have an amplitude of 0.4 for j = t and 0.8 for the j = 2 components, respectively. Thus, the population of states involving this neutron orbital will contain both I = 1 and 1 = 3 components. In the work of Kern et al. [41, the K” = 3- band head was assigned at 118.8 keV, while the K” = O- band head was assigned at 128.7 keV, with the l-, 2-, and 3- members at 143.6, 212.8, and 267.1 keV, respectively. In the present study, the K” = 3- band head assignment of Kern et al. 141was adopted. The 3- state at 118.8 keV was populated strongly in the Cd, t> reaction with both I= 1 and I = 3 transitions, and also in the (d, p) reaction. The calculations indicate that the state should be populated with 1= 1 and 3 transitions of comparable strength. The combined (d, t) strength predicted for the doublet at 116.6 keV, based on the above assignments, is S, = 0.216, S, = 0.235. For the Cd, p) reaction, the predicted strength to the doublet is S, = 0.115, S, = 0.143. Therefore, the calculations account for N 67% of the observed strength. The higher-spin members of the K” = 3- band have not been assigned. Assuming that the rotational parameter is between 20 and 35 keV, the 4- member of the band would be expected between 280 and 400 keV. A possible candidate for the 4- member is the state at 256.7 keV. However, its energy is rather low, and its strength is much too great. It is possible that the 4- member is part of an unresolved doublet, as there are several peaks between 300 and 400 keV that have significant I = 3 strength. The K” = O- band is expected to exhibit a strong Newby shift [47] with the lmember actually lying lower in energy than the O- state. The only known spin 0 state in 19*Ir is at 128.7 keV. It is populated with an 1= 1 transition with 5, = 0.039 + 0.002 in the Cd, t) reaction, and has an upper limit of S, < 0.03 in the Cd, p> reaction. The spin 0 state of the K” = O- band is calculated to have a (d, t) strength of S, = 0.029, and this agrees well with the experimental result. Kern et al. [41had assigned the l- member at 143.6 keV, but this state is too weakly populated in the Cd, t> reaction, with S, = 0.010 + 0.001 and S, = 0.027 + 0.006, to belong to the K” = O- band. The l- state at 104.5 keV has an (d, t) 1 = 1 strength of 0.061 + 0.002, which agrees much better with the predicted value of S, = 0.054, and is the only reasonable candidate for the l- member. It is also predicted to have a small I= 3 component, but a fit to the angular distribution with both I = 1 and I = 3 curves was not favoured by the F,-statistic. An upper limit of S, = 0.04 was determined for this state, which is just below the value of 0.043 predicted. There are several possible candidates for the 2- member of the band, but the 240.9 keV level is preferred. It has a strong y-transition to the l- level at 104.5 keV, a large transfer strength, and a spin of 2 is favoured by the similarity plots. By considering the y-decay characteristics, the 3- member of the band is assigned at

490

P.E. Garrett, D.G. Burke / lg21r

389.7 keV. These last three states were assigned by Kern et al. [4] as the - +‘[400], + 5 -[5121, configuration. However, the predicted strengths for this configuration are much less than observed for the levels at 104.5 and 240.9 keV. 6.5. The $ +[402], k p -[505],

configurations

The G-[505] neutron orbital occurs [45] at low excitation energy in ig90s and forms the ground state in 19iOs, and is therefore expected at low excitation energy in 1921r. This orbital originates from the h9,2 shell, and thus its wave function is dominated by the j = 4 component. The coupling to the $‘[402] proton orbital will give rise to K” = 6- and K” = 3- bands, with the K” = 6- band head expected to lie lower in energy. These orbitals would be populated in single-neutron transfer reactions with I = 5 transitions, since the wave functions remain rather pure. A strong I= 5 transition was observed at 84.3 keV in the (d, t) reaction (see Table 1). This state was determined to have I” = 3- by Kern et al. [4], and therefore it becomes the logical candidate for the - $‘[402], + s-[505], configuration. The expected strength for the K = 3 band head is S, = 0.488, which is in excellent agreement with the value S, = 0.553 f 0.038 observed. The 4- member of the K” = 3- band may be located at 278 keV, which can be identified with the level at 277.99 keV reported by Kern et al. [41with spin I” = 3- or 4-. In the (d, t) spectra there is evidence of a very weak peak at this energy, but only a partial angular distribution could be obtained since at many angles impurities cause it to be obscured. The angular distribution that is obtained is consistent with that of an 1= 5 transition, with a strength of S, = 0.34 k 0.05. This is a factor of two greater than would be expected for the 4- member, but it gives a reasonable rotational parameter of y 25 keV for the band and is the only higher-spin state in the work of Kern et al. [4] that decays to the 84.3 keV band head. From the Gallagher-Moszkowski rule, the K = 6- band head is expected to lie lower in energy than the K = 3- band head. However, it is very unlikely that the K = 6 band head lies lower than 161 keV since it would probably be in the decay path of the spin 9 isomer, as discussed in ref. [4]. As well, the K = 6 band head, expected to be populated with a strong I = 5 transition, was not detected in the (d, t) reaction below 200 keV. Therefore, there must be some coupling mechanism not accounted for in the present work that causes the Gallagher-Moszkowski rule to be broken. 6.6. The 4 +[4001, f $ -[512],

configurations

The $ +[400] proton orbital has been identified [37,45] in 191Y1931r at low excitation energies (82 and 73 keV, respectively), and coupling to the 3 -[5121 neutron orbital will give low-lying K T = 1- and 2- bands. Kern et al. [4] assigned the - $‘[4001, + +-[512], configuration to the levels at 104.8 keV (l-), 240.9 keV (2-), and 389.7 keV (3-). However, the present work has reassigned these levels to

P.E. Garrett, D.G. Burke / 1921r

491

the t +[402], - $ -[512], configuration. Since the +‘[400], amplitude in the target wave function is much smaller than that of the $‘[402], orbital, it is predicted that configurations based on the $ +[400] proton are only weakly populated, unless there is extreme final-state mixing with orbitals based on the $ +[402] proton. The level at 143.6 keV has either I” = l- or 2-, and the value of 1 is favoured by the similarity plots. In 19’Ir, a level at a relative excitation energy of 144.0 keV was populated [42] with similar Cd, t) strengths to the state at 143.6 keV in 1921r. Based on this similarity, it is considered likely that the two states have the same configuration. The level at 144.0 keV in 19’Ir was populated quite strongly in the single-proton transfer reactions, and thus the i-[512], orbital, which is the major component of the ground state of the target of 1890s, is the dominant neutron component. Since the states are only weakly populated in the single-neutron transfer reactions, the most likely configuration is - ~‘[400], + $-[5121,. Assuming an amplitude of 0.125 for the ;‘[400], orbital in the 1931rground state, the predicted (d, t) strengths to the band head in 1921r are S, = 0.002, S, = 0.0004. While these values are far less than observed for the state at 143.6 keV, there could be additional mixings with states not included in the calculations, that would increase the strength. The 2- band member would be expected between 200 and 280 keV, and is probably weakly populated. There are several candidates that meet these requirements. For instance, the state at 267.1 keV has an I”-value of Cl-), 2-, or 3-, with the similarity plots favoring the spin 2 assignment, and is populated weakly in the (d, t) reaction. There is also a 1- or 2- state at 292.4 keV, again the similarity plots favouring a spin of 2, that is part of an unresolved doublet in the Cd, t) and (d, p) reactions at 288.5 keV. The other level in the doublet has an energy of 288.4 keV, and thus the 292.4 keV state is weakly populated. This is consistent with the result of Kern et al. [4] where a weakly populated state was observed at 294 keV. The 143.5 keV state is not fed by a y-transition from the level at 267.1 keV, but is fed from the 292.4 keV level. Therefore, the 292.4 keV level is tentatively assigned as the 2- member of the K” = l- band. The K” = 2- band based on the +‘[400], + +-[512], configuration would also be weakly populated unless there is a significant amount of mixing with a configuration based on the 3’[402], orbital. This may occur if the unperturbed states are situated close in energy. An estimate [48] of the Gallagher-Moszkowski splitting, based on average values observed in this mass region, is on the order of 100 keV, so the K” = 2- band head should be between 200 and 280 keV. Once again, there are several states that would be candidates, such as the 212.8 keV level (similarity plots favour spin 21, the 225.9 keV 2- level, the 267.1 keV level (again, similarity plots favour spin 21, and the 288.4 and 292.4 keV levels, both of which are favoured to have spin 2 from the similarity plots. The level at 288.4 keV is too strongly populated to be a reasonable choice, since a strength of S, = 0.173 + 0.005 would require the dominant component to be built on the +‘[402],

492

P.E. Garrett, D.G. Burke / 19%

orbital, and the level at 292.4 keV was assigned as the 2- member of the K” = lband. Calculations for the strength were performed for each of the possible candidates, and it was found that the best agreement was achieved assuming the 2- band head was placed at 225.7 keV. The predicted (d, t> strengths are S, = 0.055, S, = 0.002, and the (d, p) strengths are S, = 0.029, S, = 0.001. The 2level at 225.7 keV has (d, t) strengths of S, = 0.066 f 0.005, S, = 0.065 f 0.021, and (d, p) strength of 5, = 0.041 f 0.002. The state at 212.6 keV is populated as strongly in the (d, p) reaction as in the (d, t> reaction, and has an 1= 1 strength that is much larger than is predicted. No higher-spin members of the band can be assigned at this time. 6.7. The $ +[400/, f + -[510],, configurations It is expected that weakly populated K” = l- and K” = O- bands based on the +‘[400], f i-[5101, orbitals should exist at low energies. From the GallagherMoszkowski rule, the K” = 1- configuration should lie lower in energy. A possible assignment for this state is the tentative l- level at 235.8 keV, which was not observed in the present work. Calculations indicate that the (d, t> strength to the K” = 1- band head would be S, = 0.002, S, = 0.0005, which would make its detection by single-nucleon transfer practically impossible. It is not possible at this time to assign the higher-spin members or the K” = O- band. 6.8. Possible interpretation for the 4 - state at 66.3 keV and the probable 4 - or 5 state at 257.6 keV The peak observed at 66.3 keV was populated with a pure I= 3 transition in the (d, t> reaction with strength S, = 0.216 A 0.008. As discussed previously, the value I” = 4- is favoured for this state. An examination of the Nilsson diagram indicates that there are two possible configurations that yield a K” = 4- band which would be populated with essentially pure I= 3 transitions, i.e. the i +[400], + z -[503], and $‘[402], + g -[503], configurations. The g-[503], orbital has been identified The %-[503], orbital [451 as a hole state at low excitation energies in 187,189P1910s. has been identified [45] as a particle state in 187W and ls70s at approximately 600 keV, but it may fall rapidly in energy with increasing neutron number. The 3 +[400], + ; _[503], configuration would not be expected to be populated strongly in the single-neutron transfer reactions since the amplitudes of the 3’[4001, orbital in the targets are small. Assuming a V2 = 0.6, the $ +[4021, + s -[5031, configuration is predicted to have a (d, t) strength of S, = 0.56, whereas only = 0.22 was observed. The predicted (d, p) strength is 5, = 0.37, but an upper limit for the I = 3 strength to the level at 66.3 keV is S, < 0.1. Therefore, it appears that the 5 +[4021, + $-[503], configuration is somewhat fragmented. A mixture of the ; +[4021, + ; - [5031, and ;‘[400], + G-[503], configurations would be necessary

P.E. Garrett, D.G. Burke / 1921r

493

to reproduce the strength. However, the particle-particle coupling matrix element is only 1.6 keV, and thus the extreme mixing that would be required cannot be reproduced in the present work. A strong I = 3 transition was observed to populate the level at 257.6 keV, with S, = 0.509 f 0.028 in the (d, t) reaction and S, = 0.431 f 0.015 in the (d, p) reaction. As explained in a previous section, this state is probably 4- or 5 since it was not observed in the ARC experiments of Kern et al. [4]. Possible interpretations for this state would be the I = 4, K” = 4-, $ +[402], + $ -[503], configuration or the I = 5, K” = 5-, 5 +[402], + 3 -[503], configuration. Since it was shown above that a fragment of the K” = 4- configuration may be needed to explain the 4state at 66.3 keV, the remaining part may be placed at 256.7 keV. The other possible interpretation that could explain the strength is the K” = 5-, 3’[402], + 3 -[503], configuration. As seen in Table 8 and Table 9, this configuration can approximately reproduce the (d, t) strength, but underestimates the (d, p) strength by a factor of 2. These suggested assignments for the 66.3 and 256.7 keV levels must be considered as speculative, since there are problems reproducing the observed strengths, and the spin of the 256.7 keV level is not known.

7. x:-Tests for the transfer strengths In the IBFFM comparison with the experimental data, a total of 14 renormalization parameters was applied to the spectroscopic strengths obtained from Paar and Brant [20]. These parameters were determined from an examination of the strength distribution for each j-transfer to final states with angular momentum Ir, In view of the renormalization, it is necessary to establish goodness-of-fit criteria to test the significance of the models’ ability to reproduce the data. The goodnessof-fit test used in this work is the ,y,” defined in ref. [lo], where

(Si-Sth)2,

x,2= AE lJ

i

Ui2

(8)

where ZJis the number of degrees of freedom. The test was performed for each reaction where the results are interpreted in terms of the IBFFM. As a comparison, the test was also performed for the Nilsson model interpretation, In order to have a meaningful x:-value, the uncertainties gi must be determined for each strength, and should include the statistical uncertainty as determined from the least-squares fitting procedure, as well as the systematic uncertainty introduced by the DWBA calculation. For states that have strengths that are (5-lo>% of the largest strength observed in the reaction, the reaction mechanism may have significant contributions from multistep processes which are not de-

494

P.E. Garrett, D. G. Burke / Ig21r

scribed by the DWBA calculations. For strong transitions it has been found that the reproducibility of relative strengths is typically within G-10)%. Therefore, a reasonable estimate of the systematic uncertainty is approximately 10% of the largest strength observed in the reaction [lo]. The uncertainty for each data point was a, = i-Y--? uifit+ (O.lS, ) where Sf is the largest strength observed in the reaction for the particular value of 1. The number of degrees of freedom used in the test is the number of strengths minus the number of parameters. The spectroscopic strengths calculated with the IBFFM depend on the wave function for the state and the renormalization constants, but all of the model parameters were fixed by fitting neighbouring nuclei or determined by the energy and static properties of the lowest-lying positive- and negative-parity state. Therefore, the only parameters that were fitted to the strengths were the renormalization parameters in Table 6, and these were determined from only the Cd, t) strengths. For the IBFFM, all states were included in the x:-tests up to an energy of 331.7 keV for the “‘Ir(d, p> and ‘931r(d, t> reactions. The energy cutoff was used because above these energies, there were many states that were not interpreted in the model. It should be noted that two levels with 1= 5 transitions, at 83.8 and 278.2 keV, which the model should have been able to interpret since the h9,2 orbital was included, were included in the x:-test. As well, for the interpreted states all the theoretical strengths were included regardless of whether strength was observed for that particular I-value. Included in the x:-test for the Nilsson model were all states which were interpreted, including the states at 66.3 and 256.7 keV. No constants in the Nilsson model were allowed to vary in order to get a better fit. The results of the xt-test for each reaction and model are listed in Table 10. As can be seen, the x:-values are large for both models, implying that neither model gives an acceptable fit. The values for the Nilsson model x,2 would increase greatly if all the states below 300 keV which were not interpreted in the model were also included in the calculation. It should be pointed out that the states predicted by the models were sometimes shifted in energy to correspond to the experimental energies. However, this

Table 10 Results of X:-test

for *“Ir v

2 X”

36 30

27 30

23 5.6

21 19

21 19

5.5 3.0

Reaction

Number

IBFFM lg31r(d, t) lglIr(d, P> Nilsson Model “lItid, PI a Includes strength

lg31r(d, t)

upper limits to experimental was observed.

of data points

strengths

*

and theoretical

strengths

for which no experimental

P.E. Garrett, D.G. Burke / 1921r

495

procedure was used for both the IBFFM and the Nilsson model predictions, and ignoring this additional “parameter” has very little effect on the X,2-values. One drawback in the IBFFM calculations is the absence of the f7,2 neutron orbitals, even though in the neighbouring odd Pt isotopes, significant amounts of j = 3 strength were observed [lo]. In the x2-test for the present case, states populated with j = ;, I= 3 transfer should not be included, but at the present time there is no available experimental information to distinguish states populated with j = 5 or j = g from each other. However, most of the x:-value reported for the IBFFM calculation arises from the 1= 1 strength which should have been explained by the model. Thus, even if the x:-test were performed on the I = 1 strength only, the conclusion that the IBFFM gives a poor fit to the strengths would still be valid.

8. Conclusions

The experiments performed in this work have provided many new results concerning the structure of 1921r. Large numbers of levels were observed with the single-nucleon transfer reactions. All the levels observed had negative parity, and most of the angular distributions could be fitted with an I = 1 and/or an 1 = 3 component. However, a low-lying level populated with an 1= 5 transition was observed. The results of the experiments have been compared with two different models, the IBFFM and a simple Nilsson model approach. The IBFFM calculations for i9*Ir were performed by Paar and Brant, and coupled two fermions to an SO(6) core of the IBM. The calculations were performed numerically since no limiting symmetry, other than that of the core, was employed. The results of the calculations predict that the wave functions are very configuration mixed, with a large number of levels predicted to be observed in single-neutron transfer populated with both I = 1 and I = 3 transitions. This was observed, and the number of states lying below 500 keV in excitation energy was approximately reproduced. However, while this is an encouraging result, there remain many problems with the IBFFM interpretation. The predicted energies of the first 3- and 4- states are much too high. The 3- state at 84.3 keV was observed to be populated with a strong I = 5 transition, but no 3- states in the IBFFM calculation are predicted to have significant I = 5 strength. In fact, it is a general trend that the calculations have trouble reproducing the spectroscopic strengths to individual states. This was clearly illustrated in Figs. 15-18. The Nilsson model calculations show some promising results, but there is an indication for the need of a more complicated treatment. The neutron orbitals expected to be populated at low excitation energies, namely the i-[510], and the z -15121, orbitals, have very similar spectroscopic strengths, especially when the

496

P.E. Garrett, D.G. Burke / 19%

effects of Coriolis mixing are taken into account. There are many levels populated in the single-neutron transfer reactions which have strengths that would be a suitable match to the predicted strengths for the two orbitals mentioned above. The problem of identifying rotational bands involving these orbitals is furthermore compounded by the fact that the spin > 2 members were not identified. The - $‘[402], + ~75051, configuration has been identified at low excitation energies. Interestingly, the K” = 3- band comes lower in energy than the K” = 6band, and thus the Gallahger-Moszkowski rule appears to be broken for this configuration. The results of the present calculations which take into account the Coriolis and particle-particle coupling cannot reproduce this. A state at 66.3 keV populated with a strong I = 3 transition has been assigned I” = 4-. This level is very interesting since in the simple Nilsson model only a mixture of the 3’[402], + $-[503], and +‘[4001, + i-[5031, band heads could explain the strength. However, the mixing between these two configurations is expected to be quite small, and the calculations of the present work cannot account for the degree of mixing required to explain the spectroscopic strength. Configurations based on the +‘[400] proton and the i-[510] and +-[5121 neutron orbitals have been tentatively identified. The population of configurations in single-neutron transfer reactions involving the +‘[400], orbital occurs because of Coriolis mixing in both the target and the final states. It is possible that a more sophisticated treatment of levels within the Nilsson model would better reproduce the levels observed in the reactions. If one assumes a constant deformation, the number of predicted l- and 2- states are depleted before all of the observed l- and 2- levels can be accounted for. A changing deformation or a non-axial deformation might be responsible for a structure more complex than predicted by the simpler approach used in the present work. However, at the present time there is no specific information regarding the nuclear deformation. The authors would like to thank Deborah Garrett for drawing all of the angular distributions, Tao Qu for his participation in the experiments, and Jean Kern for his careful reading of the manuscript. Jim Stark also played a very important role by preparing targets and by providing high quality beams with excellent stability from the tandem accelerator. Financial support was provided by the Natural Sciences and Engineering Research Council of Canada.

References [ll H.G. BBmer,R.F. Casten, I. Forster, D. Lieberz, P. von Brentano, S.J. Robinson, T. von Egidy, G. Hlawatsch, H. Lindner, P. Geltenbort, F. Hoyler, H. Faust, G. Colvin, W.R. Kane and M. MacPhail, Nucl. Phys. A534 (1991) 255

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