Multiple band structure and band termination in 157Ho towards complete high-spin spectroscopy

NUCLEAR PHYSICS A

Nuclear Physics A545 (1992) 665-719 North-Holland

Multiple band structure and band termination in "Ho Towards complete high-spin spectroscopy

D.C. Radford, H.R. Andrews, G.C . Ball, D. Horn and D. Ward

AECL Research, Chalk River Laboratories, Chalk River, Ontario, KOJ 1.10 Canada

F. Banville, S. Flibotte', S. Monaro, S. Pilotte 2 and P. Taras

La',oratoire de Physique Nucléaire, Université de Montréal, Montréal, Quebec, H3C 3J7 Canada

J.K. Johansson, D. Tucker 3 and J.C . Waddington Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, LSS 4K1 Canada M.A. Riley

Department of Physics, Florida State University, Tallahassee, Florida 32306, USA

G.B . Hagemann

The Niels Bohr Institute, University of Copenhagen, Tandem Accelerator Laboratory, Roskilde DK-4000, Denmark

I . Hamamoto

Department of Mathematical Physics, Lund Institute of Technology, P.O. Bo;: 118, S-221 00 Lund, Sweden Received 7 February 1992 Abstract : Rotational bands o157 Ho have been populated via the' 24Sn(37CI, 4n) reaction at beam energies of 155 and 165 MeV. Gamma-ray spectroscopy was performed using the 87r spectrometer at Chalk River. Many rotational bands have been observed for the first time. A detailed level scheme is presented, containing approximately 380 transitions, and the quasiparticle structure of the various bands is discussed . Band termination has been observed in the yrast states. For strongly coupled bands, B(M1)/B(E2) transition strength ratios are extracted and compared with previous measurements and theoretical expectations. Branching ratios for out-of-band E2 transitions are analysed to extract band mixing interaction strengths. Implications for rotational damping are considered. The interaction at the first backbend in the ground band is found to be strongly signature dependent ; this is evidence for a signature-dependent triaxial shape of the nucleus . E

NUCLEAR REACTIONS 124Sn(37CI, 4n) l57 Ho, E =155, 155,165 MeV; measured Ey, yy-coin ., .157 rotational band characteristics, band-mixing Iy (0, 0) Ho deduced levels, Ex , I,, J, parity, strengths. interaction

Correspondence to: Dr. D.C. Radford, Chalk River Laboratories, Chalk River, Ontario, KOJ 1JO Canada . Present address : Centre de Recherches Nucléaires, B.P. 20, 67037 Strasbourg, France. 2 Present address : Physics Department, University of Ottawa, Ottawa, Ontario, KIN 6N5 Canada . 3 Present address : AECL Research, Chalk River Laboratories, Chalk River, Ontario, KOJ 1.10 Canada . 0375-9474/92/$05 .0^ © 1992 - Elsevier Science Publishers B.V. All rights reserved

666

D.C. Radford et al. / Multiple band structure

l . Introduction

S4 Recent experimental investigations of the even-even N=90 isotones `Gd 4)] have revealed a large number [ref. ')],' s6 Dy [ref. 2 )],' ss Er [ref. 3)] and 160Yb [ref. of interesting rotational sequences, many of which have been assigned as twoquasiparticle bands. "Band termination", or a change from prolate collective to oblate noncollective structures, was also observed 5,6) in yrast or near-yrast bands at spins near or above 40tî. Such structures have not yet been observed in the odd-proton isotone '57 Ho. In earlier y-ray studies of this nucleus' - '°), only four rotational sequences were observed . These were assigned as the 2 -[523] (ground band) and, tentatively, the 2}[404] or z }[402] band '°). Particle transfer reaction studies of '57 Ho [ref. ")], however, identified single-proton states which could serve as band heads for a variety of other rotational bands. Band termination has been predicted 6,'2) at spins near or below those of the highest states previously observed . Gamma-ray branching ratios and mixing ratios have been measured for the ground band of '57 Ho [refs.',$)] and used to deduce transition strength ratios B(M1 ; J-3-J-1)/B(E2 ; J->J-2) and Q' iQ2-

V

B(E2; I --~J-1) (JK20; J-2K) B(E2 ; J~J-2) (JK20; J-1K)

At low spin, below the first backbend, these ratios show significant signature splitting, which has been interpreted as evidence of triaxial deformation '3,14) . However. certain aspects of the data have proven very difficult to reproduce in both cranking '4) and particle-rotor '3) calculations ; in particular, the large signature splitting and average value of the Q,/Q2 ratios seem to be inconsistent with the observed signature splitting of the transition energies . In an attempt to resolve some of these discrepancies betwen experiment and theory, and to search for additional rotational bands and band termination, we have performed an extensive y-ray spectroscopic study of '57 Ho. At the time of the experiment, we were developing several new tools for the analysis of yy-coincidence data (see sect. 3 .1). Our ' 57Ho results were made a test case for these new procedures, so that a particularly thorough analysis has been performed. Preliminary results have been described previously "). We have assigned over 300 new transitions to this nucleus and observed a total of ten previously unreported rotational sequences . Branching and mixing ratios have been measured for many of the observed bands, and the results at low spin in the ground band show significant discrepancies when compared to those of refs.',$). The yrast band was found to undergo band termination at a spin of z h. Sect. 2 of the present paper gives experimental details . Analysis procedures are described in sect. 3 and results are presented in sect. 4. Possible assignments for the quasiparticle structure of the observed bands are discussed in sect . 5, together

D.C. Radford et al. / Multiple band structure

66 7

with discussions of transition strength ratios, band mixing, and the observed band termination states, and comparisons of these data to theoretical expectations . 2. Experimental details

The nucleus '57 Ho was produced for study by means ofthe 124Sn(37Cl, 4n) reaction . Gamma-ray spectroscopy was performed using the 81r spectrometer '6) at the Chalk River TASCC facility. This instrument consists ofan inner ball of 71 BGO scintillator detectors, surrounded by an array of 20 Compton-suppressed HPGe detectors. The HPGe detectors are arranged in four polar rings of five each, at angles 0 = 37°, 79°, 101" and 143° with respect to the beam direction. For the present experiment, the event trigger included a threshold on the BGO ball fold (i.e. the number of detectors firing in prompt coincidence) of at least 10. During replay, a software threshold on this fold was set to 15. Three slightly different experimental conditions were used in the present experiment. In the first run, an unbacked target of thickness 1 .0 mg/cm2 was bombarded at a beam energy of 155 MeV, and a total of approximately 85 x i06 yy-coincidence events were recorded . A second run at 165 MeV, t.sing the same target, produced approximately 22 x 106 events; these were added to the data at 155 MeV for analysis of the coincidences to determine the level scheme. In a third run, also at 155 MeV, a 0.9 mg/cm2 target evaporated onto a gold backing of thickness 14 mg/cm2 was used, and approximately 45 x 106 events were recorded. The first two runs were designed to observe states to very high spin and thus used the unbacked target to avoid Doppler-shift attenuation effects. However, analysis of the angular correlations for these data showed that the lowest levels were experiencing vacuum deorientation, with consequent loss of alignment. The third run was therefore designed to avoid this with the use of the backed target. These data were not used for determination of the level scheme ; they were analysed only for the angular correlations with respect to the spin axis . In addition to the number (ID)., energy and time of each responding HPGe detector, the event stream as written to magnetic tape included : (i) The total energy H and fold K in the BGO ball; (ii) A "hit pattern" for the BGO ball, for detectors with deposited energy in the range 600 < EBGo <1600 keV. The above BGO ball information was derived arithmetically from only those BGO detectors which passed a digital timing window set approximately 25 ns wide relative to the average BGO time. 3. Analysis procedures 3.1. LEVEL SCHEME

In order to extract coincidence relationships and intensities, the unbacked target data, gated by H and K, were replayed into a 4k x 4k channel matrix, which was

66 8

D.C. Radford et al. / Multiple band structure

then symmetrised . A copy of this matrix was processed by subtracting a twodimensional background, using the prescription of ref. "), and correcting for relative detector efficiencies . "Gates", or spectra in coincidence with specific y-ray peaks, could then be rapidly inspected by simply adding the rows of the matrix between the specified channel limits. ore detailed analysis was facilitated by the use of the programs GF2, MATFIT and LF8R "'). GF2 is a program that can fit a portion of a spectrum with up to fifteen peaks on a quadratic background . It was used to fit all the peaks in contiguous segments of the one-dimensional matrix projection, over the range 60-1400 keV. The yy matrix, without the background subtracted, was then fitted using a semiautomatic least-squares procedure (MATFIT) to extract the intensities and energies of all possible coincidences between these peaks . The program does not attempt to fit the coincident energies for pairs of peaks that are not in coincidence, i.e., peaks that have a coincidence intensity of less than twice the uncertainty. The results obtained from MATFIT formed a data base, which could be inspected and processed by the program LF8R. With this program, the user can quickly and easily inspect the coincidence results for any y-ray peak, perform logical and arithmetic combinations on the results for different y-rays, and "tag" peaks with their assignments as the level scheme is constructed . This last option serves as a powerful mnemonic and documentary aid, since it identifies all assigned y-rays, and warns of doublets and higher-order multiplets. Coincidence relationships for the many contaminated peaks (i .e. y-rays where the gated spectrum contains contributions from more than one transition ; doublets, etc.) were generally inspected by requiring the listed -y-rays to be in coincidence with at least one additional peak. As the analysis proceeded, a level scheme file describing level energies, spins and parities, and transition energies an% ï t ,sties, was created and updated . This file was read by the program LF8R, which could then calculate expected coincidence intensities on the basis of the proposed intensities, branching ratios and conversion coefficients . The file included data on all bands which could be observed with significant intensity in the matrix, whether or not they were assigned to '57 Ho, so as to correct the calculated results for all known contaminating coincidences . Least-squares analysis was performed on the data base of MATFIT results to extract the most likely transition intensities. The program allowed fitting of up to 500 intensities simultaneously. Final analysis to extract the optimum intensities and energies was performed using the program ESCL8R. This program allows fast and easy inspection and fitting of the yy matrix, making use of parameterized values of the peak shape, peak width, and detector efficiency and energy calibrations. It makes use of a prescription for two-dimensional background subtraction similar to that of ref. "), and reads and updates the level scheme data file described above. All of this information is used to calculate predicted gate spectra, which are then compared to the observed spectra. That is, the program works backwards from the proposed level scheme, and attempts

D.C. Radford et al. / Multiple band structure

669

to reproduce the observed yy matrix . Least-squares fits to the matrix may be made to extract the energies and intensities of transitions in the level scheme ; as for MR, the program allowed fitting ofup to 500 parameters simultaneously. It was necessary to use intensity balances to extract the intensities of a few low-lying transitions (see table 2). . The program ESCL8R was able to reproduce the observed data to a gratifying degree of precision; a global fit for all of the '57Ho transitions yielded a reduced X2 of less than 1 .4. An example of a gate on one of the strongest and most complex peaks (at 424 keV) and the difference between the calculated and observed spectra are presented in fig. 1. Over 300 new transitions have been added to the level scheme in the present work. These were assigned to ' 57Ho either on the basis of their coincidence relationships with previously assigned transitions 7-'°), or on the basis ofthe observed EGO ball H and K associated with them and their coincidence with Ho X-rays . Since evaporated particles remove energy which would otherwise appear in the form of y-rays, each reaction channel has a characteristic sum energy and y-ray multiplicity

n

300

500

E .y (keV)

700

900

Fig. 1. Partial spectrum from a background-subtracted gate centered at 424 keV. The upper portion of the figure shows, on the same vertical scale, the difference between the observed spectrum and that text calculated by the program ESCL8R using the y-ray energies and intensities listed in table. ?. See for details .

67 0

D.C Radford et al. / Multiple band structure

associated with it. Nevertheless, since protons and neutrons do not differ a great deal in the energy they remove from the nucleus, it is not possible to unambiguously separate, for example, the p3n and 4n channels on the basis of H and K alone. owever, the H e array of the 87r spectrometer has sufficient efficiency at low energies to allow elemental identification in this mass region by means of X-ray coincidences. 3.2. ANGULAR CORRELATIONS WITH RESPECT TO THE NUCLEAR SPIN

"Spin orientation" '9), or the determination of the azimuthal angle Os of the spin vector in the plane perpendicular to the beam axis, has been used to determine angular correlations of y-rays measured in the H e detectors with respect to the spin axis. This event-by-event technique relies upon the mam, stretched-E2 -Y-rays produced by high-spin fusion-evaporation reactions. Since these y-rays are preferentially emitted perpendicular to the spin axis, the method looks for a plane of hits in the BGO ball; the most likely spin direction is then taken perpendicular to this plane. The GO ball detectors responding to y-rays are input by means of the hit pattern mentioned above, with the energy window set to enhance the relative number of stretched quadrupole transitions. In this analysis, only those HPGe detectors at 8,, = :±79* are used, since those at ®y = _+37° have little sensitivity as a function of ( .0,, - Yes) . The events are sorted into ten bins of equal width in ((A,, - 0s ). Distributions for strong y-rays of known stretched-E2 character were fitted to a sum of Legendre polynomials to deduce substate populations as a function of spin. The width of these popul-ations was independent of spin, within experimental uncertainties, and the mean was therefore used in later analysis to extract mixing ratios for strong, uncontaminated MI/E2 transitions. New transitions, previously unassigned to '57Ho, were generally assigned a stretched quadrupole or stretched dipole nature on the basis of their distributions with respect to the spin axis. In some cases of weak or contaminated transitions, no unambiguous assignment could be made; in others, parallel y-ray branches served to determine the multipolarity.

4.

exults

The level scheme of I i7 Ho, determined from the present work, is presented in fig. 2. Table 1 lists level energies and spin-parities, and table 2 presents the assigned y-ray energies, intensities, multipolarities and mixing ratios, for transitions where these could be determined with reasonable certainty. The intensities are determined from the coincidence data by the procedure outlined in sect. 3.1 above. Dashed or broken lines and parentheses in the level scheme indicate tentative assignments.

D.C. Radford et al. / Multiple band structure

16

671

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Fig. 2. The level scheme of 157 Ho deduced from the present work. Dashed or broken lines and braces indicate tentative assignments. The width of the indicated transitions is proportional to the relative intensity ; filled space represents y-ray intensity, open space represents intensity carried by internal conversion. For clarity, the figure is broken into three portions . The inset in the first portion shows the lower part of band 1 on an expanded vertical scale. Some levels of band 1 are reproduced in the second portion so that the decay of the other bands into them may be indicated . The excitation energies of the levels are listed in table l, and energies and intensities of the transitions are listed in table 2.

D.C. Radford et al. / Multiple band structure

672

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The following sections present more detailed results for each of the bands, using the labelling scheme of fig. 2 (bands 1 to 10). 4.1 . BANDS 1 AND 2

Examples of spectra from gates on bands 1 and 2 are presented in fig. 3a . The yrast states of 157 o were first observed in in-beam w-ray spectroscopy by Grosse et A20) , and later extended by Hagemann et aL 7,8) and Simpson et al. 9.1° ). The strongest branches in our proposed scheme for bands 1 and 2 agree with the scheme

D.C. Radford et al. / Multiple band structure

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Fig . 2-continued

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D.C Radford et al. / Multiple band structure TABLE

Ex (keV)

J 7r

Band 6-continued 47+ 5399.3(3) 2 49+ 5777.0(3) 2 51+ 6163.1(3) 253+ 6557.3(4) 2 55+ 6961.0(4) 57+ 7377.7(5) 2 59+ 7808.3(7) 2 61+ 8252.5(6) + 8713 .6 (13) 65 + 9192.5(8) z (t7+ 9688.4 (16) (69+) 10203.4 (11) (10734.9 (20)) ( L1 ` ) (z3+) 11280.6 (17) 2

(z )

Band 7 525 .5(4) 654 .45(13) 873 .4003) 1179.63 (15) 1569.57 (17) 2036.78 (18)

s2 92 132 17-

,1 z 25-

675

1-continued

Ex (keV)

2573 .62 (21) 3173 .25 (24) 3822 .9(3) 4512.70) 5234.3(4) 5986 .9(4) 6782 .4(6) 7621 .5(9) 8510.5 (11) 9449.4(16) 10439.8 (19) 11482.5 (27) a8 53.10 (17) 203 .6007) 374.59(18) 566.62 (19) 786.71(23) 1002.38 (23) 1276.0(6) 1489.2(3) 1822.1(8)

JIr

29z 33z 37z 412 452 49532 5'

(62' ) (z5- ) ( )) (z_ 5+ 2 7+ 2 9+ 2 11+ 13+ z 15+ 2 (17+) 2 19+ 2

(21+)

Ex (keV)

J 7r

2022.4(3) 2589.7(5)

23+ 2 (27+)

Band 9 174 .67 (15) 358 .11 (13) 661 .87 (14) Band 10 910 .09 (24) 1342.45 (18) 1852.10 (16) 2405.41 (12) Miscellaneous levels 1695.58 (17) 1861 .8(3) !055.78 (18) 2156.93 (23)

(i*+ ) (2 ) (11+) 2

152 192 23-

2 272

19+ 2

( 2 +) (23+)

predict a strong 1016-1117 keV coincidence for which we observe no evidence . The sudden departure of the yrast level energies from a smooth behaviour as a function of spin is understood in terms of "band termination" ; see sect. 5.4 for details. The 1154 and 1368 keV transitions at the top of our scheme have not been previously reported ; both of these transitions are only tentatively assigned stretched-E2 multipolarity, as they are too weak for spin-orientation analysis . With the additional states above and below the crossing of bands 1 and 2, there are many possible branches for decay of the states both in-band and out-of-band . Most such branches are indeed observed, though some only tentatively. B(E2)/B(E2) ratios deduced from the measured branching ratios provide highly accurate information on the strength of the interaction between these two bands; see sect. 5 .3 for a detailed discussion of the results. Values of B(M1)/B(E2) and Q1 / Q2 , deduced from the measured y-ray branching and mixing ratios, are presented in table 3 and in figs. 4 and 5. For band 1 and signature a = - 2, these ratios are in significant disagreement with the results of Hagemann et aL 7.8). The discrepancies arise from differences in the cascade-tocrossover branching ratios, and are discussed in ref. -'1 ; . Due to the large signature splitting, the measurements are very sensitive to the efficiency calibration at low

D.C. Radford et al. / Multiple band structure

676

TABLE 2 Observed transitions in Energy (keV)

a)

a)

h)

Intensity

211 .52(9) 214.50 (13) 215-6606) 218 .94(6) 220.10 (20) 222 .4603) 223 .8(4)

12.3 (15) 7l.0 (40) 5.5(5) 99.0 (50) 0.46 (12) 1.03 (13) 0.13(4) 0.69(12) 0.64 (12) 7.4(4) 2.8(4) 97.0 (40) 3 .9(4) 0.54(8) 2 .54(21) 9.0(8) 4.48 (24) 3.3(3) 139.0(50) 2.9(3) 54.2 (17) 4.6(3) 4.4(3) 1 .34 (18) 4.4(3) 1 .26(25) 15.0(7) 2.22 (21) 3.25 (22) 32.4(ll) 35.4(12) 12.5(5) 4.l7 (22) 0.94(14) 2.75 (18) 1 .42 (13) 1 .33 (13) 4.l0 (20) 1 .l1 (14) 2.46 (19) 1 .28 (24)

228.13 (10) 236.31(7) 236.58 (20) 237.54(3) 237.9(5) 238.99 (20)

4.7(5) 8.5(4) 2.72 (25) 54.2(17) 0.88 (20) 1 .67 (15)

66.96(7) 83.58(3) 99.26(6) 104.490) 107.00) 121.57 (11) !28.9 (5) 129-98(16) 143.0(4) 143-99(5) 144.5503) 148.290) 150.50(8) 154.51 (20) 156.15 (11) 161 .17(6) 162 .72(7) 166 .20(10) 167.45 (3) 170.99(9) 178.72(3) 179.27(8) 180.04(9) 183.44(9) 187.16(8) 187.62 (25) 188-08(5) 192 .03 (10) 201 .92 (11) 202 .69(4) 204 .7(3) 206 .97(5) 210.68(9) 210.7(4)

224,22(4)

20 ! (7)

lti polarity E1 M1 M1 M1 M1 (M1) E2 (M1) M1 M1 El M1 M1 (M1) M1 M1 M1 M1 M1 M1 M1 M1

band

E2 M1 M1 E2 M1 M1 M1 M1 M1 M1 (M1) (El) (M1) M1 E2 M1 'lâl M1 E1 Ml Ml M1 M1 M1

4 5 4 2 4 6

M1

Ho

Initial

4 1 6 1 2 9 7 9 2 6 4 1 8 9 2 4 2 5 1 8 1 6 4 9 5 5 1 8 4 1 2 5 6 5 7 6 8 7 8 4 1

M1

1 :57

i

Final spin

band

spin

7

1 1

7

2 9 2

25 z Il z 37

2 (21) 9

2 2) 35 2 27 z 9

2

15 z 7

2

(22) 31 z 9 33

2

z 13

2 9 2 19 2 29 2 11 2

(z) 27 2 -4i 2

11 z 11

6 1 1 8 7 4 1

6 1 1

8 8 2 4 2 5 1

8

1 6

4 9 5 4 1

2

8

2 35 2

1

13 2 23 31 2 31

2 25 2

13 2 23

2 15 2

13 2 13 2

15 z 33

2 27 2

9 2

33 z

is-2 37 2 17 2 33 i

4

2 7 2 23 2 9

2

35

2 s 2 5 2 9 2 33 2 25 2 9 2 13 2 5 2 7 2 29 2 7 2 31 2 27 2 11 z 7

2 17 2 27 z 9 2

2

(2) 13 2

2 4 6

-0.16(3)

9 2

(M)

1 5 4

-0.21(3)

11

(i)

1

-0.13(3)

2 29 2 7 2

(M)

7 8 4 2

-0.15(5)

2s

2 5 6

8

-0.16(4)

(2)

21 z 33 2 29 2 29 2

9

Mixing ratio

-0.13(5) -0.04(5)

( ) 9 2 11 2 13

2 31 2 25 2 7 2

-0 .10(4)

31 2 33 2 35 2 1s 31 2-

-0.08(6)

DC Radford et al. / Multiple band structure

677

TABLE 2-continued

Energy (keV)

Intensity

241 .38(4) 243.24 (14) 244.13(7) 245.46(3) 246.62 (12) 246.7(3) 255.47 (21) 257.39 (17) 263-02(15) 263.76(3) 264.5(4) 265.37 (22) 267.00 (16) 271 .94(4) 273.5(3) 273.60(4) 275.54 (13) 283.15 (25) 283.8(3) 283.77 (14) 286.4(4) 288.1(6) 29l.30 (13) 291.82 (15) 292.81 (16) 293.85 (20) 296.34(7) 302.40 (10) 303.76 (l l) 303.9(6) 305 .0(4) 305.74(13) 306.23(7) 306.8(3) 308.7(7) 309.23 (22) 310.05(4) 315.74(4) 315.8(4) 316.85(4) 318.9(3) 321.09(4) 321 .5(7) 322.6(6) 323.26(7) 324.58 (21) 327 .0(6) 333.59 (13) 334.27 (20)

14.0(5) 3.l4 (20) 7.7(4) 8l.0 (30) 3.47 (23) 1.l7 (14) 1.63 (13) 1.97 (15) 2.54 (20) 4l.1 (13) 1.01 (16) 2.28 (21) 2.06 (15) 49.3 (17) 2.5(3) 36.6 (12) 3.05 (18) 1.69 (19) 1.9l (23) 3 .40 (22) 0.95 (14) 0.5l (10) 3.6(3) 2.63 (22) 2.67 (22) 2a13 (19) 3.5(3) 4.52 (23) 2.9(4) 0.75 (16) 0.46(12) 3.29(19) 9.2(4) 0.77(8) 0.60(14) 2.l9 (23) 47.9 (15) 98.0 (30) 2.0(5) 3l.9 (10) 2.l6 (19) 21 .0(7) 1 .08 (22) 0 .95 (25) 8.4(4) 3.7(4) 0.72(18) 3.7(3) 3.0(4)

Multipolarity M1 E2

mi

M1 M1

mi mi

M1 M1 M1 M1 M1 mi

E2

mi

M1 M1 M1 mi mi

M1 M1 M1 mi

Mi '1 (El) M1 E2 M1 (MI) M1 E2 E1 M1 M1 M1 E2 M1 M1 E2 M1 E2 M1 E2 E1 M1 M1 M1

Initial

Final

band

spin

band

spin

1 6 5 1 4 2 4 4

2 27

1 6 5

29

4 2 6 4 5 1 1

2 4 4 4 5 4 6 2 3

4

4 7 5 9 5 9 4 7 7 6 3 i 1 4 2 2 8 5 6 4 6 3 3

2 35 2 2 33 2 71

2 31 19 2 37 2 29

2 21 2 29 2 13 2 35 2 35

2 23 2 25 2 3 2 29 34

2

2 29 2 39 2 41 2 272 37

2

37 2

(2) 37 2

(12) 43 2 17 2

13 2 39 2 43 2

21 2 15 2 41 2 43 2 33 2

1

4 2 4 4 4 2 6 4 4 1

1

2

4

4

4

5

4

6

10

3

4 4

9 5 9 6 8

-0.20(3)

32

-0.09(3)

2 69 2 29 2 17 2 35 2 2 19 2 27 2 9 2 33 2 33

2

2 21 2 23 2 37 2 2% 37

3 3

6

-0.08(6)

2 27 2 37 2 39 2 25 35

2

(2) 5 2 (i) 25

2

2 3

2 2

41 2

15 2 31

1

2

29 2

2

i1

7 8 6 3 1

-0.09(3)

33

4

5 2 2 2 8 4 6 1

45 2 2 432

23

Mixing ratio

13 2 2 32 2 2

-0.20(6)

2 21 9

2 z3

192 25 2 i9 23

2

-0 .11(6)

D.C. Radlord et al. / Multiple band structure

678

TABLE 2-continued

Energy (keV) 335.21(15) 337 .81(16) 339.71(13) 341 .21(10) 343.0(8) 344-02(23) 345 .3(6) 345 .6(3) 345 .64(18) 350.8(6) 353.4(3) 353 .9(5) 358 .1(5) 356 .3i (11) 358-66(4) 360-96(8) 361 .48(5) 362 .3(4) 363 .0(3) 364.61(25) 365.3(4) 366.79(9) 367.7(3) 367 .9(3) 369 .73(6) 370.1(4) 373.17(7)

380.0 (12)

3R0.52 (18)

381 .8(6) 381 .96(7) 388 .9(6) 389 .10(5) 389 .94(7) 389.95(7) 391 .3(4) 393 .0(5) 393.75(4) 397.31(7) 397.7(5) 397.8(4) 406 .0(3) 406.3(4)

408 .47 (24) 411 .4(3) 412 .1(3) 412 .5(4) 412 .8(3)

Intensity 2.99(20) 2.77 (18) 4.02(23) 7.9(6) 0.46(12) 2 .00 (23) 0.7(7) 2.8(6) 4.0(6) 0.24(20) 1.76 (21) 1.26(16) 0.39(12) 3.4(3) 36 .1 (12) 14.6(6) 35.7 (12) 1.27 (24) 1.55 (21) 2.31(21) 1 .l9 (16) 10.0(4) 1.99(21) 2.22 (25) 12.8(5) 1 .31 (20)

Multipolarity mi mi mi

E2 M1 M1 M1 M1 mi

(El) E2 M1 (El) M1 M1 M1 M1 M1 E2 M1 Ml E2 M1 mi

0.72 (20)

M1 M1 E2 E2

0.89 (22) 12.1(6) 1.8(3) 26.5(9) 10.0(4) 13.8(6) 2.10(23) 2.0(3) 80.1 (25) 11 .1(4) 1 .l0 (20) 1 .61 (19) 1.80 ;21) 2.1(5) 1.36 (15) 2.5(3) 1.53(21) 1.59 (23) 2.29 (23)

M1 E2 mi M1 E2 E2 M1 M1 E2 M1 M1 (E2) M1 M1 (E2) mi E2 M1 mi

10 .1(4)

4.0 ( 3j,

E2

Final

Initial band

spin

band

spin

4

45 217 2 47

4

43

4

45

3 4

4 6 5 5 5 5 7 5 5 9 3 1 2 2 3 8 4 5 2 2 3 2 4 5 1 2 10 .1 5 1 7 6 4 3 1 2 4 5 3 10 6 10 8 3 5

2 11 2 03 2 43 2 45

49

2 41 2 5 2 29 2 53

2 (27)

37

2 25 2 47

2 33 49 2 11 2 49 2 57 2 35 2 67 2 51 2 49 2 51 2 31 33 2 37 2 27 2 13 2 47 2 29 2 21 2 31 2 53 2 55 2

17

2 51 2 55 2 27 2

53 2

15 2 23 2 23 2 13 2 59 2 51 2

Mixing ratio

2 45 2

3

7

4 6

2 2 41 2 41

5

43

5

47 2 39

5 5 9 5 5

(i)

1 1

i-52 23

1

2

2 25

2 51 22 7

1

2

2

1-52 31

2 3 8 4 5 2

2

3 2 4 5 2 1 1

4 5 1

7 6 4 3 1

2

4 (M)

3

1

(M) 1 8

3 5

-0.17(3)

47 _ 2 7

2

47 2 55 2 31 2 65 2 4-92 47 2 49

+0.09(13)

1/ 2

29 2 33 2 27 2 9 2 45 2 27 2 17 2 27 2 51 2 53 2 13 2 49 2 53 _ 2 (z3) 51 2 15 2

(i) 23 2 9 2 57 2 49 2

-0.15(8)

679

D.C Radford et al. / Multiple band structure TABLE 2-continued

Energy (keV) 414 .4(3) 416 .7(4) 418 .48(8) 422 .02 (22) 422.57 (21) 423 .5(5) 424 .18 (4) 424 .38 (19) 424.39 (10) 426.18 (15) 432.4(3) 435 .76 (20) 438 .54 (13) 440 .10) 440 .4(5) 441 .61(4) 442.7(8) 443 .27(9) 447 .45 (14) 448 .7(8) 449 .66(7) 458 .303) 460.35(6) 463 .4(3) 467.21(7) 469 .4 (14) 469 .89 (20) 470 .9(3) 474.4(6) 477 .03 (20) 479.0(6) 480 .44(7) 483 .20(9) 486 .81 (20) 488 .77(4) 489 .3(6) 495 .27(7) 497 .4(6) 499.60 (11) 501 .30(5) 502 .09 (12) 503 .43(9) 504.88 (25) 509 .66 (19) 512 .74(3) 515 .5(3) 517 .7 (10) 517.87 (20)

Intensity 3.0(4) 1 .5009) 7.2(3) 4.5(4) 5.2(4) 1 .6(3) 15,,?.') (50) 7.8(5) 11 .2(7) 4.3(3) 2.8(4) 2.58 (23) 4.69 (24) 2.90) 1 .65 (25) 33.901) 1 .20) 14.2(6) 5.9(4) 0.76 (20) 11 .6(5) 0.4608) 15 .4(7) 2.8(5) 8.2(3) 0.54 (20 ; 2.93 (22) 1 .55 (17) 1 .2706) 4.2(3) 2.2(3) 14.4(6) 10.0(4) 3.3(3) 72.8 (23) 1 .10) 15 .8(7) 1 .6(3) 9.5(5) 38.403) 9.9(6) 12.3(6) 3.3(3) 8.0(6) 159.0 (50) 3.20) 0.52 (22) 1 .72 (17)

Multipolarity

mi

Ml Ml E1 M1 Ml E2 Ml E2 M1 E2 E2 M1 Ml Ml E2 Ml E2 E2 MI E2 M1 E2 El E2

mi

M1 El M1 E1 E2 E2 E2 E2 E2 (E2) E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 Ml M1

Final

Initial band 10 4 2 4 1 4 1 2 4 2 10 8 2 2 5 2 4 5 2 4 6 3 4 4 7 4 2 6 4 4 6 5 4 8 1 8 4 1 4 2 4 6 5 10 1 5 3 7

spin

band

19

1 4 2 1 1 4 1 2 4 2

2 53 2 13 57

2 33 2 59 2 19 2 $5 2 15

2 63 2

L92

15 z 59 2 31

55 2 37 2 6i 2 33 2

Z-1

63 2 33 2 57 2 17 2 35 2 25 2 65 2 57 23 2 62 is

2 35 2 35 2 35 2 19 2 21 2

(2) 19 2 35 2 37 2 39 2 33 _3s

2 2 35

spin 19 2 55 2 Z

Mixing ratio

-0.1202)

31 2 57 2 15 2 53 2 11 2 61 2

10 8 2

2 57 2 29

1 5 2

2 23

4 5 10 4 6 3 4 2

33 2 59 2 29 2

2 61 2

2 55

2 13 2 33 21 2 63 2

7

4

2

2 5 25

1

4 1

65 2

5 4

2 21

2

5

1 2

g I

8 4 2 4 2 4 6 b

23

10

23 39 2 61 2 13 2

1

4 3

1

2

2 15

1 2 23 25 29 2 21 1 i 2

2 2 9 2

-0.1800)

D.C. Radford et al. / Multiple band structure

680

TABLE 2-continued

Energy (keV)

h)

h)

522 .3(5) 522.76(7) 532.4(5) 532.5(7) 533.20) 536 .84(11) 537 .37(4) 538.56 (16) 541 .82(9) 546 .1(5) 546 .53 (12) 548 .52(8) 552 .59(9) 553 .31 (20) 554.6(8) 560.85 (13) 561 .34(4) 565 .56(4) 566.6(5) 566.90(iî) 567.3(4) 568.35 (11) 574 .71 (13) 577 .6001) 578 .5(5) 580.20 (14) 582.88(4) 586.17 (15) 587.60) 588 .3(5) 5945(5) 593 .2(7) 595 .4(3) 596.81 (14) 598 .55 (12) 599.63 (12) 602.87(5) 606 .0(4)

1.9(5) 17.3(8) 1 .61 (13) 1.24 (25) 2.5(3) 6.80) 47.305) 6.9(4) 11.4(6) 1.40 (24) 9.1(4) 15.6(7) 11 .5(5) 6.5(5) 1 .6(5) 10.4(6) 70.4 (22) 53.2(17) 4.3(4) 22.300) 2.2(3) 12.4(6) 4.6(4) 15 .7(8) 3 .0(3) 10.2(7) 132 .0 (40) 10.1(5) 3.9(3) 3.0(4) 34.4(11) 2.4(5) 3.8(3) 9.7(5) 11 .8(6) 6 .6(3) 44.7 (15) 4.1(8)

610 .6(6) 613 .32(5) 614 .0 (12) 621 .56 (18) 626 .09 (13) 629.40 (18) 630.48(4) 631 .87 (19) 635.64 (11)

2.7(3) 60.0 (20) 1 .6(6) 6.7(4) 11 .5(5) 8.1(5) 103 .0 (30) 8.7(7) 12.0(5)

609 .18 (19)

h)

Intensity

4.0(4)

Final

Initial

Multipolarity

band

E1 E2 E2 Ml E2 E2 E2 E2 E2 (E2) E2 E2 E2 E2 Ml E2 E2 E2 El E2 (E2) E2 E2 E2 El E2 E2 E2 E2 El E2 Ml E2 E2 E2 E2 E2 Ml E2 E2 E2 Mi E2 E2 E2 E2 E2 E2

4 4 5 2 8 7 2 4 4 8 5 4 6 10 10 5 1 2 4 4 8 4 6 4 4 4 1 5 5 4 2 10 6 6 4 7 2 10 4 4 1 10 4 3 5 1 3 6

spin

band

spin

37

2 4

is-

2 Z12 27 2 61 2 23 2 29 2 41 2 39 2 31 2

(il ) 37 2 23 2 37 2 27 2 15 2 29 2 25 2 35 2 17 2 2s 2

( 27 ) 41 2 23 2 27 2 19 2 29 2 27 2 39 2 39 2 33 2 43 2 19 2 39 2 39 2 43 2 33 2 33 2 27 2 39 2 39 2 29 2 23 2 43 2 41 2 41 2 31 2 37 2 41 2

2 17 2 23 2 59 2 i2

8 2 8 7 2 4 4 8 5 4 6 10

9

25

37 2

L5-2

27 2 (17)

1

4 1 1 1 4 8 4 (M)

4 1 4 1 5 6 1 2 1 5 6 4 7 1 1

5 6 1 1

5 3 5 1 1

6

33 2 19 2 33 2 23 2 13 2 25 2 21 2 31 2 15 2 21 2 23 2 37 2 19 2 23 2 17 2 25 2 23 2 35 2 35 2 31 2 i2 17 2 35 2 35 2 39 2

9

Z92-

29 2 25 2 35 2 35 2 2s 2 21 2 39 2 37 2 37 2 27 2 33 2 37 2

Mixing ratio

D.C. Radford et al. / Multiple band structure

681

TABLE 2-continued Energy (keV) 637.94(5) 638.3(6) 639.9(3) 640.95 (15) 642.8(3) 643 .5l (22) 649.69 (14) 650.l4 (14) 654.5(4) 658.5(3) 663.96 (10) 665.2(3) 666.7(6) 669.96 (14) 671.4(3) 674.92 (10) 682.05(6) 689 .3(3) 689 .7(3) 689.74 (17) 691 .7(4) 693 .0(9) 696.13 (15) ~,97.33 (19) 698.74 (24) 700.13 (25) 701 .2(3) 704.32 (10) 716.7(7) 719.4(3) 721 .58 (20) 722.0 (15) 725.60 (14) 730.2(4) 730.69(6) 732.0(9) 734.1(3) 734.4(3) 734.69 (13) 745.1(3) 747.6(5) 752.64 (22) 755.3(3) 758.32 (25) 761.39 (13) 763.78 (20) 766.60 (25) 767.04(7)

Intensity 42.9 (14) 3.3(4) 5.7(4) 10.4(5) 6.5(6) 7.8(6) 5.0(3) 8.4 (5) 3.2(3) 2.96 (24) 18 .3(8) 6.3(5) 2.6(4) 10.0(5) 4.0(4) 15.2(6) 26.7(9) 7.1(7) 7.8(8) 4.7(3) 4.1(4) 1.6(4) 14 .1(8) 8.1(5) 5.3(4) 5.2(4) 4.7(4) 15.3(6) 1 .9(3) 6 .4(5) 3.87 (23) 0.5(5) 10.0(5) 5 .3(5) 35.l (12) 1 .6(4) 10.3 (ll) 8.6(9) 15.5(8) 5 .6(4) 2 .3(3) 3 .28 (22) 5.l(4) 7.0(5) 12.5(6) 7.4(4) 6 .9(5) 24.5(9)

Multipolarity E2 El El E2 E2 E2 E2 E2 E1 El E2 El E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 El E2 E2 E2 E2 El El E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 El E2 E2 E2 E2 >2

Initial band 2 4 4 4 3 3 7 3 4 4 1 4 5 6 3 4 2 5 5 7 6 3 1 5 5 3 6 4 4 4 7 10 6 3 2 5 5 5 4 6 6 7 5 5 4 6 5 2

Final spin 4-52 23 2 45 2 45 z 45 2 43 2 37 z 39 2 27 2 47 2 33 z 21 z 43 z 43 2 47 z 47 2 47 2 !i52 43 2

43-2 45-2

37 2 35 z 29 z 4-52 492 4-52 492 29 2 25 z 45 i 15 i 47 2 51 2 49 2 49 i 47 2 49 2 51 2 49 i Î2 49 2 27 z 51 2 53 z 51 i 53 2 51 2

4 4

9

band

spin

2 1 2 4 3 3 7 1 1 2 1 1 4 6 3 4 2 5 5 7 5 2 1 1 6 3 6 4 1 1 7 1 6 3 2 6 5 5 4 6 5 7 1 5 4 6 5 2

41 2 21 2 43 2 41 z 41 2 i2 33 2

9

is2-

25 2 45 2 29 z i2 39 z 39 2 43 z 43 2 43 2

9

4-12 39 2 37 2 4-12 33 2 31 2 27 2 4.12 45 z 4.12 45 2 27 z 23 2 41 2 11 2 43 2 47 2 45 2 45 z 43 2 4-52 47 2 45 2

45-2

45 z 25 2 47 2

4-92-

47 2 49 2 47 z

Mixing ratio

D.C Radford et al. / jWultiple band structure

682

TABLE 2-continued

Energy (keV)

Intensity

Multipolarity

767 .6(7) 773 .83 (16) 774.4(9)

4.7(7) 6.6(4) 2.30)

14.0(6) 6.5(4) 4.8(4) 1.89 (21) 6.8(4) 5.0(4) 7.6(4) 12 .0(6) 26.0(9) 5.3(4) 9.9(6) 1.75 (23) 1 .1(3) 3.500) 1 .58 (23) 2 .0(5) 11.6(6) 21.2(8) 1 .8(3) 2.0(4) 6.2(5) 9.5(5) 10.7(5) 5.5(4) 3.8(4) 1.3l (20) 11 .5(6) 2.0(6) 19.4(8) 3.7(4) 1.9(4) 1 .4(4) 17.0(7) 4.6(4) 9.3(6) 8.1(8) 2.8(8) 9.5(8) 4.5(4) 0.81 (18) 3.0(6) 3.2(3) 3 .8(5) 8.5(6) 7.4(8)

780.30 (20)

`')

h)

788 .97 (13) 792 .78 (20) 794.2(4) 795.5(4) 797.95 (22) 799.00) 805 .70 (19) 814.34 (15) 815 .79(8) 820.40) 829 .25 (20) 829 .5(5) 837 .5 (14) 838 .6(9) 839.1(6) 839.8(8) 840.12 (19) 842 .86(9) 847 .3(7) 849 .6(8) 851 .3(3) 857.46 (18) 866.12 (17) 870 .8(4) 874 .8(4) 889 .0(7) 891 .36 (17) 894.2 (14) 894.26 (17) 897.3(6) 897.6 (10) 905.3 (11) 908 .43 (11) 915 .0(4) 918 .09 (21) 918 .9(4) 924.1 (13) 926.85 (25) 930.2(4) 938-900 940 .0(6) 942 .5(4) 943 .6(6) 943 .8(3) 946 .3(4)

7.0(4)

Final

Initial band

spin

band

spin

E1 E2 E2

(M) 3 5

1 3

E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E1 E2 E2 (E2) E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 (E2) E2 E2 E2 E2 E2 (E2) E2 E2 E2 (El) E2 E1 E2 (E2) E2 E2 E2 E2 E1

4 (T) 5 7 6 3 5 4 2 6 2 6 6 10 7 5 4 2 6 5 3 5 4 3 6 7 4 (T) 2 2 5 6 2 5 4 (M) 10 5 3 7 6 6 3 4 (M)

19 2 53 2 25 2 53 2 55 2 7s 2 s5 2

i9 2 49 2 21 2 49 2

E2

6

s3 2 55 2 55 2 57 2 57 2 53 2 57 2

il2

23 2 59_ 2 19 2

2

(5 ) 59 2 59 2 55 2 59 2 59 2 57

2

61 2 61 2 L92 61 2 (61) 63 2 79 2 57 2 29 2 63 2

(2)

59 2 65 2 65 2 23 2) 23 2 25 2

61 2

(i5 ) 65 2 23 2 63 2 67 2 19 2

4

6 4 2 5 7 6 3 5 4 2 6 1 1 5 1 7 5 4 2 6 6 3 5 4 3

6 7 4 2 2

1

5 6 2 5 4 1

1 1

3 7 6 4 3 4 1

sl 2

71 2

51 2 42-

2

sl 2 51

2 53 2 53 2 49 2 53 2 27 2 23 2 55 2

ls 2 53

2 55 2 55 2 51 2 55 2 55 2 53 2 57 2 57 2 55 2 57 2

(5i) i92 75 2 53 2 2s 2 59 2 59 2 55 2 61 2 61 2 21 2 19 2 23 2 57 2

(2) 61 2 19 2 59 2 63 2 17 2

Mixing ratio

D.C. Radford et al. / Multiple band structure

683

TABLE 2-continued Energy (keV)

b)

b)

b) b) b)

b) b) b)

b)

b) b)

948 .79 (14) 958.63 (11) 962 .5(9) 964 .7(7) 969 .1(4) 970.2(4) 971 .00 (15) 974.8(9) 977.44(13) 990.5 (11) 995.1(5) 997 .33 (25) 1003 .9(9) 1009.50) 1010.9(8) 1012.6(9) 1015.8(5) 1017.30) 1032.2 (10) 1035.90) 1036.9 (12) 1042.7 (19) 1045.1 (10) 1046.6 (12) 1049.8(3) 1052.0(9) 1052.8 (20) 1053 .6(9) 1063.0(4) 1069.8(5) 1077.2 (13) 1083.9 (35) 1088.2 (2') 1099.2(7) 1111 .8(9) 1112.5(8) 1117.2(4) 1123.8 (40) 1127.8(7) 1138 .2(7) 1153.9 (12) 1159.7 (19) 1183.8 (16) 1367.9(9)

Intensity 13.0(5) 17.9(7) 1.5(5) 4.1(5) 7.0(5) 5.0(5) 14.0(6) 2.0(8) 14.4(6) 0.92 (18) 4.5(5) 8.5(5) 2.3(5) 4.4(4) 2.8(4) 1.5(5) 4.0(4) 6.4(4) 1 .2(3) 8.6(6) 2.1(6) 0.54(18) 2.1(10) 1.7(4) 8.1(5) 3.0(10) 2.0(7) 5.4(8) 5.2 (4) 3 .7(4) 1 .3(3) 0.7(3) 0.5(3) 3.0 (4) 2.5(6) 3.8(9) 5 .2(4) 0.5(3) 2.1(8) 2.2(3) 1 .6(3) 1.3(3) 1.4(4) 1.80 (25)

Multipolarity E2 E2 (E2) E2 E2 E2 E2 (E2) E2 (E2) E2 E2 E2 E2 (E2) (E2) E2 E2 E1 E2 (E2) (E2) E2 (E2) E2 E2 (E2) E2 E2 E2 (E2) E2 E2 (E2) E2 (El) E2 E2 (El) E2 (E2) E2 E2 (E2)

Initial band 2 2 5 10 4 5 2 6 2 7 3 4 3 5 6 5 2 4 6 2 3 7 3 6 4 3 4 4 (T) 2 6 3 3 4 3 (M) (T) 3 (M) (T) 2 3 3 (T)

Transition intensity taken from intensity balance . b) Transition tentative . (M) Miscellaneous levels . (T) Band termination levels. a)

Final spin

band

71 2 63 2 (67 ) 27 2 69 2 69 2

§11

7

(i ) 67 2

(29 ) L52 71 2 47 2 73 2

020 (2) 75 2 73 2 23 2 02 (29)

(2 49

2

(

75 2 51 2

)

8

(2 ) 77 2 83

2-

69 2

(2 55

2 53 2

1

( 29 i92

-

L9-

(z) 2 2 57 2

(2) 87 2 (2) 61 2 65 2

(ZI )

2 2 5 1 4 5 2 6 2 7 3 4 2 5 6 5 2 4 1 2 3 7 2 6 4 2 4 4 (T) 2 6 2 2 4 2 1 (T) 2 1 (T) 2 2 2 (T)

Mixing ratio

spin 67 2 59 2 63 2 23 2 65 2 65 2 57 2 (

63 2

)

(25 ) 61 2 67 2 43 2 69 2 65 2 67 2 71 2 69 2 21 2 61 2 t-52

( (

45 2 71 2 47 2 77 2 73 2 79 2 65 2

) )

(z) 51 2 49 2 75 2 55 2 17 2 75 2 53 2 19 2 83 2 75 2 57 2 61 2 87 2

Ey (keV)

n é

b oa sa yw

W

A

â m

0

A

n

Fig . 3a. Partial spectra from typical clean gates set on transitions in bands 1 and 2. The gates have had the calculated background subtracted. Prominent peaks are labelled with expected coincident transition energies to the nearest keV. An asterisk indicates peaks from known contaminant transitions. In the case of some doublets and higher-order multiplets, more than one transition is expected to be in coincidence with the gating transition with reasonable intensity . In such cases, i..th -m-raim are indicated even Wht[q the are de enerate to the , .nearest keV.

Z

0)

Û

En .61 C 3

aD 0-

v .C U

C C

0

Otp

D.C. Radford et al. / Multiple band structure

685

966

N N 4) Y

W

Y O O Cb

C9

M

O

W O

O

C) O IO

0i

M C C C O

0£L O 0

969ORL t99 OS9 $1#9'£t9 -~

Z£9'0£9 -ç £l9

IL9

Z£9'0£9

O 0 n

C .

OSe99 i49'£î9 0

O O Q

OD

ih

à6£'O£ 6S£'SS£ 9l£ 01£'60£

O 0

9££

K£

Z6Z

tLZ'ZLZ

0 O Co

0

o (a

0 0 ~

0 0 N

1 auuoy0 j ad sjunoo IDN

Z

a rW c 0 U

U

a) c c0 L

250

3

500 700

Ey (keV) 800

e

900

Fig. 3c. As for fig. 3a, but for gates set on transitions in band 4.

600 1000

Sum of

1 700

Gotes

549,542,483 keV

1100

0 C C 0 L U 0 a N C 0 U r Z

Fig. 3d. As for fig . 3a, but for gates set on transitions in band 5.

E., (keV)

n

400

N N

N

1-

.Z

0 11, r

~1

O, di

Ey (keV)

N A

is 41-Pl.

in band 6. Fig . 3e. As for fig. 3a, but for gates set on transitions

n~

600

T'

780,820,875 keV

Sum of Gates

726,798 keV

Sum of Gates

ô

s

A

C . b

v

A

â, ro

0

â

00 00

Z

a a c 0 U

U

C O t

c

150

IA

350

E,y (keV)

10

Ey (keV) 450

550

900

Fig . 3f. As for fig . 3a, but for gates set on transitions in bands 7, 8 and 9.

250

M a

a

n

306,467,753 keV

Sum of Gotes

650

D.C. Radford et al / Multiple band structure

690

O O

0 O

0 O

0

CD

co

0 o C .a C y C O

O O

O O

C 4.

N u

w O O M

C O H

Lr ar

M

bo i..

1O r

O O N

O O N

O

jauuoy: j ad sjunoo }aN

Co M

du

D.C. Radford et al. / Multiple band structure TABLE 3 Deduced values of B(M1)/B(E2) and QI/Q2 for 157 Ho Band

J

E,, (keV) Q-i-J-2)

E,, (keV) (J-J-1)

1

11 2 13 2 15 2 17 2 19 2 21 2 23 2 25 2 27 z 29 2 31 2 33 2 35

188 .1 271 .9 315 .7 393 .8 424.2 488 .8 512.7 561 .3 582 .9 613 .3 630 .5 664.0 696 .1

104.5 167 .4 148 .3 245 .5 178 .7 310.0 202 .7

33 2 35 2 37 2 39 2 41 2 43 2 45 2 47 2 49 2 51 2 53 255 2 57 2 59 2 61 2 63 2 67 2 71 2 37 2 39 2 41 2 43 2 45 2 47 2 49 2 51 2 53 2 55 2 57 2 59 2 61 2

318 .9 366.8 441 .6 501 .3 537 .4 590 .5 637 .9 682 .1 730 .7 767 .0 815 .8 842 .9 894 .3 908.4 971 .0 958 .6 977 .4 948 .8

162 .7 204 .1 237 .5 263 .8 273 .6 316.8 321 .1 361 .0 369 .7 397 .3 418 .5 424 .4 469 .9 438 .5 532 .5 426.2 367.7 246.7

631 .9 650.1 626.1 643 .5 642.8 671 .4 700.1 730 .2 773 .8 799 .0 851 .3 870 .8 930 .2

358 .3 291 .8 334 .3 309 .2

2

3

358 .7 224.2 389.1 241 .4 422.6 273 .6

333 .6 337 .8 362 .3 367 .8 406.0 393 .0 458.3 412.5 517 .7

S e) -0 .15(5) -0 .21(3) -0 .13(3) -0 .20(3) -0.16(3) -0.20(6) -0.13(5) -0.17(3) -0.10(4) -0.09(3)

-0 .04(5) -0.08(6) --0.09(3) --0.08(6) -0 .11(6) +0 .09(13) -0 .15(8) -0 .12(12) -0.1800)

B(M1)/B(E2) (ILN/e - b)2 0.92(6) 0.59(3) 0.65(3) 0.431 (20) 0.57(3) 0.410 (21) 0.59(3) 0.418 (20) 0 .62(3) 0 .43(3) 0 .66(3) 0.33(3) 0.9303) 1 .06 (12) 1 .9100) 1 .38(6) 1 .27(6) 1 .17(5) 1 .39(8) 1 .07(5) 1 .14(7) 1 .03(6) 1 .30(7) 0.93(6) 1 .36 (12) 0.56(5) 1 .35 (10) 0.34(7) 1 .6604) 1 .66 (20) 3 .1(4) 0 .56(7) 0 .9700) 0.45(6) 0.7000) 1 .1305) 1 .6209) 0 .5802) 1 .1608) 0 .8302) 1 .40) 0 .23(9) 1 .38 (23) 0.3907)

QI/Q2 0 .8(3) 0 .78 (11) 0.73 (17) 0.6600) 0.9708) 0.67 (20) 0.9(3) 0.6101) 0.80) 0.8(3)

0 .800) 1 .2(9) 1 .2(4) 1 .1(8) 1 .3(7) 1 .005) 1 .800) 1 .202) 1 .4(8)

D.C. Radford et al. / Multiple band structure

692

TABLE

3-continued

Band

J

E.,, (keV) (J-), J-2)

E., (keV) (J-~J-1)

4

',

341 .2 382 .0 424.4 460.3 495 .3 522 .8 548 .5 566.9 577.6 580.2 541 .8 502 .1 483 .2 499 .6 538 .6 568 .4 598 .5 640.9 674.9 704.3 734.7 761 .4 789.0 814.3 840.1 866.1 891 .4 918.1 943.8

180.0 201 .9 222.5 237.9 257.4 265 .4 283 .2 283 .8 293 .8 286 .4 255 .5 246.6 236.6 263 .0 275 .5 292.8 305.7 335.2 339.7 364.6 370 .1 391 .3 397 .7 416 .7 423 .4 442 .7 448 .7 469 .4 474 .3

0.30(3) 0.176 (16) 0.183 (20) 0.058 (14) 0.145 (14) 0.184 (20) 0.158 (20) 0.146 (20) 0.229 (25) 0.17(3) 0.27(3) 0.50(5) 0.36(4) 0.310) 0.64(6) 0.34(4) 0.50(4) 0.55(5) 0.63(5) 0.36(4) 0.24(4) 0.48(6) 0.26(5) 0.41(6) 0.52 (11) 0.40(9) 0.27(7) 0 .24(9) 0.70 (11)

353.4 373.2 443.3 480.4 546.5 586.2 629.4 689.7 689.3 734.1 734.4 758.3 766.6 794.2 805 .7

166 .2 207 .0 236 .3 244 .1 302 .4 283 .8 345 .6 344 .0 345 .2 388 .9 345 .6 412 .8 353 .9 440 .4 365 .3

1 .51(22) 0.67(4) 0.52(4) 0.63(5) 0.59(5) 0.68(6) 0.78 (12) 0.65 (10) 0.25 (25) 0.42(8) 1 .1(3) 0.78 (10) 0 .7201) 0.86(15) 0.72 (11)

243 .2 323 .3 389 .9 449 .7

144.0 179 .3 210.7 239 .0

0.45(4) 0.223 (19) 0.194 (15) 0.129(14)

'i '-' 'e `-; --,' 29 2

;; 3s 37 2 2-9

42

a2 47 2

2 42-

2 2 s2 57 59 2 2 2 2

5

9

;`

;s

2

-,' 2

2 43

2 47 2

'

2 2

2 5-5 57 2

6

-,' 2

'

2

8 a)

B(Ml)/B(E2) e . b)2 OAN/

Q1/ Q2

D.C. Radford et al. / Multiple band structure

693

TABLE 3-continued

Band

J

E,. (keV) (J-J-2)

E,, (keV) (J->J-1)

}z5

503 .4 552 .6 596 .8 635 .6 670.0

264.4 288 .1 308 .7 327 .0 343 .0

0.096 (16) 0.063 (13) 0 .11(3) 0.120) 0.100)

321 .5 363 .0 412 .1 435 .8

171 .0 192 .0 220.1 215 .7

1 .2(3) 0 .85 (14) 0.54 (10) 0.54(7)

37 i9'

z °-; 8

z '-'z 13 z

''-2s

S-)

B(M1)/B(E2) (AN/e - b)

`') In the calculation of B(M 1)/B(E2), S is assumed to have the value (0.2 :1--0.1) except for those transitions for which a measured value is quoted. Since S enters eq. (2) only as a factor in (1 + S=), the uncertainty that this assumption introduces in the value of B(Ml)/B(E2) is estimated to be at most a few percent.

y-ray energies. We have checked our calibration by means of intensity balances, after correcting for internal conversion . This indicated that our relative efficiencies were correct for energies down to 200 keV; below that, minor corrections were applied to the efficiency calibration, using the results of tt'le intensity balances . Since the efficiency curve was derived from "singles" spectra of calibration sources, it is likely that these errors resulted from the yy time gate and poorer time resolution for germanium detectors at low energies . The correction was approximately 7% at 148 keV and 20% at 104 keV, and could be calculated quite accurately. The errors of all intensities quoted in tables 2 and 3 include a contribution for the uncertainty in the efficiency calibration. 4.2. BAND 3

Examples of spectra from gates on band 3 are presented in fig. 3b. No levels of band 3 have been reported in previous studies. Cascade transitions are observed to a spin of z (tentatively 2' ). Values of B(M 1)/ B(E2), deduced from the measured y-ray branching ratios, are presented in table 3 and fig. 4. In addition, we observe many weak transitions from band 3 to the yrast levels (band 2); these are discussed in sect. 5.3 . Although these transitions are all individually classified as tentative in table 2 and fig. 2, the net flow of intensity from band 3 to band 2 is unmistakable, since spectra gated by transitions at the top of band 3 clearly show peaks arising from band 2. At the bottom of band 3, the decay is primarily -Lo the 3)5- and 2;states of band 1, although these are not yrast. The higher energy decays to the states of the same spin in band 2 are relatively unfavoured .

D.C. Radfora et al. / Multiple band structure

694

5/2

15/2

25/2

35/2

45/2

55/2

65/2

2.2

z

0 .2

`r 1 . 8

t --D 0.6

i 0 .6

t 0 .2 1 .6 1 .2 0 .8 0 .4

Band 6

0 .0 5/2

15/2

25/2

35/2 45/2 Spin (J)

55/2

65/2

Fig. 4. Values of B(M 1; J -> J -1)/ B(E2 ; J - J - 2), deduced from the measured y-ray intensities and mixing ratios . These results are also listed in table 3. The heavy lines show results of calculations using the extended geometrical model of refs. 28,29)' with nc signature-splitting term included . See sect. 5.2 for details .

a = +1/2 -" -1/2

2 .5

O o

a = -1/2 - +1/2

Band 2

0 .5 5/2

15/2

25/2

35/2

Spin

45/2

55/2

Q,/Q2, deduced from the measured y-ray intensities and mixing ratios . These results are also listed in table 3. The heavy line shows results of the triaxial particle-rotor calculations of ref. 13).

Fig. 5. Values of

D.C. Radford et al. / Multiple band structure

695

4.3. BAND 4

The upper portions of this band were previously reported by Simpson et al. '°). Much of the population in the band decays through many weak branches to bands 1, 2 and 5 at around spins 2' and 23, so that Simpson et al. were unable to follow the band below this point, or to make definite spin assignments. Nevertheless, they recognized the two rotational sequences as signature partners . Sample gate spectra are shown in fig. 3c. We have been able to follow the decay of the band to its band head at 67 keV. A level at 65 keV has been observed in the (a, t) and (3He, d) studies of Panar et al. "), and assigned as the 2+ member of the z+ [404] band . This spin assignment is confirmed by the pattern of transitions from band 4 to bands 1 and 2, together with their spin-orientation distributions, which are consistent with stretched-dipole character. That the band has even parity is confirmed by the intensity balance for the 67 keV transition, which is strongly suggestive of El multipolarity since Ml or E2 transitions would be approximately a factor of five weaker due to internal conversion 22). We are able to observe cascade transitions in band 4 to a spin of z' Values of B(M 1)/ B(E2), deduced from the measured y-ray branching ratios, are presented in table 3 and fig. 4. In addition, we observe many weak transitions from band 4 to the yrast levels (bands 1 and 2) for states up to 2'+ . At spins 29 and 39, the band crosses, and mixes with, band 5. See sect. 5 .3 for a detailed discussion of these results. 4.4. BANDS 5 AND 6

Examples of spectra from gates on bands 5 and 6 are presented in figs . 3d and 3e . No levels of these bands have been reported in previous studies. The spins and parity of band 5 are established by the stretched-E2 out-of-band transitions between bands 5 and 4 at around spins 29+ and 32+ . Similarly, the spins and parity of band 6 are established by three sets of out-of-band stretched-E2 transitions between bands 5 and 6, at around spins 2s+ , 2s+ and 2+. At the bottom of these bands, the decay is primarily to bands 1 and 4, and to otherwise unobserved states at 1696, 1862, 2056 and 2157 keV. Not all of the y-ray flux feeding the lowest members of band 6 is accounted for, which is indicative of unobserved weak branches from those states. Plots ofthe differences in excitation energy between bands 4, 5 and 6, as a function of spin, are presented in fig. 6. Stretched-E2 transitions between the bands occur at points where states of the same spin come close enough for band mixing to occur. Sect. 5.3 presents a discussion of the bandmixing interaction strengths extracted from the observed y-ray branching ratios and level energy differences . Cascade transitions are observed to a spin of z' in band 5, and to a spin of z (tentatively 23) in band 6. Values of B(M1)/B(E2), deduced from the measured y-ray branching ratios, are presented in table 3 and fig. 4.

D.C. Rad,;ord et al. / Multiple band structure

696

c

45/2

35/2

25/2

55/2

65/2

75/2

50

C

m-150

19.4 kev

23 .0 kev

Fig. 6. Differences in excitation energies between the even-parity bands 4, 5 and 6 as a function of spin. Spins at which pairs ofbands cross and mix, resulting in observable out-of-band branchings, are indicated by the arrows. The energy differences at those spins are also given .

4.5. BANDS 7, 8 AND 9

Examples of spectra from gates on bands 7, 8 and 9 are presented in fig. 3f. The spins and parities of these bands are deduced from the (a, t) and ('He, d) work of Panar et al. ") as described below. Band 7 is a single rotational sequence of seventeen transitions, with no evidence of a signature partner, indicating strong signature splitting. The alignment pattern and signature splitting of this band strongly suggest a 2 - [541 ] assignment (see sect. 5.1 .5. for details). Band 7 decays in part to the strongly-coupled band 8 which can

D.C Radford et al. / Multiple band structure

69 7

be followed only to relatively low spins. Panar et al. observe levels which they assign as favoured states of the 1- [541] band at 525 keV (z - )and 651 keV (2 - ), and the z +[402] band head at 52 keV. The difference of 126 keV between their 2 - and 54states agrees quite well with the observed 129 keV transition at the bottom of band 7. Furthermore, the difference of 599 keV between their 2 - and ~+ states agrees very nicely with the total energy of the decays from band 7 to the bottom of band 8, suggesting an assignment of z + [402] for band 8. The 53 keV ;+ state is also seen in the electron capture decay of 1-57 Er [ref. 23)] from which we take the energy listed in table 1 . The weak decays from bands 7 and 9 to bands 1 and 4 confirm this excitation energy, but do not allow unambiguous independent spin assignments. Rather, we adopt the assignments of Panar et al. for the lowest levels of bands 7 and 8. The 296 and 212 keV transitions from band 7 have spin-orientation distributions consistent with stretched-dipole character. The 304 keV transition should therefore have the same multipolarity as the 219 keV y-ray, both of which, while somewhat contaminated, show distributions consistent with stretched-E2 character. Panar et al. report a level at an energy of 175 keV, with a proton stripping assignment of 1=2. In 157 Er decay 23 ), a state at 174 keV is observed, which decays via a 121 .4 keV M1 transition, in excellent agreement with the energy of a 121 .6 keV y-ray observed by us in the decay of band 9. There are some inconsistencies in the spin assignment and y-decay of this 174 keV level from electron capture, as pointed out by Helmer 2;), but the M1 assignment for the 122 keV transition is consistent with the (, )+ assignment from Panar et al. Our spin-orientation results for this y-ray suggest stretched-dipole character, supporting the 2 over the j assignment, while the 183 keV y-ray has a distribution consistent with stretched-E2 character. The energies of the 183 and 304 keV transitions are suggestive of rotational structure, so we tentatively place them in one band, band 9, and use the above information to assign spin-parities of 2+, 2+ and z+. Cascade transitions are observed to a spin of' in band 8. Values of B(M 1)/ B(E2), deduced from the measured y-ray branching ratios, are presented in table 3 and fig. 4. 4.6. BAND 10

Band 10 is a short sequence of weak transitions which is populated from the bottom of band 2, and quite rapidly decays to band 1 . No clear evidence of a signature partner could be found. Almost all y-rays associated with the band are strongly contaminated ; nevertheless, it proved possible to extract intensities and energies with reasonable uncertainties. Sample gate spectra are shown in fig. 3g. '57 No levels of this band have been reported in previous studies of Ho. If we exclude the possibility of M2 or higher multipolarity transitions competing with E1, M1 or E2 decays, then the feeding of the highest level of band 10 from

69 8

D.C Radford et aL / Multiple band structure

the '-, state of band 2, and its decay to the 2 - level of band 1, determines its spin-parity as`_ -. The decay of the lower levels of band 10 to band 1 likewise requires stretched-E2 character for the 553, 510 and 432 keV transitions, and provides the remaining spin assignments. 5. Discussion S.I . QUASIPARTICLE CONFIGURATIONS AND ALIGNMENTS

To assist in identifying the quasiparticles involved in the various bands, experimental values of the aligned angular mome -,tum ("alignment", i) were extracted from the data using the prescriptions of ref. 24) . A reference term, representing the contribution from collective rotation ofthe nucleus, was subtracted, using the Harris parameterization 25) with parameters J( , = 32.1 MeV-' h2 and J, = 34.0 MeV-; h4 . These values were chosen by Riley et al. 2) since they give a nearly constant alignment for the a = + ; signature of band 2 in '57 Ho. The values of the alignment are plotted in fig. 7 for all rotational sequences observed in 157 Ho. Table 4 provides a summary of the alignment gains and critical frequencies for the observed backbends and upbends in 157 Ho. Detailed discussion of quasiparticle assignments and alignments, and comparisons with expectations from the cranked shell model 24) (CSM), are given in the following subsections. The discussions make extensive reference to various quasiparticles close to the Fermi surface, using the nomenclature summarized in table 5. In order to facilitate comparisons with '56®y, this quasiparticle nomenclature is adopted from ref. 2 ), with several additions . In the following discussion, there will be many references to the detailed work of Riley et al. 2) on 1s6Dy . In large part, this is because a model of 157 Ho where the TABLE 4

Summary of the observed alignment gains and crossing frequencies for bands in '57Ho Band 1-2 2(a = -)

1-3 4 4 5 6 7 7

Quasiparticle assignment (A p B,) - (Ar B P )AB AAB -> A~,B~,C~,AB (A p B,) -(A,, BP )ABCD (E p , Fp )-(E P , F,)AB (EP FF,)AB (EP FP )A pB,AB (A P Bp )AE-~ (A P BF,)ABCE A,A(X, Y)-A,ABC(X, Y) Xp -> X PAB XpAB-> X pApBpAB

hW,:

(MeV) 0.27 0.48 0.32 0.26 -0.42

0.37 0.37 -0.35

di (h) 9.0 5.5 10.5 9.3 -5 .0 5.2 5 .1

D.C Radford et al. / Multiple band structure 50

150

250

350

450

699

550

Q

-Mci (keV)

Fig. 7. Experimental values of the aligned angular momentum, using the Harris `5) parameters JO = 32.1 MeV-' b` and J, = 34.0 MeV-3 h4 . The value of K was taken as 2 for bands 1 through 4, 9 for band 5, '-; for band 6, z for bands 7 and 9, and 5 for bands 8 and 10.

odd proton is coupled to observed two- and four-quasi particle excitations of a 156Dy core seems to work extremely well, and is able to explain much of the behaviour observed in the present work. 5.1 .1 . Bands 1 and 2. The ground band of 157 Ho (band 1) is based on the z -[523] single-proton orbital 11,2°). "Backbending" was observed for this band by Grosse et al. 2°), and is understood in terms of a crossing with a band in which the z -[523] proton is coupled to a pair of rotationally-aligned i13/2 neutrons . In the CSM quasiparticle nomenclature of table 5, these are the A and B quasineutrons, while the two signatures of the z -[523] proton orbital are Al, and Bp .

70 0

D.C Radford et al. / Multiple band structure TABLE 5

Quasiparticle labelling scheme adopted for Label Quasineutrons

(ho) = 0)

Nilsson state + [651] 3 + [651]

; + [660]

(+, - ;)2

2

2

F

3J521]

X

+ 202 _ 2)2

"J5051 2

A~, BP CV

(-, - ; ),

- [523] 7 J5231 - [5321 5 J5321

Y

Quasiprotons

Asymptotic

(7r, a),,

A D

'57 Ho

Fp

Xr

(-,

J5051

+ ; ), -21)2

(-, +

; + [404] ; - [541]

)3

The initial alignment of band 1 is approximately 1 .6h. The gain in alignment between bands 1 and 2 is 9.0h, and the crossing occurs at a frequency of hw, = 0.27 MeV. In '56Dy, the first backbend has a very similar alignment (ai =9.8h) and frequency (hw,, = 0.28 MeV) . The CSM calculations of ref. ') have the pairing gap ,1,,, adjusted to reproduce the observed 156Dy crossing frequency ; the AB neutron pair is then predicted to carry an alignment of 10 .2h, in good agreement with the observed value for '57 Ho and its neighbouring even-even isotones. A second crossing is observed at a hw, = 0.48 MeV in the a = - ; signature of band 2, with 41i = 5.5 h. In the neighbouring even-even isotones, the second crossing in the yrast band is due `') to the alignment of a pair of 7rh  /2 , A,,B,, . Since the A,, (B p ) quasipi oton is already present in the a = - (a = +) signature of band 2, such a crossing is Pauli-blocked . As discussed by Simpson et al. y), the next allowed crossings are BPCP (a = - 1) and A P D. (a = + ;). Since CSM calculations for these crossings are in good agreement with the observations, they support a B.C. assignment for the 0.48 MeV crossing in band 2, and also tentatively suggest that the upturn at the highest observed states in the a = + 2 signature could be due to the A.D. crossing . All of our data are consistent with this interpretation . Above the B PC P crossing, band 2 undergoes band termination ; see sect. 5.4 for a discussion of these results. 5.1 .2. Band 3. Band 3 shows a strong alignment gain, at a critical frequency of 0.32 MeV and an alignment with respect to band 1 of 10.5 h. This is greater than J'i

D.C Radford et al. / Multiple band structure

701

that of the first backbend (AB) and is significantly larger than CSM predictions for the alignment of any other single quasiparticle pair. Thus it seems that this crossing must involve the alignment of more than two quasiparticles. Very similar effects are observed in the continuations of the ground bands in ' S"Er, where the large alignment gain is attributed ') to a crossing in 116 Dy and which four quasineutrons, ABCD, are aligned. In CSM calculations for this mass region'), the BC and AD crossings are predicted to occur at frequencies of around 0.36 Met', and sufficiently close together to form one continuous upbend, with a total alignment of 11 .2 . Based on the systematics from the neighbouring even isotones and the good agreement with CSM calculations, we therefore make the assignment of ApABCD (a = -1) and Bp ABCD (a - + ;) for band 3. The configurations BpAC and APAC, which have the same signatures as Ap and Bp respectively, are expected lower in energy than ApBC and BpBC, since the signature splitting of A and B is larger than that of Ap and Bp . However, they can be ruled out since the signature splitting of the resultant bands would be opposite to that observed . Since band 3 has more aligned angular momentum than band 2, the two bands tend to approach one another at high spins. Indeed, they should cross one another at spins higher than those observed ; this would be the neutron CD crossing for ~y band 2, predicted'`) at hw c =-- 0.56 MeV. At the highest observed spin, -, in the a = + ; signature, bands 2 and 3 are separated by only 117 keV, at which point they may be expected to begin to repel one another to an observable extent . Some of the upturn at the top of band 2 in fig. 7, tentatively assigned as due to the A,Dp crossing, could be due to this interaction, although band 3 shows no equivalent downturn. The situation could well be complicated by bands 2 and 3 both beginning to undergo the ApDp crossing . 5.1 .3. Band 4. As discussed in sect. 4.3, the energy of the j + level in band 4 is in good agreement with that of a 65 keV level observed in ref. "), and assigned in that work as the j+[404] level on the basis of the ratio of the ( ;He, d) and (a, t) cross sections and its spectroscopic strength. This, together with the lack of signature splitting and the values of the B(M 1)/ B(E2) ratios, lead us to an assignment of z +[404] for band 4. This assignment is consistent with that of Simpson et al. who observed the top half of band 4. The aligned angular momentum for band 4 is plotted in fig. 7 . It shows that band 4 undergoes a backbend due to the alignment of the AB quasineutrons at a very similar frequency (0.26 MeV) and alignment gain (9.3h) to that of the yrast band. Above this crossing, the band shows a very smooth and gradual upbend, centered at hw,, =%-- 0.42 MeV and with a total di - 5 h. This behaviour is discussed in ref. '°), 56 and is very similar to that of the yrast band in ' Dy [ref.')] . In both cases, the upbend is attributed to the alignment of the Ap Bp quasiproton pair with a very large interaction strength (approximately 600 keV) '°). This crossing is blocked in bands 2 and 3, but not in band 4.

702

D.C Radford et al. / Multiple band structure

At yet higher frequencies, the a = + ; signature of band 4 shows the beginnings of another discontinuity, at hw, = 0.52 MeV. This could possibly be due to the alignment of the second pair of 1"i 13/2, i.e. the CD crossing, although the lack of any discontinuity in the accompanying a = - 2 signature would then be difficult to explain. As discussed in sect. 5.4, it is possible that this discontinuity is due to band termination . 5.1.4. Bands 5 and 6. These two bands show a number of very interesting features . They cross one another at least three times, but the interaction (I VI) between them is extremely weak, from 0.6 to 1 .1 keV, as discussed in sect. 5.3. A plot of the difference in their excitation energy is given in fig. 6. Although very similar to one another in many respects, bands 5 and 6 are different in their B(M 1)/ B(E2) ratios (see fig. 4) and in the degree to which they show signature splitting. While the splitting of band 5 is comparable to that of band 1, band 6 shows no splitting over the entire observed spin range. The bands have very similar alignment plots, so much so that they are almost indistinguishable in fig. 7. They both have initial alignments of about 8 h and undergo an alignment gain of Ai ~- 5.2h at hw c = 0.37 MeV. This upbend is in excellent agreement with the CSM prediction 2 ) of di = 5.9h and hw c = 0.36 MeV for the alignment of the BC quasineutron pair, and also with the observed BC crossings in several bands of '54Gd,'S613y and ' -""Er [ref.'-;)]. The large initial value of i indicates that the bands start out as three-quasi particle structures, and the apparent blocking of both the AB and ApBp crossings suggests the presence of both the A quasineutron and either the Ap or B p quasiproton . There are several good candidates for such three-quasiparticle structures, involving two neutrons in addition to the odd proton. In 'S6Dy, four two-quasineutron bands are observed, and assigned the structures AE, AF, AX and AY 2 ). As expected, all four bands undergo the BC crossing, while the AB crossing is blocked. If these bands are coupled to the yrast odd-proton ; - [523] structure of 'S' Ho (i.e. AP and Bp), a total of eight rotational sequences should be expected, four of each signature. Since the expected excitation energy of these bands are very similar, it is perhaps likely that some of the four bands mix quite strongly, so that we will talk of quasiparticle assignments for bands 5 and 6 only in terms of the dominant components, without expecting the configurations to be pure. Band 5 is assigned as the 3 - [523]OAE configuration, or ApAE (a = + ;), BpAE (a= - ;). This is done on the basis of: (i) The observed signature splitting, which is very comparable to that of band 1 . (ii) The B(Ml)/B(E2) ratios, which are in excellent agreement with theoretical predictions for this configuration, but significantly larger than those expected for configurations such as 2 - [523]OAX or j- [523]OAY (see sect. 5 .2) . However, the predictions for the ; - [523] O AE and 27- [523]OAF configurations, and for transitions between them, are identical, and thus do not serve to discriminate against configurations involving the AF quasineutrons.

D.C Radford et al. / Multiple band structure

70 3

(iii) The observed AE, AF signature splitting in '56Dy, which leads us to predict that the 2 - [523] O AE configuration should lie lower than the 2 -[523]OAF configuration . However, it should also be noted that the a = -2 AP AF and BpAE configurations (both of which involve one unfavoured quasiparticle) are expected to lie much closer together than the a = + 2 A~,AE and B,,AF configurations (which involve zero and two unfavoured quasiparticles, respectively) . Thus we cannot completely rule out an assignment of ApAF for the a = - 2 signature of band 5. In a weak coupling model, the ' 56 Dy AE band head at E,, = 2408 keV, J' = 9would couple with band 1 in '5' Ho to give states at E,, = 2408 keV, J' = 25+ and E,, = 2491 keV, J' = 2' + . Band 5 does indeed start at those spins, and with excitation energies of 2368 and 2555 keV. This is another example of very good weak coupling of the odd proton to the 156Dy core. The quasiparticle structure assignment for band 6 is more ambiguous. One candidate is the 2 -[523]OAF configuration . In a weak coupling model this would have band 6 beginning at E,, = 2346 keV, J -ff _ 23 +, in excellent agreement with experiment. The residual interaction for A,,O AF would then be - -75 keV, very similar to the --40 keV A,,OAE residual interaction from band 5. However, the lack of any observed signature splitting is then very difficult to explain, and the B(Ml)/B(E2) ratios are also in significant disagreement with theoretical expectations,which would be identical to those for band 5 if E and F have the same alignment. We favour a second candidate, namely A PAX (a = +2), A P AY (a = - ;). This assignment requires a stronger residual interaction of about -220 keV to bring the excitation energy down to the observed value. However, the X, Y quasineutron pair are not expected to exhibit signature splitting, nor are they observed to do so in neighbouring even-Z nuclei . This explains the lack of any splitting in band 6. In addition, the B(M 1)/ B(E2) ratios are in much better agreement with expected values. In ' 56 Dy, the AY and AF bands (bands 9 and 10 of Riley et al. 2)) cross twice, with a very weak interaction of I VI < 4 keV. While a little larger than the observed '5' Ho, this does also seem to fit VI between bands 5 and 6 in the general weak coupling picture quite well. The weak interaction is presumably due, at least in part, to a large difference in K between bands 5 and 6. Band 6 decays via many weak branches, and in large part to levels which are far from yrast. Presumably, this is because band 6 has a significantly higher K than the other observed bands, and thus tends to decay to other high-K states. The difference in decay patterns from bands 5 and 6 is further evidence that their quasiparticle structures have significantly different components. The A,Bp crossing is blocked in all four sequences of bands 5 and 6, due to the occupation of either the Ap or B,, orbital. However, the BpCp crossing should be blocked by the B P only in the a = - 2 signature of band 5. Indeed, the a = + ; signature of band 5 is beginning to show signs of an impending crossing at the highest observed spins, although the Bp Cp crossing here must occur at a slightly higher frequency than in band 2, where it has hoc --- 0.48 MeV. Band 6, or the other

704

D.C Radford et al. / Multiple band structure

hand, shows no sign of any crossing up to hw = 0.53 MeV. If our assignments are correct, this must presumably be due to a change in deformation which causes the BpCp crossing to be delayed. 5.1.5. Band 7. As discussed in sect. 4.5, we assign band 7 as the ! - [541] band, on the basis of its exhibited alignment pattern, its strong signature splitting, and the excellent agreement with the level energies of Panar et al. The general features of the band fit well with the systematics of i'_[541] bands observed in heavier odd-proton nuclei (e.g. ref. `'1) ) . The strong signature splitting of this K = ; band allows us to see only the favoured signature. It undergoes an upbend at hw, 0.35 MeV, assigned as the Pi 131 :! AB crossing, but at a higher critical frequency and with a larger interaction strength than for the 4- [523] and + [404] bands. Details of this crossing, and the significance of its frequency in terms of the nuclear 27) . deformation, have been discussed by Gascon et al. Band 7 should also undergo a rh  / , A,B p crossing, since the alignment of this pair is not blocked. The very smooth nature of the AB crossing makes it difficult to untangle what is happening at higher spins; however, the ApBp crossing is probably the reason why the alignment of band 7 continue to increase above hw = 0.45 MeV, where it runs parallel to that of band 4. 5.1.6. Bands 8 and 9. As discussed in sect. 4.5, Panar et al. ") observe a level at 52 keV, which they assign as the + [402] state, an assignment which we adopt for band 8. They also observe the 174 keV level at the bottom of band 9, and tentatively suggest that it, and another state at 215 keV, could be associated with the 1 + [411] band. Another possible assignment for band 9 would be - + [411 ]; however, Panar et al. suggest a state at 272 keV as the band head for that band. We see no evidence for a signature partner to band 9; this tends to support the ! + [411] assignment, which would be expected to show signature splitting and have a favoured signature of a = + ;, while the ~ + [411] has a favoured signature of a = - ; . However, the observed transitions are quite weak, and since it appears that the only reason band 9 is observed at all is its poulation in the decay of band 7, even a favoured signature partner may be unobservable in the present work. Band 8 appears to undergo the AB crossing, although we are unable to follow it to spins where the backbend is complete. This band has no signature splitting at the lowest spins, but splitting develops quickly as the spin increases, so that the a = - ; signature of band 8 is depressed in energy with respect to its signature partner. This is probably due to mixing with some other unobserved band, quite possibly the continuation of band 9. 5.1.7. Band 10. Band 10 is assigned odd parity, as discussed in sect. 4.6. It shows only a small alignment, so that it must be based on a single quasiproton . The level energies are inconsistent with this band's being the signature partner of the ! - [541 ] band (band 7), so the only plausible odd-parity candidates are 2 - [514] and 5- [532] . The 9- [514] can be eliminated since Panar et al. assign its band head at 998 keV, an assignment which is strongly supported by the systematics of the 2 - [514] energy

D.C. Radford et al. / Multiple band structure

705

in this mass region. On the other hand, the signature of the observed states of band 10 corresponds to the favoured signature of the 2 -[532] band, and the aligned angular momentum shown in fig. 7 agrees well with that expected for a 2 -[532] orbital. We therefore adopt an assignment of 2 -[532] for band 10. Panar et al. observe a state at 585 keV in the (a, t) reaction, but not in the (3He, d) reaction, which may be a possible candidate for the 2 state of the 2 -[532] band. Such an assignment would be in excellent agreement with an extrapolation of our observed level energies to lower spin. 5.2. TRANSITION STRENGTH RATIOS

The intensities and mixing ratios of table 2 have been used to calculate y-ray branching ratios, fil, and hence B(M1)/B(E2) and Q,/Q2 ratios, using the standard relations: E ;,(J --> J-2) 1 N '` B(Ml ; J --> J-1) --0.593 __> B(E2; J~J-2) E ;,(J j-1) Jl(1+S'`) e- b Q1/ Q2-

8 2 2 (JK20; J-2K) E y (J>J-1) 1l(1+ô) (JK20, J-1K)

(2) (3)

ES(J~J-2)

The results are presented in table 3 and figs. 4 and 5. Previous measurements 7") have been published only for bands 1 and 2. For low spins, where the signature splitting in the cascade y-ray energies is large, there are serious discrepancies between our measured branching ratios and those from previous work, as discussed in sect. 4.1 and ref. 21 ). Figs. 4 and 5 also present results of calculations from the particle-rotor model (for Q1/Q2, taken from ref. 13)) and the geometric model of Dönau and 29) Frauendorf `'s) (for B(M 1)/ B(E2)) . For the latter, the extended formalism of ref. was used, and the B(Ml) calculated according to B(M1 ;J->J--1)=

3 2{ J2-K2[(ltde'/hw)(g1-9R)K1 87J +(g2

where

9R)K2+(g3-gR)K3 + . . .]

- K[(g1 - gR)i1+(g2 9R)i2 + (g3 - 9R)i3 + K = K, + K2 + K3+' '

. . . ] }2N,

Here the subscripts 1, 2 and 3 refer to the quasiparticles, or aligned pairs of quasiparticles, that couple to form the band, and Ae' is the signature splitting in the level energies in the rotating frame. Quasiparticle 1 is the only quasiparticle which is special in the formula, and then only by virtue of the signature-splitting term; it is the quasiparticle which is assumed to contribute both signature partners

706

D.C Radford et al. / Multiple band structure TABLE 6

Parameters used in the calculation of B(M1)/B(E2) Band

91

1 2 3 4 5 6 8

1.13 1.13 1.13 0.70 1.13 1.13 1.32

K,

i,

g,

K,

i,

27

1 .7 1 .7 1 .7 0.0 1.7 1.7 0.0

-0.21 -0.21 -0.21 -0.21 -0.21

0 0 0

8.9 10.5 10.5 5.5 5.5

2

;

93

K3

i3

94

K4

i4

0.24 -0.23

-2 21

1 .7 0.4

-0.21

1

5 .3

to the band. To obtain eq. (4), one assumes a "semiclassical" picture in which the total angular momentum J lies on the plane specified by both the rotation axis and the symmetry axis. The B(E2) was calculated assuming a constant Qo of 5 .5 e - b, which corresponds to a rough average of the values from ref. 27) . Table 6 lists the gi , .K; and ii parameter values used in the B(M 1) calculation for the various bands. The value of 9R was taken as Z/ A. Two sets of calculations for the B(Ml)/B(E2) ratios were performed. The first, shown as the heavy lines in fig. 4, neglected the term in eq. (4) arising from the signature splitting (®e'). This term attempts to account for the erect of the signature splitting on the M1 transition strength, assuming axial symmetry. When it is included in the calculations for bands 1, 2 and 3, we obtain the results shown as the heavy lines in fig. 8. The calculations without signature splitting (fig. 4) show excellent general agreement with the data. This agreement gives extra confidence in our quasiparticle assignments, especially for bands 5, 6 and 8 . The calculations in fig. 8 show a drastic overestimate in the signature splitting for band 1, and an underestimate for bands 2 and 3. This effect has been seen in the other odd isotones of 15' Ho, and other nuclei in this region, and is discussed at length by Hagemann and Hamamoto 30) . It arises from the assumption of axial symmetry used in the derivation of eq. (4), and is therefore evidence of y-deformation. Using a more complete analysis of the signature splitting in both the B(M 1)/ B(E2) ratios and the level energies, Hagemann and Hamamoto deduce that the value of y in band 1 is most probably in the order of -10° to -15°. In band 2, y could be slightly positive . Many other calculations for B(Ml)/B(E2) and/or Q,/ Q2 ratios in 157 Ho have been reported in the literature; these include calculations with the triaxial particlerotor model (e.g. refs. 8,13)), the symmetric particle-rotor model with y-vibration 3'), a rotating shell model 14), a quasipartcle-vibration coupling model 32) and the interacting boson-fermion model 33). In general, models without static triaxial defor-

D.C Radford et al. l Multiple band structure

5/2 O N

15/2

25/2

® ® ®

a = +1/2 -~ -1/2

o o

a = -1/2 -~ +1/2

-

35/2

45/2

707

55/2

65/2

55/2

65/2

N

cj 1 .5

Bond 2

Bond 1

N

m 0 .5 m

0 .6 0 .2

5/2

15/2

25/2

35/2 45/2 Spin (J)

Fig . 8. Values of B(M 1 ; J ~ J -1)/ B( E2 ; J -> J - 2 ), deduced from the measured y-ray intensities and mixing ratios . The heavy lïnes show results of caculations using the extended geometrical model of refs . 29,3°;, with the signature-splitting term included . See sect. 5.2 for details .

mation consistently calculate too large a splitting for the B( M l ) strengths in band 1 . Most calculations for Q,/ Q2 are roughly consistent with those shown in fig. 5. 5.3 . OUT-OF-BAND TRANSITIONS, BAND MIXING AND DAMPING

In our analysis of the yy coincidence data obtained in the present work, we have attempted to identify all branches from the observed states to the full degree of detail allowed by the data . This approach has made evident a large number of out-of-band transitions, particularly around states where bands of the same parity and signature cross one another, and thus produce accidental degeneracies and mixing of levels . This in turn makes possible an accurate analysis of B(E2)/B(E2) transition strength ratios, to deduce new information on band mixing. A two-band-mixing analysis of seven such band crossings is summarized in table 7. Listed are the two crossing bands, the spin and energy separation of the closest levels, the observed in-band and out-of-band transition energies and the

D.C. Radford et al. / Multiple band structure

708

TABLE 7 Deduced values of A'= B(E2)/B(E2) for out-of-band transitions and interband interaction strengths extracted from two-band mixing calculations in ' 57 Ho Bands 1,2

Adopted VI (keV)

Spin')

4Er a) (keV)

Ey (keV)

E'. (keV)

P

61 .1

664.0 318.9 441 .6 631 .9

380.0 602 .9 380 .5 693 .0

0.64 (18) 0 .86(8) 0.25l (19) 0 .12(3)

27 .9 (21) 29 .3(5) 27 .9(5) 22 .9 (23) b)

28 .6(5)

48(3) 47 .9(8)

47.9(8)

A'

1

VI (keV)

1,

15

130.6

696 .1 366 .8

497 .4 565 .6

0 .61 (10) 0 .61(3)

4,5

?9

19.3

353 .4

560.8

0.58(8)

4,5

39

23 .0

538.6 538 .6 586 .2 586 .2 598 .5 689 .7

609.2 609 .2 515 .6 515 .6 621 .6 666.7

0 .31(4) 0 .52(7 ) `') 0 .61(6) 0.44(7 ) `') 0.47(3) 0.39(7)

4,6

i

13 .8

538.6 538.6

610.6 610.6

5,6

35

1 .5

4804 503 .4 586 .2 596 .8

504 .9 479 .0 587 .6 595 .4

0 .177 (19) 0 .22(3) 0 .38(4) 0 .40(4)

0 .5400) 0.5901) 0.6001) 0.6101)

0.58(8)

5,6

45

2 .4

689 .3 701 .2 734.4 745 .1

698 .7 691 .7 732 .0 747 .6

0.70(9) 0.93 (12) 0.19(5) 0 .41(7)

1 .1(3) 1 .2(3) 1 .00) 1 .20)

1 .13 (20)

5,6

59

2 .3

839.8 847.3

849.6 837 .5

0 .90) 0 .67 (23)

1 .1(6) 1 .2(7)

1 .1 (5)

3,2

47

z

321 .8 314 .4 284.9 272 .4 241 .1 229.5 203 .4 188.7

671 .4 700.1 730 .2 773 .8 799 .0 851 .3 870 .8 930.2

1003 .9 1045 .1 1052 .0 1088 .2 1083 .9 1123 .8 1111 .8 1159 .7

0 .076 (19) 0 .05(3) 0 .09(3) 0 .016(9) 0 .030 (14) 0.02102) 0.13(3) 0.089 (24)

?7 z

406.3 411 .4 381 .8

432 .4 509 .7 553 .3

838 .6 924.1 964.7

0.046 (14) 0.018(5) 0.039(6)

.19 51 53 5$ 57 î 59

10 ' I

0.21(3) =0.0 `' )

9.10)

9 .1 (3) `)

11 .21 (24) 11 .40 ) `') 11 .46 (19) 11 .2 (4) `') 9 .21(25) 8.7(6)

10 .0(8)

5 .90)

--0

') The spin and excitation-energy difference is given for the point at which the two bands are closest to one another, i .e., for the states which are expected to be most strongly mixed . Initial state is a member of band 3 ; branching ratio included for completeness . `) See also discussion in sect . 5 .3 .2 . of text. `') A' corrected for mixing between bands 5 and 6 at J = 25 . See text for details .

D.C. Radford et al. / Multiple band strisvture

709

B(E2)/B(E2) ratios, A , - B(E2; A, B(E2; A,

B,-2) = B(E2 ; B, A,-,1 B(E2 ; Bj

Aj -2) B,_,)

(6)

where A and B are the two mixing bands. Each such ratio provides an independent measurement of the interband interaction strength, I VI, according to the following expression:

where R=

Eg.j EA.i _, -- EB,, _, EA,i

-

(8)

In deriving this expression, mixing of the wave functions at both spin J and J -2 is taken into account . Identical B(E2) strengths (in the absence of mixing) are assumed for the two bands, and all non-diagonal matrix elements are assumed to be equal to zero. 5.3.1. The crossing between bands 1 and 2. Several features ofthe results presented in table 7 are of special interest. The first two crossings., between bands 1 and 2, are adjacent in spin, and are for the two different signatures. There is clear and striking signature dependence for I VI, with the favoured signature having an interaction strength almost twice that of the unfavoured signature. This effect has been previously discussed by Hagemann et al. 34) . Both cranking and particle-rotor calculations 35,36) predict I VI in even-even nuclei to be an oscillating function of the Fermi level, A, in a high-j subshell. Thus the signature dependence of I VI in odd-Z nuclei may be simulated by a shift in A,, (or a shift in deformation) between the two signatures of the odd proton . Close to one of the minima in I VI, where the variation is rapid, even a small shift will cause a signature dependence . If this shift passes one of the nodes, where the actual value of V changes sign, then the signature dependence will change its phase, and over a narrow region the two signatures could actually have opposite sign in V. In the following, we use a model to try to estimate this signature dependence . In a cranking approximation, the odd proton is a spectator in the band crossing, so that the strength of I VI is trivially independent of the signature, as long as the signature-partner bands have the same shape for a given rotational frequency. In particle-rotor calculations for odd-Z nuclei, the signature independence of I VI is not a trivial consequence even in the case of the same shape for the two bands . In the upper part of fig. 9 we show the strength I VI calculated in a particle-rotor model for axially-symmetric shape, for the crossing between a 7rh  / 2 band and a irh  i2( vi, 3 / 2) 2 band . It is seen that a slight signature dependence for I V1 appears for large values of I VI. However, when the strength I VI is smaller than about 70 keV,

710

D.C Radford et al. / Multiple band -ructure

IVI/K

IX P /K=-0.101

0 .10-

0.10

0.05

0 -1 .0

-0.8

-0 .6

-0 .4

Fig. 9. Absolute values of the interaction strength 4' between the band with an odd h/, quasiproton and the band with an odd h,, quasiproton plus two i,3i2 quasineutrons, aS a function of ~~eutron shell-filling A  in the i,3,, shell, calculated using an axially-symmetric particle-rotor triodes . 1n the lowcf part of the figure a neutron-proton QQ interaction is introduced so as to simulate both the configuration dependence and the signature dependence of the deformation, using the model of ref. 3' ). The solid and dashed lines show the values for the favoured and unfavoured signatures, respectively. The proton Fermi level (AP/K) = -0.10 is chosen to be appropriate for "'Ho. The single-particle energies in a single -j shell are used and the approximate positions of !1 values for the neutron i,3i, shell are indicated on the (A/ K) axis in the upper part of the figure . The pairing gap parameters used are (JP/A) =0.40 and (4 /K) = 0.30. The energy unit K is about 3 MeV in the present example.

the strength for the favoured signature (solid line) is identical to that for the unfavoured signature (dashed line) . As discussed in the previous section, a comparison of the signature dependence of the B(Ml)/B(E2) ratios with the signature splitting of the routhians provides evidence for a considerable non-axial symmetry in band 1, with y most probably in the order of -10° to -15°. We also have good reason to believe that the value of y could be signature dependent, since the driving force with respect to 'Y of the ; - [523] quasiprotons is quite different for the two signatures . However, calculations of I VI with non-axial symmetry y < 0 in the one-quasiparticle band and y :- 0 in the three-quasiparticle band - the realistic situation in many odd-proton rare-earth nuclei, including '$' Ho - has so far not been performed, either in a cranking approximation or in a particle-rotor model .

D.C Radcord et al. / Multiple band structure

71 1

In ref. ;'), it was shown that it is possible to simulate the realistic situation by using a particle-rotor model with axial symmetry and introducing a neutron-proton interaction of QQ type with its strength adjusted to reproduce the observed signature splitting in energies both before and after the band crossing . In the lower part of fig. 9 we show the interaction strength I VI calculated using the model of ref. ;'). It is seen that introducing the np interaction (so as to simulate both the configuration dependence and the signature dependence of the deformation) leaves the oscillating behaviour of I VI as a function of shell-filling unchanged; however, the phase shift of the oscillation now depends on the signature, and a prominent signature dependence in I V1 appears, especially for smaller values of I V1 . 5.3.2. The crossings between bands 4, 5 and 6. The relative excitation energies of bands 4, 5 and 6 are presented in fig. 6. The bands cross with observable mixing at the spins indicated by the arrows, and with interaction strengths summarized in table 7. One striking feature of the data is the very weak interaction between bands 5 and 6, which varies from 0.6 to 1 .1 keV, and is an order of magnitude weaker than the interaction between bands 4 and 5. The very weak interaction is made immediately evident by examining the energy separations ; the ~s+ states of bands 5 and 6 differ by only 1 .45 :L 0.14 keV. It is also interesting to note the weak spin dependence of the interaction between bands 5 and 6. This may be due, at least in part, to the BC quasineutron alignment, which begins between the first and second crossings of the bands. The decay of band 4 to band 6 via the 611 keV transition ( ;y+ 35+) could be due to mixing between bands 4 and 6 at Jr = ~9+ . However, none of the other transitions expected from such mixing could be observed . States of band 5 are strongly mixed with both band 4 (at J' _ y + ) and band 6 (at J-ff _ I + ), so the 611 keV transition may also arise from the component of band 5 in the initial and final mixed levels . Indeed, to a good approximation, all of the 611 intensity can be accounted for in this way. It is also possible to correct the B(E2)/ B(E2) ratios for transitions between bands 4 and 5 to take account of the 611 keV y-ray intensity, assuming that the interaction between bands 4 and 6 is too weak to produce significant mixing. These modified values are also given in table 7, and produce considerably better consistency between the B(E2)/B(E2) ratios for the 539, 609, 586 and 516 keV transitions. It is evident from fig. 4 that the B(M 1)/ B(E2) ratio involving the 353 keV transition at the bottom of band 5 is anomalously large. This, together with the strong 697 keV transition from the 2y+ state, suggests that the 353 keV y-ray has a smaller B(E2) than expected. The origin of this effect is not clear, although it could conceivably be due to mixing ofthe 2s+ state . However, a reduced B(E2) for the 353 keV transition would produce an error in the I VI extracted from the 561 keV branch to band 4, since it would have the effect of invalidating the assumptions behind equation (7). Increasing the strength of the 353 keV transition by a factor of two, to bring the B(M 1)/ B(E2) ratio in line with the other values for band 5, would reduce the I V1 for bands 4 and 5 at J ' = 29+ from 9.1 (3) to 7.7 (5) keV.

71 2

D.C Radford et al. / Multiple band structure

5.3.3. Decays from band 3 to band 2, and from band 10 to band 1 . Many weak, tentative stretched-E2 transitions from band 3 to the yrast states are shown in fig. 2. Although these transitions are all individually classified as tentative, the net flow of intensity from band 3 to band 2 is unmistakable . It is possible to use equation (7) to extract an interaction strength between the two bands, but in this case the ratio R is very close to unity, producing strong destructive interference between the two components of the out-of-band B(E2). Thus any difference between the in-band transition quadrupole moments will produce a large change in the extracted value of I VI. Moreover, the observed B(E2)/B(E2) ratios are sufficiently small (ranging from 0.02 to 0 .13) that even a single-particle contribution to the off-diagonal matrix element will strongly affect the final transition strength . The same statements can also be made about the stretched-E2 transitions between bands 10 and 1, but to an even greater extent, since R is still closer to unity (0.93 to 0 .99) and the B(E2)/B(E2) ratios are all less than 0.05. 5.3.4. 1 decays from band 4 to bands 1 and 2. The decay from band 4 to the yrast states by electric dipole transitions is spread over a wide range of spin, from the band head at ;+ to a spin of at least 4-'+ . The observed branching ratios can be used to deduce B(El)/B(E2) transition strength ratios ; these are presented in table 8. The ratios are remarkably constant, although there is possibly a tendency for an increase as the spin increases, and the ratio for the 640 keV transition from the as+ state is considerably larger than the average . With Qo - 5.5 e - b the ratios given in table 8 correspond to B(EI) values of the order of 2 x 10-4(e - f)-. This is 1 to 2 orders of magnitude larger than can be obtained with a reasonable effective charge (about 0.2e). Similar observations exist in surrounding nuclei ;8). In the present case, the Nilsson configurations 7+ [404] and -[523] have large components of the g,i2 and h /2 shell-model states, respectively . Since the standard El matrix element between these major components vanishes, an enhancement due to octupole softness is required to reproduce the observed El strength. A calculation of such octupole-enhanced B(E1) values and their spin dependence can be found in ref. 39). The excitation energy of band 4 relative to the yrast states is typically only 300 to 350 keV. Nevertheless, the flow of intensity from band 4 is quite significant, so much so that the authors of ref. '°) were unable to follow the band below a spin of 4'+ . 5.3.5. Population patterns. With the many bands and their detailed decay patterns established in the present experiment, it is possible to extract new information about the average decay flow. In fig. 10 the total flux in each of the individual bands is shown as a function of spin. It is instructive to compare this population pattern with the excitation energies shown in fig. 11 . This leads to the following conclusions : (i) In general, the population decreases with excitation energy above yrast, but there are also considerable variations which can in most cases be traced to structural changes such as alignments and band crossings.

D.C Radford et al. / Multiple band structure

71 3

TABLE 8 Deduced values of B(El)/B(E2) for "Ho Initial band

Initial spin (J)

E,, (keV) (J -* J - 2)

Final band

E,, (keV) (J -, J -1)

B(El)/B(E2) (10 -6 fm -2 )

4 4 4

~ ; ;

341 .2 382 .0 424 .4 460 .3 495 .3 522 .8 548 .5 566 .9 577 .6 580 .2 502 .1

1 1 1 1 1 1 1 1 1 1 1

324 .6 422 .0 477 .0 566 .6 578 .5 665 .2 638 .3 719 .4 654 .6 716 .7 588 .3

0.048(6) 0.031(3) 0.037(4) 0.024(2) 0.022(3) 0.037(3) 0.031(4) 0.035(3) 0.036(4) 0.026(4) 0.037(5)

2 2 2 2

463 .4 522 .3 639 .9 658 .5

0.057 (10) 0.033(9) 0.17305) 0.073(7)

4 4 4 4 4 4 4

2s

-,'

~y

~

2

25

2' 2 ;

4 4 4 4

,s ~'

483 .2 499 .6 640 .9 674.9

5

'

353 .4

1

697 .3

0.057(8)

218 .9

8

306 .8

0.0033(4)

128.9 218 .9

9 9

296 .3 211 .5

0.029(9) 0.027(2)

183.4

1

358 .1

0.013(5)

7 7 7 9

;s

;`1 1)

-

(ii) The high-spin cut-off in population occurs at different spins in the various bands and is therefore also subject to structural differences. The terminating states are very favoured in energy and receive a great deal of population . (iii) The odd-parity bands are spread more in both population and energy than the even-parity bands, and have a different differential population with spin, i .e., different side-feeding intensities . Over a rather broad region, band 4 is very close in energy to band 3, but has a population almost twice as large . These observations suggest that the analysis of the odd- and even-parity bands should be kept separate . Band 4 should then be considered as yrast for the even-parity bands. We now compare bands for which the population slope is similar. This can be done for both parities separately, and in selected spin ranges which do not include structural effects. Assuming that the sidefeeding into a particular state takes place by "statistical" E1 transitions, and including the enhancement from the tail of the giant dipole resonance, the feeding probability should depend on E ;, . If this feeding comes from states at energy U, then knowledge of the branching Pr to a state at

D.C Radford et al. / Multiple hand structure

714 100

100

10

10

. en

C N C

15

25

Spin

35

45

v

5

15

25

Spi n

35

45

Fig. 10. Total population in each of the individual bands as a function of spin. The populations are obtained by summing all intensity, including internal conversion, depopulating levels in the band. Band-termination states are also included, although they cannot properly be said to form a band.

energy E compared to P,. to the yrast state at E,., allows us to extract the energy

For the odd-parity bands 3 and 7, we obtain (U - E_,.) -1 .1 and 1 .3 MeV over the spin range 20 < J < 25, respectively, and (U - E,.) -1 .2 MeV for band 7 over the range 25 < J < 30. For even parity, the only reliable estimate can be obtained for band 5 (in comparison to the "yrast" band 4) with ( U - E,.) - 0.9 MeV over the range 25 < J < 30. If the difference in energy between band 2 (odd-parity yrast) and band 4 of --0.22 MeV is added, then the total excitation energy from which the sidefeeding occurs into the even-parity states is -1 .1 MeV, very similar to that for the odd-parity states . If the transition probability varies as the third power of E,,, rather than the fifth power, then the above results will change to ( U - E,.) - 0.7-0.9 MeV.

D.C Radford et al. / Multiple band structure 5

15

25

35

715 45

1200

800

400

0

5 Fig. 11 . Excitation energies of observed levels in 157 Ho, with an arbitrary rigid rotor term subtracted for the purposes of display.

Such estimates may be of value in the understanding and modeling of the decay flow in simulation calculations utilized in analysis pertaining to rotational damping; see also the following subsection . 5.3.6. Implications for rotational damping calculations. A wide range of inter-band interaction strengths are observed in the present work, from 0.6 keV for bands 5 and 6, to 48 keV for bands 1 and 2, and even to about 600 keV from an analysis of the slope of the upbend produced by the Ap Bp crossing in band 4 [ref. '°)]. As we saw in sect. 5.3.2, very weak interactions may still produce strong band mixing, and even produce transitions between bands which are not directly mixed (such as bands 4 and 6).

71 6

D.C. Radford et al. / Multiple band structure

Calculations of rotational damping, such as those in ref. 4"), typically use a single average spreading width to describe the interaction of an unperturbed band with its neighbours . For the regime close to the yrast line, where the spreading width is less than the average level separation (-750 keV from yrast in this mass region 40)), mixing is assumed not to occur, and thus no rotational damping is predicted . All levels observed in the present work fall within this regime; nevertheless, strong out-of-band transition strength is observed, particularly in the even-parity bands between spins `' and ,yea. For example, the average number of sequential E2 transitions within band 5, following population of that band between those spins, is less than 2. In the region where the mean spreading width is greater than but still close to the average level separation, a uniform spreading is usually assumed . However, the present results may lead us to expect that there would still be considerable variation in the actual spreading of individual bands at a given spin ; this should increase the average damping width. Thus calculations of rotational damping may well benefit from a careful analysis of the variation in inter-band interaction strengths, especially in the low-energy regime. We observe a large number of bands, to a maximum excitation energy of about 700 keV above yrast. Many out-of-band transitions arising from single-particle or weakly-enhanced E1 and E2 strength are observed, especially from bands 3 and 4, to the yrast states. At higher spins, where the band intensity is reduced and the higher y-ray energy reduces the detector efficiency, many more such transitions are expected to fall below the limit of what is observable . It is hoped that these out-of-band decays and hand mixing observations, the most comprehensive so far obtained in any high-spin study, will provide additional input for, and constraints on, models used for rotational damping calculations and simulations .

5.4. BAND TERMINATION

A plot of excitation energies for the observed bands of 157 Ho, with a rigid rotor term subtracted, is presented in fig. 11 . For the highest odd-parity states, a sudden onset of irregularity in y-ray energies appears in this figure as especially low-lying states with spins of ;5h ' and , h. This behaviour may be understood 4') in terms of band termination, or a change in shape from well-deformed prolate to weaklydeformed oblate. The ", - state would then be described as a closed '46Gd core with eleven valence particles in the fully-aligned ir[(h  /2) 312,/2 7-5P[(f7/2)3!h9/2)3 (i13/2) 2 ]30+ configuration . The state has one f,/2 neutron anti3 4 aligned, generating the 7r[(h1/2) 127/2 _14(f7/2) +(h9/2)2(il3/2)2J24+ configuration. These states are analogous to the band-termination 46+ and 40+ states in '5KEr [refs . 5'6'4' respectively . The level energies are in qualitative agreement with the calculations of ref. 41) .

D.C. Radford et al. / Multiple band structure

717

In the lifetime measurements of Gascon et al. 27 ), evidence was found for long-lived ::-75) . Indeed, these workers conclude that states (T . 1 .1 ps) at very high spin (j_ their data are consistent with a lifetime for the 2- state of at least 8 ps, which in turn would imply a transition quadrupole moment of Q, < 1 e - b. This extremely weak collectivity is nicely consistent with the band-termination scenario presented 'S_ here, where the favoured and x'- states are single-particle in nature and have oblate shapes with small -deformations (c -- -0.1). For even-parity states, band termination is predicted 6,12) to occur at spins z h and ; . As mentioned in sect. 5.1 .3, band 4 begins to show an unexplained discontinuity at K' + . It is perhaps possible that this is due to band termination; further data on level lifetimes and higher-spin states might be able to confirm or exclude this possibility. 6. Conclusion

A comprehensive, detailed level scheme for '57 Ho, containing over 380 transitions, has been presented. This scheme was extracted from the data using new analysis tools '$) . Many bands have been observed for the first time, and quasiparticle assignments are suggested for all of the observed bands. B(Ml)/B(E2) cascade-tocrossover transition strength ratios have been extracted for all bands for which two signatures are observed . In all cases, the results are in satisfactory agreement with expectations from the geometrical model 28,29), using the proposed quasiparticle assignments. Many of the observed multi-quasiparticle bands arise from coupling of the odd proton to observed two- and four-quasi particle excitations of a '56Dy core. This picture seems to work extremely well ; the interaction strengths, crossing frequencies and alignment gains at the AB and ApBp crossings are very similar for '57 Ho and '56Dy, and residual interactions between the two-quasi neutron bands in 156 13y and the odd proton, to give bands 5 and 6, are small . The yrast levels undergo band termination at spins of z- and -, in excellent agreement with theoretical predictions 4' ). Band termination at a spin of + may also have been observed in the lowest even-parity band. The proposed level scheme is rich in band crossings and out-of-band decay branchings. These provide a wealth of detailed information on band mixing and interaction strengths . The interaction between the ground band and S-band at the first backbend is found to have a strong signature dependence. This is excellent evidence not only for triaxial deformation of the ground band, but also that the two signatures have different triaxial deformations, i.e., different values of y. A wide range of inter-band interaction strengths is observed, with two bands (bands 5 and 6) having an interaction of only I VI - 0.6 keV at one crossing . On the other hand, upbends in the 2 + [404] and !-[541] bands have very strong interactions, probably around 600 keV. We are also able to draw new conclusions about the

71 8

D.CC Radlord et al. / Multiple band structure

excitation energy of the quasi-continuum bands from which sidefeeding of the observed discrete bands occurs . These results may have important implications for calculations of rotational damping. We gratefully acknowledge very helpful discussions with V.P. Janzen, W. Nazarewicz, 1. Ragnarsson, L.L. Riedinger, N. Schmeing and J. Simpson. References 1) J.D. Morrison, J . Simpson, M.A. Riley, H.W. Cranmer-Gordon, P.D. Forsyth, D. Howe and J.F. Sharpey-Schafer, J. of Phys. G15 (1989) 1871 2) M .A. Riley, J. Simpson, J.F. Sharpey-Schafer, J.R. Cresswell, H. W. Cranmer-Gordon, P.D. Forsyth, D. Howe, A.H. Nelson, P .J. Nolan, P.J. Smith, N .J. Ward, J.C. Lisle, E. Paul and P.M. Walker, N ucl . Phys. A486 (1988) 456 3) J. Simpson, P.A. Butler, P.D. Forsyth, J.F. Sharpey-Schafer, J.D. Garrett, G.B. Hagemann, B. Herskind and L.P. Ekstrom, J. of Phys. G10 (1984) 383 4) L.L. Riedinger, O. Andersen, S. Frauendorf, J.D. Garrett, J.J. Gaardhoje, G.B. Hagemann, B. Herskind, Y.V. Makovetzky, J.C. Waddington, M. Guttormsen and P.O. Tjom, Phys. Rev. Lett. 44 (1980) 568 5) J. Simpson, M.A. Riley, J.R. Cresswell, P.D. Forsyth, D. Howe, B.M. Nyakô, J.F. Sharpey-Schafer, J. Bacelar, J.D. Garrett, G .B. Hagemann, B. Herskind and A. Holm, Phys. Rev. Lett. 53 (1984) 648 ; P.O. Tjom, R.M. Diamond, J.C. Bacelar, E.M . Beck, M.A. Deleplanque, J.E. Draper and F.S. Stephens, Phys. Rev . Lett. 55 (1985) 2405 6) M.A. Riley, J.D. Garrett, J.F. Sharpey-Schafer and J. Simpson, Phys . Lett. B177 (1986) 15 7) G.B. Hagemann, J. D. Garrett, B. Herskind, G. Sletten, P.O. Tjom, A. Henriquez, F. Ingebretsen, J. Rekstad, G. LOvhoiden and T.F. Thorsteinsen, Phys. Rev. C25 (1982) 3224 8) G.B. Hagemann, J. D. Garrett, B. Herskind, J. Kownacki, B.M . Nyakô, P.J. Nolan, J .F. SharpeySchafer and P.O. Tjom, Nucl. Phys. A424 (1984) 365 9) J. Simpson, P.D. Forsyth, D. Howe, B.M. Nyakô, M.A. Riley, J.F. Sharpey-Schafer, J . Bacelar, J.D. Garrett, G.B. Hagemann, B. Herskind, A. Holm and P.O. Tjom, Phys. Rev. Lett. 54 (1985) 1132 10) J. Simpson, D.V. Elenkov, P.D. Forsyth, D. Howe, B.M . Nyakô, M.A. Riley, J.F. Sharpey-Schafer, B. Herskind, A. Holm and P.O. Tjom, J. Phys. G12 (1986) L67 11) J.D. Panar, O. Straume and D.G. Burke, Can . J. Phys. 55 (1977) 1657 12) 1 . Ragnarsson, private communication 13) 1 . Hamamoto and H. Sagawa, Phys. Lett. B201 (1988) 415 14) M. Matsuzaki, Y.R. Shimizu and K . Matsuyanagi, Prog. Theor. Phys. 79 (1988) 836 15) D.C . Radford, Proc. Workshop on nuclear structure, The Niels Bohr Institute, May 1988; D.C . Radford, H .R. Andrews, D. Horn, D. Ward, F. Banville, S. Flibotte, P. Taras, J. Johanssen, D. Tucker and J.C. Waddington, Proc. Conf. on high-spin nuclear structure and novel nuclear shapes, Argonne National Lab ., April 1988 16) H.R. Andrews, E. Hagberg, D. Horn, M .A . Lone, H . Schmeing, D. Ward, P. Taras, J . Gascon, J.C. Waddington, G. Palameta, V.T. Koslowsky and O. Hdusser, "Proposal for a National Facility - The 8-;r Spectrometer", AECL-8329 (1984) 17) G. Palameta and J .C. Waddington, Nucl. Instr. Meth. A234 (1985) 476 18) D.C. Radford, Proc. 1989 Int . Nucl. Phys. Conf., S5o Paulo, Brazil, Aug . 1989 19) F. Banville, M.Sc. Thesis, Universit6 de Montr6al (unpublished) 1988 20) E. Grosse, F .S. Stephens and R.M. Diamond, Phys. Rev. Lett. 32 (1974) 74 21) G.B. Hagemann, J.D. Garrett, B. Herskind, G. Sletten, P.O. Tjom, A. Henriquez, F. Ingebretsen, J. Kownacki, J. Rekstad, G. Ltdvhoiden, T.F. Thorsteinsen, B.M . Nyakô, P.J. Nolan and J.F. Sharpey-Schafer, Nucl . Phys. A487 (1988) 677 22) R.S. Hager and E.C . Seltzer, Nucl. Data A4 (1968) 1

D. C Radford et al. / Multiple band structure 23) 24) 25) 26) 27)

28)

29)

30) 31) 32) 33) 34)

35) 36) 37) 38) 39) 40) 41)

71 9

R.G. Helmer, Nucl. Data Sheets 55 (1988) 71, and references therein R. Bengtsson and S. Frauendorf, Nucl . Phys. A314 (1979) 27, Nucl. Phys. A327 (1979) 139 S.M. Harris, Phys. Rev. B138 (1965) 509 L .L. Riedinger, H .-Q. Jin and C.-H. Yu, Nucl . Phys. A520 (1990) 287c, and references therein J. Gascon, C.-H . Yu, G.B . Hagemann, M.C. Carpenter, J.M. Espino, Y. Iwata, T. Komatsubara, J. Nyberg, S. Ogaza, G. Sletten, P.O. Tjom, D.C. Radford, J. Simpson, A. Alderson, M.A. Bentley, P. Fallon, P.D. Forsyth, J.W. Roberts and J.F. Sharpey-Schafer, Nucl. Phys. A513 (1990) 344 F. Dönau and S. Frauendorf, Proc. Conf. on high angular momentum properties of nuclei, Oak Ridge, Tenn., 1982, ed. N. R. Johnson (Harwood Academic, New York, 1983) ; F. Dönau, Nucl. Phys. A471 (1987) 469 V.P. Janzen and S. Frauendorf, private communication ; V.P. Janzen, Z.-M . Liu, M.P. Carpenter, L.H . Courtney, H.-Q. Jin, A.J. Larabee, L.L. Riedinger, J.K. Johansson, D.G. Popescu, J .C. Waddington, S . Monaro, S. Pilotte and F. Dönau, Phys. Rev. C, to be published G.B. Hagemann and 1. Hamamoto, Phys. Rev . C40 (1989) 2862 A. Ikeda, Nucl . Phys. A439 (1985) 317 M. Matsuzaki, Proc. Int . Conf. on high spin physics and gamma-soft nuclei, Pittsburgh, PA, 1990, ed. J .X . Saladin, R.A . Sorensen and C.M. Vincent (World Scientific, Singapore, 1991) N. Yoshida, H. Sagawa, T. Otsuk and A. Arima, Nucl. Phys. A503 (1989) 90 G.B. Hagemann, 1 . Hamamoto and D.C. Radford, Proc. Int . Conf. on high spin physics and gamma-soft nuclei, Pittsburgh, PA, 1990, ed. J.X. Saladin, R.A. Sorensen and C.M. Vincent (World Scientific, Singapore, 1991) R. Bengtsson, I. Hamamoto and B. Mottelson, Phys. Lett. B73 (1978) 259 J. Almberger, I. Hamamoto and G. Leander, Phys. Lett. B80 (1979) 153 I. Hamamoto, Phys. Lett. B179 (1986) 327 P.A . Butler, Proc. Int . Conf. on high spin physics and gamma-soft nuclei, Pittsburgh, PA, 1990, ed. J.X. Saladin, R.A. Sorensen and C.M. Vincent (World Scientific, Singapore, 1991) I. Hamamoto, J. H61ler and X .Z. Znang, Phys. Lett . B226 (1989) 17 B . Lauritzen, T. Dossing and R.A. Broglia, Nucl . Phys. A457 (1986) 61 I . Ragnarsson and T. Bengtsson, Int . Conf. on selected topics in nuclear structure, Dubna, USSR, June 1989