high-spin states, lifetime measurements and isomers in os

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Nuclear Physics A 728 (2003) 287–338

www.elsevier.com/locate/np

High-spin states, lifetime measurementsand isomers in181Os

D.M. Cullena,∗, L.K. Pattisona, J.F. Smitha, A.M. Fletchera,P.M. Walkerb, H.M. El-Masrib, Zs. Podolyákb, R.J. Woodb,

C. Scholeyc,1, C. Wheldonc,2, G. Mukherjeed,3, D. Balabanskie,4,M. Djongolove, Th. Dalsgaardf, H. Thisgaardf, G. Slettenf,F. Kondevg,5, D. Jenkinsg,6, G.D. Dracoulish, G.J. Lanei,7,

I.-Y. Leei, A.O. Macchiavellii , F. Xuj

a Schuster Laboratory, University of Manchester, Manchester M13 9PL, United Kingdomb Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom

c Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdomd Department of Physics, University of Massachusetts, Lowell, MA 01854, USA

e Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USAf Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen, Denmark

g Physics Division, Argonne National Laboratory, Argonne, IL 60439, USAh Department of Nuclear Physics, RSPhysSE, Australian National University, Canberra, ACT 0200, Aus

i Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USAj Department of Technical Physics, Peking University, Beijing 100871, China

Received 5 August 2003; received in revised form 28 August 2003; accepted 1 September 2003

* Corresponding author.E-mail address:[email protected] (D.M. Cullen).

1 Present address: Department of Physics, University of Jyväskylä, P.O. Box 35, FIN-40351, JyvFinland.

2 Present address: Kernphysik II, GSI, Max-Planck-Straße 1, D-64219 Darmstadt, Germany.3 Present address: Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA.4 Present address: University of Leuven, Celestijnelaan 200 D, B-3001, Leuven, Belgium.5 Present address: Nuclear Engineering Division, Argonne National Laboratory, Argonne, IL 6

USA.6 Present address: Department of Physics, University of York, Heslington, York YO10 5DD, United King
7 Present address: Department of Nuclear Physics, RSPhysSE, Australian National University, Canberra,
ACT 0200, Australia.

0375-9474/$ – see front matter 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.nuclphysa.2003.09.001

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288 D.M. Cullen et al. / Nuclear Physics A 728 (2003) 287–338

Abstract

The level scheme of18176Os has been investigated with the150Nd(36S,5n) reaction. The low-K

rotational bands built upon the 9/2+[624], 7/2−[514] and 1/2−[521] neutron configurations havbeen extended and other new bands established. The configurations of these low-K bands arediscussed within the framework of the cranked-shell model. The lifetimes for some of thein the 9/2+[624] and 1/2−[521] collective rotational bands were also measured using the DoShift Attenuation method. The large deformations deduced are found to be consistent withpredicted from theoretical Total Routhian Surface calculations. These results support the idfor these low-K states the nuclear shape is axially symmetric and allows theK quantum number tobe defined and the associatedK-selection rule to be upheld. This behaviour apparently contraststhat of the higher-K states in181Os.

In the higher-spin regime, two new high-K intrinsic states, withKπ = 37/2+ and Kπ =41/2+, were established, along with the fragmented decay of aKπ = 33/2− intrinsic state. Theconfigurations and excitation energies of these experimentally determined intrinsic states arto be in excellent agreement with theoretical calculations based on a fixed shape Nilssonplus BCS pairing. The structures on top of these intrinsic states do, however, show very dbehaviour. A relatively regular high-K rotational band was observed on top of theKπ = 41/2+state but not for the other newly-established intrinsic states. Theoretical configuration-conspotential energy surface calculations suggest that the irregular transition sequence above thKπ =37/2+ intrinsic bandhead state, the limited excitations observed above the other intrinsic stathe observation of fragmented and non-hindered decays, are due to these configurations beinto an appreciableγ softness. These calculations reveal that theKπ = 41/2+ configuration is lesssusceptible to distortions in theγ plane than any of the other high-K states. 2003 Elsevier B.V. All rights reserved.

PACS:27.70.+q; 21.10.Jx; 21.10.Re; 21.10.Tg

Keywords:NUCLEAR REACTIONS150Nd(36S,5n),E = 160 MeV; measuredEγ , Iγ , γ γ -coin., DSA.181Osdeduced high-spin levels,J , π , configurations,T1/2, quadrupole moments. Cranked shell-model analysis.Gammasphere array

1. Introduction

Nuclei in the mass-180 region of the nuclear chart are well known for their abundof isomeric, or long-lived, states [1]. These arise because of the particular high-Ω single-particle orbitals which are near the well-deformed proton and neutron Fermi surfacecoupling of the individual NilssonΩ quantum numbers leads to the intrinsic quantnumber,K, which is the sum of the individual-particle intrinsic angular momenprojected onto the nuclear symmetry axis. The isomerism or long-lifetime of these nstates arises becauseK is an approximately conserved quantum number. For an exhigh-K state to decay it is subject to theK-selection rule which states that, for an allowtransition,K λ, whereK is the change inK between the two states andλ is themultipolarity of the connecting transition. For every order of so-calledK forbiddenness,ν,
(ν =K − λ) the transition is expected to be hindered by an order of magnitude [2] overthe Weisskopf single-particle estimate.

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D.M. Cullen et al. / Nuclear Physics A 728 (2003) 287–338 289

In order for theK quantum number to be defined for a particular nuclear statenucleus must be deformed and axially-symmetric. In the mass-180 region of the nchart this condition is generally met for the mid-shell nuclei. Many high-K states with longlifetimes have been identified in theZ = 72 hafnium isotopes from170–184Hf [1] and in theZ = 73 tantalum isotopes from175Ta [3] to 185Ta [4]. In theZ = 74 tungsten isotopemany high-K states are known including a seniority ten,Kπ = (34+), multiquasiparticlestate in178W [5,6] and multiquasiparticle isomeric states in theZ = 75 rhenium nucleare established from179Re [7] to 185Re [8]. Most of the decays from these isomgenerally obey theK-selection rule and their underlying single-particle configurationsbe deduced from the properties of the collective rotational bands built upon the isostates.

In contrast, as the atomic number is increased, a change in the goodnessK-selection rule has been observed. In182Os a large breakdown in theK-selection ruleoccurs [9]. AKπ = 25+ isomeric state was observed to decay directly to the yrast(with smallK) via a single-M1 transition of energy 1061 keV. The reduced hindrafactor for the decay,fν = 2.2, was observed to be one to two orders of magnitude smthan predicted based on theK-selection rule. Reasons discussed for this unexpected dwere (a) a susceptibility toγ softness which results in a loss of axial symmetry throeither shape fluctuations [10] (tunnelling through theγ -deformed shapes) or (b) orientatifluctuations [11] (mediated by, for example,K=1 Coriolis mixing). Since the recenobservation of the transitions built upon theKπ = 25+ isomeric state in182Os, newtheoretical ideas have been developed [12]. Tilted axis cranking (TAC) calculationspresented evidence thatγ vibrations can effectively compete with collective rotationsgenerating angular momentum in a nuclear shape that is susceptible toγ distortions. Thesecond largest case of breakdown of theK-selection rule has been observed in183Os whereaK = 17 transition was observed to decay from aKπ = (43/2+) isomeric state directlyinto theKπ = 9/2+ ground-state band [13]. The existence of this decay path wasreasoned to be observed due toγ softness. These ideas are also backed up by the propof the bands built upon the isomers. The structures of these bands are irregular andgenerally extend for more than a few transitions. In addition, their isomeric half-livemuch shorter (generally a few ns) than would be expected based on theK-selection rule.

The present work was motivated to identify transitions above a known 34± 6 nsisomeric state in181Os [14,15]. The properties of these newly identified states havecompared with theoretical multiquasiparticle blocked BCS calculations and configuconstrained potential energy surface calculations. Although a regular structurestablished on top of aKπ = 41/2+ isomeric state, this was not the case for the other neobserved intrinsic states. Some of these were observed to have short ( few ns) half-livesand rotational bands that only survive for a few transitions; behaviour more reminiscthat observed in the heavier and moreγ -soft Os nuclei, discussed above. A more detadecay pattern for theKπ = 33/2− intrinsic state decay was also deduced with manydecays established feeding both known, and some newly identified low-K levels in181Os.

The transition quadrupole moments of the low-K bands were also measured establiing the deformation of the low-K bands. These results support the idea that in the lowK

regime the nuclear shape is predominately axially symmetric and shows that theK quan-tum number and associatedK-selection rule should be reasonably well obeyed. However,

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recent evidence for aγ softness was recently presented for the 9/2+[624] and 1/2−[521]bands in181Os from recoil-distance lifetime measurements [16]. Indeed, the configtion constrained potential energy surface calculations [17] performed in this work rthat the higher-K states in181Os are susceptible to an appreciableγ softness. This workalso reports the extension of the rotational bands built upon the 9/2+[624], 7/2−[514] and1/2−[521] configurations up to spins of 73/2-, 79/2- and 73/2-h, respectively. The configurations and observed band crossings of these, and other newly established badiscussed within the framework of the cranked-shell model.

2. Experiment

High-spin states were populated in181Os with the150Nd(36S,5n) reaction. The36Sbeam was supplied by the 88-inch cyclotron at the Lawrence Berkeley National Laboand the data were recorded with the one hundred and one escape-suppressed gedetectors of the GAMMASPHERE array [18]. The natural beam pulsing frequency14.2 MHz resulted in a beam pulse every 70.4 ns. Copper absorbers of thic≈ 0.38 mm were used in front of the germanium detectors to reduce the number ofX-raysbeing detected. Energy and efficiency calibrations were obtained with133Ba and152Eusources placed at the target position. Two150Nd targets (enriched to 89.9%) were usedthe experiment. Firstly, a thin 0.7 mg/cm2 target was employed to enhance the observaof the high-spin states in181Os. A 7.7-pnA beam with energy 160 MeV was used wthis thin target and a total of 5.0 × 1010 unpacked quadruple-coincident events wcollected. Secondly, a 1.0 mg/cm2 target was used with a 7.3 mg/cm2 backing of197Au.The backed target was employed to stop the nuclear recoils in the focus of the arobserve isomeric decays, and to permit a Doppler shift attenuation method to be ato deduce the lifetimes of some of the states in the collective bands. A 5.0-pnAwith energy 160 MeV, was used and a total of 9.8× 1010 unpacked quadruple-coincideevents were collected. The beam current was adjusted in both cases to limit therate in the individual germanium detectors to 4–5 kHz which resulted in an event rapproximately 10 kHz for aγ -ray fold condition of 4. Theγ –γ coincidence timingwindow was defined such that the maximum allowed time difference between angermanium detectors, which were considered to be part of the same event, was≈ 1 µs.

3. Data analysis and results

3.1. Low-K states

The partial level scheme for the low-K structures in181Os is shown in Fig. 1. Osmium181 was previously studied to intermediate spins in Ref. [19]. This new level schemdeduced from a variety of two-, three- and four-dimensional matrices. Gates were
in these matrices and theγ -ray intensities and coincidence relationships were used todetermine the order of theγ rays in the level scheme. These data were analysed using both

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energies are given in keV, while the widths of the arrowsconversion. The high-K states built upon theKπ = 35/2− state

Fig. 1. Partial level scheme for181Os established from this work which focuses on the low-K states. Transitionindicate their relative intensities, with the white parts showing the calculated component from internaland above are shown in Fig. 7.

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the “Radware” [20] and the “UPAK” [21] software packages. The energies and intenof all of the transitions associated with the low-K states in181Os are given in Table 1.

Information about transition multipolarities was obtained from a directional correlfrom oriented states (DCO) analysis [22,23]. A matrix was constructed with onecontaining detectors at 79, 81, 90 and 100 and the other axis containing detectoat 17, 32, 163 and 148 using the thick-target data. DCO ratios,RDCO (defined below),were established for the more strongly-populated transitions, see Table 1. For eacratio, a gate was set on a known-E2 transition and values for the unknown transitiocalculated according to

RDCO = Iγ (17,32,163,148) gated by(79,81,90,100)Iγ (79,81,90,100) gated by(17,32,163,148)

. (1)

For pure transitions, these values were found to beRDCO ≈ 0.6 if the unknown transitionis a stretched dipole-,RDCO ≈ 1.0 for stretched quadrupole- andRDCO ≈ 1.2 for

Table 1The energies, intensities and DCO ratios for all of theprompt low-K γ -ray transitions observed in181Os inthis work, see text for details. If no DCO ratio is given then the spin assignment is based upon the preestablished level scheme [19] or upon the best estimates according to the most-likely multipole combbetween the states

Eγ Iγ RDCO/Assignment Band Jπi → Jπf

43.1(1) 67.7(15) 0.68(8)/M1 2b 11/2+ →9/2+73.9(6) 44.2(12) 0.60(4)/M1 2a 13/2+ →11/2+88.8(6) 22.4(30) 2a 25/2+ →23/2+91.0(8) 1.0(9) 5a 23/2− →21/2−93.9(1) 20.0(30) 3b 3/2− →1/2−

102.9(1) 57.3(4) 3a 5/2− →1/2−107.5(4) 182.5(64) 2a 21/2+ →19/2+107.8(3) – 0.57(3)/E1 2a 9/2+ →7/2−108.2(4) 41.4(63) 0.64(1)/M1 2b 17/2+ →15/2+118.2(6) 11.5(5) 0.99(3)/E2 2a 13/2+ →9/2+123.6(2) 34.1(62) 0.77(12)/M1 5b 25/2− →23/2−123.7(1) 291.2(90) 0.55(1)/M1 1b 9/2− →7/2−130.8(1) 233.9(85) 0.49(4)/E1 4b 23/2− →21/2+148.5(1) 212.4(87) 0.52(2)/M1 1b 11/2− →9/2−149.0(3) 100.7(89) 0.23(1)/M1 2b 15/2+ →13/2+160.2(1) 64.3(78) 0.48(12)/M1 5a 27/2− →25/2−170.5(1) 85.1(50) 0.47(4)/M1 1b 13/2− →11/2−188.5(1) 14.8(9) 6a 25/2− →25/2−190.0(4) 10.6(35) 5b 29/2− →27/2−191.0(1) 43.9(35) 0.54(5)/M1 1a 15/2− →13/2−195.4(1) 21.6(10) 8a 41/2+ →39/2+204.0(1) 35.5(20) 4a 25/2− →23/2−208.8(1) 36.1(32) 1b 17/2− →15/2−213.0(7) 2.4(12) 5b 25/2− →21/2−214.6(1) 28.2(10) 4b 27/2− →25/2−217.9(5) 10.6(35) 3b 7/2− →5/2−222.2(1) 30.6(20) 0.84(12)/M1 5a 31/2− →29/2−
223.0(3) 114.6(50) 1.13(4)/E2 2b 15/2+ →11/2+
(continued)


Table 1 (continued)

Eγ Iγ RDCO/Assignment Band Jπi

→ Jπf

225.6(3) 20.6(32) 0.50(5)/M1 1a 19/2− →17/2−226.0(3) 18.4(10) 8a 37/2+ →35/2+227.0(1) 127.7(125) 3b 7/2− →3/2−229.1(4) 40.6(20) 4a 29/2− →27/2−231.7(1) 447.7(15) 3a 9/2− →5/2−238.5(3) 17.8(32) 1b 21/2− →19/2−246.4(1) 27.0(20) 0.43(9)/M1 5b 33/2− →21/2−252.4(2) 33.6(44) 0.39(6)/E1 1a 23/2− →21/2−257.1(7) 65.3(50) 0.39(3)/M1 2b 19/2+ →17/2+257.1(3) 54.8(10) 0.79(2)/E2 2a 17/2+→13/2+262.3(1) 75.5(43) 1b 25/2− →23/2−267.5(3) 20.8(38) 0.84(10)/M1 1a 27/2− →25/2−271.8(1) 670.4(567) 0.92(3)/E2 1a 11/2− →7/2−275.5(5) 96.9(121) 1b 29/2− →27/2−276.4(3) 31.1(50) 0.70(4)/M1 1b 29/2− →27/2−283.8(2) 31.5(41) 1a 31/2− →29/2−284.0(3) 10.5(44) 1.54(12)/E2 5a 27/2− →23/2−290.8(1) 27.9(20) 5b 37/2− →35/2−312.1(2) 19.6(3) 5a 27/2− →25/2−316.3(1) 26.3(20) 5a 39/2− →37/2−318.6(1) 1000.0(367) 0.97(2)/E2 1b 13/2− →9/2−322.4(1) 21.5(10) 5a 41/2− →39/2−342.8(1) 66.2(41) 3b 11/2− →7/2−343.1(1) 415.4(130) 3a 13/2− →9/2−346.2(2) 19.6(35) 5a 43/2− →39/2−349.8(3) 34.6(82) 5b 29/2− →25/2−361.5(1) 708.4(290) 0.96(4)/E2 1a 15/2− →11/2−364.8(2) 340.4(128) 0.97(2)/E2 2a 21/2+ →17/2+365.3(6) 148.9(146) 1.00(5)/E2 2b 19/2+ →15/2+374.6(8) 45.7(38) 2b 23/2+ →21/2+395.2(1) 196.7(65) 3a 29/2− →25/2−399.9(1) 662.6(230) 1.01(2)/E2 1b 17/2− →13/2−412.4(2) 72.2(88) 0.80(5)/E2 5a 31/2− →27/2−412.5(2) 1.0(9) 5a 35/2− →29/2−418.0(2) 13.1(20) 4b 27/2− →23/2−421.8(1) 418.3(95) 3a 17/2− →13/2−430.8(1) 24.8(30) 3b 15/2− →11/2−431.1(3) 12.5(20) 1.27(19)/E2 5a 27/2− →25/2−434.3(1) 635.7(240) 0.96(2)/E2 1a 19/2− →15/2−435.0(1) 342.6(110) 3a 25/2− →21/2−440.1(1) 285.6(94) 3a 33/2− →29/2−442.4(2) 24.5(30) 4a 29/2− →25/2−451.7(2) 15.3(20) 6a 29/2− →25/2−455.1(1) 380.5(120) 3a 21/2− →17/2−463.8(2) 469.5(167) 1.01(2)/E2 2a 25/2+ →21/2+464.4(1) 640.6(240) 1.03(3)/E2 1b 21/2− →17/2−467.9(3) 15.1(30) 5b 33/2− →29/2−475.2(1) 31.6(20) 4a 31/2− →27/2−

+ +
482.4(6) 146.2(73) 1.02(11)/M1 2b 23/2 →19/2(continued on next page)


Table 1 (continued)


→ Jπf

488.7(1) 58.4(41) 3b 19/2− →15/2−488.9(2) 18.6(30) 2b 27/2+ →25/2+490.4(1) 565.8(210) 0.99(3)/E2 1a 23/2− →19/2−498.3(2) 15.1(20) 3b 31/2− →27/2−509.7(2) 15.2(30) 3b 27/2− →23/2−512.6(1) 525.9(190) 0.99(3)/E2 1b 25/2− →21/2−516.3(1) 49.1(30) 0.95(13)/E2 3a 29/2− →25/2−516.7(2) 21.7(30) 3b 23/2− →19/2−518.0(1) 35.1(30) 4a 33/2− →29/2−521.4(1) 41.9(35) 0.57(13)/E2 5a 35/2− →31/2−524.9(2) 14.1(20) 3b 35/2− →31/2−526.5(1) 197.8(68) 3a 37/2− →33/2−531.4(1) 461.3(190) 1.00(2)/E2 1a 27/2− →23/2−535.0(5) 79.1(25) 1.10(25)/M1 5b 25/2− →23/2−536.0(2) 2.9(20) 3b 39/2− →35/2−547.9(1) 413.1(148) 0.94(7)/E2 1b 29/2− →25/2−547.9(2) 410.1(670) 0.97(2)/E2 2a 29/2+ →25/2+560.7(1) 346.9(140) 0.95(4)/E2 1a 31/2− →27/2−563.6(2) 23.0(30) 6a 33/2− →29/2−565.3(1) 285.2(140) 1.03(7)/E2 1b 33/2− →29/2−565.7(1) 51.1(50) 5b 37/2− →33/2−566.7(1) 80.6(73) 1a 35/2− →31/2−567.5(1) 210.0(140) 0.97(4)/E2 4b 35/2− →31/2−574.7(1) 159.8(91) 0.97(6)/E2 1b 37/2− →33/2−577.4(4) 132.5(68) 1.00(3)/E2 2b 27/2+ →23/2+585.4(8) 11.3(42) 2b 31/2+ →29/2+586.9(3) 289.3(123) 1.01(3)/E2 2a 41/2+ →37/2+596.5(3) 4.5(6) 1a 33/2− →29/2−597.5(1) 188.8(120) 1a 39/2− →35/2−599.7(3) 485.1(206) 0.97(3)/E2 2a 37/2+ →33/2+601.3(4) 285.6(139) 1.05(2)/E2 2a 33/2+ →29/2+606.5(1) 49.9(29) 6b 37/2− →33/2−607.3(1) 69.4(47) 1.24(12) 5a 39/2− →35/2−614.7(1) 104.3(65) 4a 37/2− →33/2−618.5(1) 147.2(50) 3a 41/2− →37/2−620.2(2) 25.0(30) 5c (45/2−)→ (41/2−)621.8(1) 55.1(32) 6a 25/2− →21/2−624.6(1) 99.8(62) 1.00(6)/E2 4a 33/2− →29/2−627.6(3) 190.1(81) 1.01(3)/E2 2a 45/2+ →41/2+629.1(1) 118.7(79) 1.03(4)/E2 1b 41/2− →37/2−631.5(2) 50.0(50) 0.83(6)/E2 4b 31/2− →27/2−634.8(1) 65.3(50) 1.03(4)/E2 4b 35/2− →31/2−639.0(1) 34.0(30) 6a 29/2− →25/2−639.3(2) 68.9(59) 4b 39/2− →35/2−640.7(3) 21.1(35) 5b 41/2− →37/2−643.3(7) 70.8(429) 2b 43/2+ →39/2+645.1(6) 103.8(318) 0.99(3)/E2 2b 31/2+ →27/2+647.7(1) 38.8(29) 5c (41/2−)→37/2−

− −
649.1(2) 13.8(20) 6b 41/2 →37/2(continued)


Table 1 (continued)


→ Jπf

653.1(5) 82.0(72) 0.96(5)/E2 2b 39/2+ →35/2+654.8(26) 2.7(20) 2b 35/2+ →33/2+661.3(2) 11.7(32) 0.96(13) (I = 0) 5a 23/2− →21/2−663.2(1) 90.2(79) 1.01(3)/E2 1a 43/2− →39/2−669.4(2) 24.2(32) 5a 43/2− →39/2−671.4(5) 104.0(58) 1.00(4)/E2 2b 35/2+ →31/2+673.9(1) 64.7(47) 0.84(7)/E2 4a 37/2− →33/2−678.3(4) 10.8(30) 5b 45/2− →41/2−680.9(1) 68.2(50) 1.11(16)/E2 4a 41/2− →37/2−685.0(2) 14.3(20) 6a 37/2− →33/2−695.5(7) 7.1(26) 5a 27/2− →23/2−696.8(2) 10.9(10) 5c (49/2−)→ (45/2−)698.0(5) 8.6(29) 5b 49/2− →45/2−699.8(2) 22.9(35) 5a 47/2− →43/2−702.8(1) 89.8(73) 0.94(4)/E2 1b 45/2− →41/2−704.8(1) 99.4(35) 3a 45/2− →41/2−708.2(4) 145.3(81) 1.03(4)/E2 2a 49/2+ →45/2+710.0(3) 18.0(32) 0.80(7)/E2 2b 47/2+ →43/2+710.9(1) 31.6(29) 4b 43/2− →39/2−718.4(2) 16.4(20) 6b 45/2− →41/2−719.4(4) 13.0(29) 5a 51/2− →47/2−722.3(5) 5.2(30) 5b 53/2− →49/2−725.1(1) 51.9(47) 0.60(13)/E2 4a 45/2− →41/2−732.6(2) 75.1(76) 0.93(7)/E2 1a 47/2− →43/2−735.5(4) 8.8(20) 5b (57/2−)→53/2−735.8(3) 9.3(20) 6a 41/2− →37/2−741.9(1) 35.7(20) 4b 47/2− →43/2−747.6(8) 5.7(29) 5a 55/2− →51/2−747.7(1) 50.1(44) 0.76(19)/E2 4a 49/2− →45/2−749.5(1) 27.1(20) 0.79(6)/E2 1d 53/2− →49/2−750.9(5) 6.4(20) 5b (61/2−)→57/2−756.1(6) 4.1(20) 6b 49/2− →45/2−760.2(1) 23.4(20) 0.94(14)/E2 1c 51/2− →47/2−764.0(1) 29.3(20) 4b 51/2− →47/2−766.3(3) 10.7(20) 6a 45/2− →41/2−766.4(1) 49.2(20) 0.83(5)/E2 1d 49/2− →45/2−777.4(3) 4.0(10) 5a 59/2− →55/2−780.9(1) 65.8(30) 0.68(4)/E2 3a 49/2− →45/2−786.0(3) 29.4(65) 0.68(4)/E2 1b 49/2− →45/2−786.4(9) 6.0(30) 5b 25/2− →21/2−786.5(2) 17.9(20) 0.68(4)/E2 1c 55/2− →51/2−788.1(1) 16.9(10) 5c 53/2− →49/2−788.2(3) 14.4(38) 4a 57/2− →53/2−793.9(4) 28.0(57) 2b 51/2+ →47/2+801.2(1) 39.4(30) 0.46(9)/E2 1a 51/2− →47/2−802.3(7) 85.7(82) 2a 53/2+ →49/2+802.4(4) 1.4(10) 6a (49/2−)→45/2−804.6(2) 18.1(20) 4b 55/2− →51/2−

− −
805.8(3) 1.7(10) 5a (63/2 )→59/2(continued on next page)


Table 1 (continued)


→ Jπf

807.5(5) 6.4(20) 6b 53/2− →49/2−809.8(5) 1.0(9) 5b 21/2− →19/2−826.0(1) 24.8(20) 1d 57/2− →53/2−829.2(1) 27.4(20) 5a (67/2−)→ (63/2−)833.1(2) 14.4(20) 6a (53/2−)→ (49/2−)840.9(4) 27.7(62) 1b 57/2− →53/2−844.0(1) 44.1(30) 1a 55/2− →51/2−846.3(1) 64.7(30) 3a 53/2− →49/2−847.0(2) 25.8(20) 1b 59/2− →55/2−847.5(4) 29.4(68) 3a 53/2− →49/2−848.2(1) 61.3(32) 1.3(1)/E2 (I = 0) 4a 21/2+ →21/2+849.4(2) 18.5(20) 6a (57/2−)→ (53/2−)854.3(3) 11.6(20) 6b 57/2− →53/2−858.0(1) 21.7(20) 1c 59/2− →55/2−859.0(2) 10.9(10) 5c (57/2−)→ (53/2−)876.7(6) 20.5(70) 2b 55/2+ →51/2+897.7(8) 10.5(50) 1b 61/2− →57/2−897.9(3) 44.8(78) 2a 57/2+ →53/2+898.0(1) 22.0(20) 1a 59/2− →55/2−898.7(3) 7.4(21) 5a 23/2− →19/2−899.0(1) 22.0(20) 3a 57/2− →53/2−912.6(3) 5.3(10) 3c 57/2− →53/2−925.8(3) 7.3(10) 1c 63/2− →59/2−931.4(23) 3.3(41) 1b 65/2− →61/2−954.2(42) 8.7(24) 2b 59/2+ →55/2+956.0(3) 2.9(9) 3c (61/2−)→ (57/2−)956.5(19) 26.7(23) 4a 21/2+ →19/2+973.5(2) 10.7(10) 3a 61/2− →57/2−979.6(1) 14.7(10) 1a 63/2− →59/2−982.6(3) 8.8(10) 1c 67/2− →63/2−997.3(5) 24.8(85) 2a 61/2+ →57/2+

1007.7(2) 7.7(9) 3c (65/2−)→ (61/2−)1023.5(2) 7.9(9) 1c 71/2− →67/2−1029.1(1) 12.1(9) 3a 65/2− →61/2−1031.7(6) 8.9(30) 2b 63/2+ →59/2+1053.3(5) 0.5(3) 5b 21/2− →17/2−1051.7(2) 7.8(9) 3c (69/2−)→ (65/2−)1055.6(2) 7.8(9) 1c 75/2− →71/2−1077.4(4) 3.6(6) 1a 67/2− →63/2−1088.0(9) 0.9(6) 3c (73/2−)→ (69/2−)1089.3(4) 2.6(6) 1c (79/2−)→75/2−1090.6(9) 4.9(20) 2a 65/2+ →61/2+1092.7(9) 4.0(30) 2b 67/2+ →63/2+1105.7(5) 1.8(6) 3a 69/2− →65/2−1143.9(8) 2.9(3) 1a (71/2−)→67/2−1155.5(5) 1.0(9) 3a 73/2− →69/2−1181.8(9) 4.8(30) 2a 69/2+ →65/2+1212.9(3) 8.7(6) 4a 21/2+ →17/2+1263.4(9) 14.7(26) 2a (73/2+)→ (69/2+)
1321.9(9) 1.7(59) 2a (77/2+)→ (73/2+)

uld notses and

inations were

n1

d 1es,

ns,rtaintyt with

1


unstretched dipole- and unstretched quadrupole-transitions. Where DCO ratios cobe established, the spins and parities are shown in the level scheme with parenthethese are the best estimates according to the most likely transition multipole combbetween the states. In the absence of long lifetimes only dipole and E2 multipolaritieconsidered.

The7/2−[514] bands1a, 1b, 1c, 1dBands 1a and 1b, based on the one-quasiparticle 7/2−[514] configuration, have bee

extended from spins 51/2h [19] to spins 71/2h, see Fig. 1. Two new sequences, bandscand 1d , were established to feed into bands 1a and 1b at spins 47/2h and 45/2h,respectively. The triple-gated spectrum in Fig. 2(a) shows the extension to bana,Fig. 2(b) shows the extension to band 1b, and Figs. 2(c) and (d), the new sequencbands 1c and 1d , respectively. The DCO ratios for theγ rays which link band 1c toband 1a and band 1d to band 1b, via the respective 760.2- and 766.4-keV transitioare given in Table 1. These DCO ratios favour an E2 assignment, although the uncefor the 760.2-keV transition is fairly large. This E2 assignment is, however, consisten

Fig. 2. Triple-gated spectra for the 7/2− [514] bands observed in this work from the thin-target data. (a) Banda;triple-gated spectrum from all non-diagonal combinations of the gatelista/b/b where list a = (272,361,434,490,531,561,567,598,663,733) keV and list b = (801,844,898,980) keV. (b) Band 1b; triple-gatedspectrum from all combinations of the two gatelistsc/d/786 where listc = (319,400,513,565) keV andlist d = (575,629,703) keV. (c) Band 1c; triple-gated spectrum from all combinations of the gateliste/f/g,where liste= (272,361,434,490,531,561,567,598,663,733) keV, list f = (760,787) keV and listg = (858,
926,983) keV. (d) Band 1d ; triple-gated spectrum from all combinations of the gatelisth/i/766, where listh= (319,400,513,565) and listi = (575,629,703) keV.

nusual

of theis

nss 2spins

ethe


the smooth energy increase expected for a collective transition. In a perhaps more umanner, the 33/2− state in band 1b was established to decay to the 29/2− state in band 3awith a 596.5-keV transition, see Fig. 1. This is likely due to the chance degeneracy29/2− states in band 3a at 2385 keV and band 1b at 2416 keV, but other reasons for thdecay are discussed in Section 4.2.4.

The9/2+[624] bands2a, 2bThe 9/2[624] one-quasiparticle bands, bands 2a and 2b, have been extended from spi

55/2h to spins 77/2h see Fig. 1. Figs. 3(a) and (b), show triple-gated spectra for bandaand 2b, respectively. These bands exhibit a large signature splitting such that above35/2+, the 37/2+ state in band 2a lies below the 35/2+ state in band 2b.

The1/2−[521] bands3a, 3b, 3cThe bands based on the 1/2−[521] quasiparticle orbital, bands 3a and 3b, have been

extended. Band 3a was extended from spin 57/2h to spin 73/2h, however, band 3b wasfound to be weakly populated and only extended from spin 27/2h to 39/2h, see Fig. 1.

Fig. 3. Triple-gated spectra for the 9/2+ [624] and the t-bands observed in this work from ththin-target data. (a) Band 2a; triple-gated spectrum from all non-diagonal combinations ofgatelistj/j/j , where listj = (118,257,365,464,548,601,600,587,628,708,802,899,997,1091,1182) keV.(b) Band 2b; triple-gated spectrum from all non-diagonal combinations of the gatelistk/k/k, where listk = (223,365,482,577,645,671,653,643,710,794,877,954,1032) keV. (c) Band 4a; triple-gated spectrumfrom all non-diagonal combinations of the gatelistm/m/m, where listm = (443,518,615,681,725,748,766,
788) keV. (d) Band 4b, triple-gated spectrum from all non-diagonal combinations of the gatelistn/n/n, wherelist n= (639,711,742,764,805,847,874,896,932) keV.

ta.

d 3ed in0-keV-keV

fornot,

th it

toeV


Fig. 4. Triple-gated spectra for the 1/2− [521] bands observed in this work from the thin-target da(a) Band 3a; triple-gated spectrum from all non-diagonal combinations of the gatelisto/o/p, where listo = (103,232,343,422,455,435,395,440,526,618,705,781,846) keV and listp = (902,973,1029,1106,1156) keV. (b) Band 3c; triple-gated spectrum from all non-diagonal combinations of the gatelisto/o/q, wherelist o as above and listq = (913,1008) keV.

Gates placed on band 3a at low frequency give evidence for interband transitions to banbfrom the 9/2− to 7/2− states. The associated 13.7-keV transition was not observthis work due to its low energy, however, its presence is implied because the 227.transition in band 3b was observed in the spectra gated on the 421.8- and 455.1transitions in band 3a. In a similar manner to bands 1a and 1b, band 3a is crossed byanother sequence, band 3c, at spin 53/2h. Figs. 4(a) and (b) show triple-gated spectrabands 3a and 3c, respectively. A DCO ratio for the 912.6-keV linking transition couldbe extracted in the present work. In an analogous manner to band 1a, discussed abovethe 29/2− state in band 3a was observed to decay to the 25/2− state in band 1b with a516.3-keVγ -ray transition. The DCO ratio for this transition 0.95(13) is consistent wibeing an E2 transition which is in turn consistent with the spin 25/2− of the state to whichit feeds in band 1b.

Bands4a, 4bBands 4a and 4b have been extended [19] from spins 53/2− to spins 71/2− in the

present work, see Figs. 3(c) and (d). Bands 4a and 4b were also observed to decaybands 1a and 1b from the 37/2h to 31/2h states via 673.9-, 634.8-, 624.6- and 631.5-k
transitions, see Fig. 1. The DCO ratios for these linking transitions are only consistent withE2 assignments, see Table 1. In addition, this spin assignment is consistent with the decay

chtioe

alysis

ectedwasns (ofenergyformer

5

7

w

tes toeVose large, in this86.4-,ellowsd 5

5-,nd

in

atedlower-

gtent

1


of bands 4a and 4b through anIπ = 21/2+ state at excitation energy 1744 keV, whidecays to bands 2a and 2b via 848.2-, 956.5- and 1213.5-keV transitions. A DCO racould only be extracted for the 848.2-keVγ -ray,RDCO = 1.3(1) which was assigned to ban M1(I = 0) transition. This assignment and associated spin of 21/2h for the 1744 keVintrinsic isomeric state is consistent with the assignment deduced from the DCO anof the linking transitions to bands 1a and 1b discussed above.

In the present work, a detailed search for the rotational band which might be expto be built upon theKπ = 21/2+ isomeric state was undertaken. Although this bandnot established tentative evidence for a series of low-energy coincident transitioenergy 176-, 222-, 251-, 254-, 256-, 279- 289- and 301-keV) and a series of higher-transitions (of energy 474-, 506-, 510- and 568-keV) were observed, see Fig. 1. Themay be the M1- and the latter the E2-transitions associated with theKπ = 21/2+ isomericstate, but more data would be required to fully test this.

Bands5a, 5b, 5bIn this work, the bands labelled 5a and 5b, have been extended to high spin, banda

from spin 45/2h to spin(67/2)h, and band 5b from spin 39/2h to spin(61/2)h. A loneγ -ray transition, of energy 647.7 keV, was reported in Ref. [19] to feed into the 3/2hstate in band 5b. In this work the rotational band, labelled band 5c, which is built uponthe 4173-keV state, was established up to spin(57/2)h, see Fig. 1. Figs. 5(a) and (b) shotriple-gated spectra for bands 5a and 5c, respectively.

Band 5a was previously established [19] to decay from the 2301- and 2017-keV staband 1b with 432.1- and 661.5-keVγ -ray transitions, respectively and from the 2141-kstate in band 5b to band 1a with a 535.0-keVγ -ray transition. The respective DCO ratiassociated with the these three transitions, 1.27(19) and 0.96(13), 1.10(25), havuncertainties and do not allow unambiguous spin assignments to be made. Howeverwork, several new linking transitions were established (of energy 695.5-, 898.7-, 7809.8- and 1035.3-keV) from bands 5a and 5b to bands 1a and 1b, see Fig. 1. The absencof any significant state lifetimes (greater than a few ns) for these linking transitions atheir multipole order to be deduced along with the spin of the 1926-keV state in banb.The likely nature of the 661.5-, 535.0-, 809.8-keVγ rays are M1 transitions and the 695.898.7-, 786.4-, 809.8- and 1035.3-keVγ ray transitions are E2, revealing that the spin aparity of the 1926-keV state in band 5b is 21/2−. This is in contrast to that reportedRef. [19].

New decays were also established from the 25/2−, 29/2− and 33/2− states in band 5ato bands 3a with 312.1-, 330.7- and 412.5-keV transitions, respectively. The triple-gspectrum, Fig. 5(a) shows these weak transitions and also those transitions from thespin part of band 3a. No DCO ratios were established for theseγ rays. The correspondindecays from band 5a to band 3b were not observed in this work, however, this is consiswith the large signature splitting between bands 3a and 3b.

Bands6a and6bIn Ref. [19] two transitions were reported to feed from a new band into the spin 2/2−

state in the 1/2−[521], band 3a. We have established two new rotational sequences whichlie above these states, labelled bands 6a and 6b in Fig. 1. Figs. 6(a) and (b) show triple-

d 5

the

for8 keV

forof

sitions

ergythisgavek we


Fig. 5. Triple-gated spectra for bands 5 observed in this work from the thin-target data. (a) Bana;triple-gated spectrum from all non-diagonal combinations of the gatelistr/r/r , where listr = (412,521,607,669,700,719,748,777) keV. (b) Band 5c; triple-gated spectrum from all non-diagonal combinations ofgatelists/t/t , where lists = (350,468,566) and listt = (648,620,697,788,859) keV.

gated spectra for bands 6a and 6b, respectively. DCO ratios could not be establishedthe 621.8-, 639.0- and 808.3-keV transitions in the present work. However, the 217bandhead state in band 6a was observed to decay to the 25/2− and 21/2− states in band 3awith 188.5- and 621.8-keV transitions, respectively. A likely transition combinationsuch decays are M1(I = 0) and E2(I = 2), respectively, giving a spin and parity25/2− for the 2178-keV state in band 6a. (Assignments of 23/2− or 23/2+ cannot be ruledout with the present data.) No DCO ratios were established for the 606.5-keV tranwhich links band 6b to 6a and as a result the spins of band 6b were not deduced in thiwork.

3.2. High-K states

3.2.1. Prompt and delayedγ -ray transitionsIn a previous study of181Os [14] an isomeric state was reported at an excitation en

of 3740 keV with a 34(6) ns half-life. In this work, we have measured the half-life ofstate to be 24(4) ns, see later. In addition, preliminary work by Sletten et al. [15]evidence for a few tentative transitions which were built upon this state. In this wor
have usedγ -ray timing information, with respect to the beam pulsing of the cyclotron,to construct various delayed/early, early/delayed and delayed/delayed matrices, across the

the

s ofe thosepulse.sitionse partnly thesed tosomeric

DCO3.1)

ate thenitialrementssitions


Fig. 6. Triple-gated spectra for bands 6 observed in this work from the thin-target data. (a) Band 6a; triple-gatedspectrum from all non-diagonal combinations of the gatelistu/u/v, where listu= (103,232,343,422,455) keVand listv = (685,736,766) keV. (b) Band 6b; triple-gated spectrum from all non-diagonal combinations ofgatelistu/u/w, where listu as above and listw= (607,649,718) keV.

isomer. In this reportγ -ray transitions are defined as prompt if they occur within 25 nthe primary beam pulse from the cyclotron. The transitions denoted as delayed arwhich were detected with a time greater than 26 ns after the primary cyclotronThe delayed/early matrices were constructed from gating on several delayed tranwhich lie below the 3739-keV state, and selecting any prompt transitions which werof the same event. The delayed/delayed matrices were constructed by selecting odelayedγ -ray transitions. These prompt and delayed coincidence matrices were uestablish the prompt level scheme above, and the delayed level scheme below, the istate. The partial level scheme deduced is shown in Fig. 7. In addition, a delayedmatrix (with axes as previously described for the prompt DCO matrix in Sectionwas also constructed to deduce the multipolarities of the transitions which depopulisomer. Since the lifetime of this isomeric state is short, a sufficient fraction of the ialigned angular momentum survives dealignment in the target to make these measupossible. Table 2 gives the energies, intensities and DCO ratios for all of the tranassociated with the decay of the 3739 keV, isomeric state.

3.2.2. States above the3739keV isomeric state, bands7a, 7b, 8a, 8b and9a, 9b
In order to deduce which states feed the 3739-keV isomeric state the delayed/early
matrix was analysed. This matrix had the condition that a delayed 318.6-keV transition

D.M

.Culle

neta

l./Nucle

ar

Physics

A728

(2003)

287–338

303

ay scheme established in this work below theKπ = 35/2−ies, with the white parts showing the calculated component from

Fig. 7. Partial level scheme focussed on the isomeric state at 3739 keV in181Os and the highly fragmented decisomer. Transition energies are given in keV, while the widths of the arrows indicate their relative intensitinternal conversion.

t/earlyw the

rlyic

sdelayedviouslyination


in band 1b must be present in an event before any promptγ rays in the same evenwere incremented into a two-dimensional matrix. In a similar manner other delayedmatrices were constructed, gated on a delayed 159.5-keV transition directly beloisomer and a 421.8-keV transition in band 3a. The projection of these delayed/eamatrices revealed a group of new promptγ -ray transitions which feed the isomer

Table 2The energies, intensities and assignments for the all of thedelayedtransitions observed below theKπ = 35/2−isomeric state in181Os in this work. If no band assignment is given then theγ ray belongs to the intrinsic statebelow the isomer that were not associated with any known band, see Fig. 7. The DCO ratios are from theDCO matrix, see text for details. If no DCO ratio is given then the spin assignment is based upon the preestablished level scheme [19] or upon the best estimates according to the most-likely multipole combbetween the states


→ Jπf

43.5(8) 9.4(9) 2b 11/2+ →9/2+74.0(2) 20.0(99) 2a 13/2+ →11/2+

102.7(1) 9.4(9) 3a 5/2− →1/2−107.6(8) 1.0(5) 2a 21/2+ →19/2+107.8(1) 9.4(9) 2a 9/2+ →7/2−117.8(5) 2.0(5) 2a 13/2+ →9/2+108.2(4) 4.9(20) 2b 17/2+ →15/2+123.0(5)a 0.2(1) 0.60(11)/M1 5b 25/2− →23/2−123.5(1)a 9.4(9) 0.60(11)/M1 1b 9/2− →7/2−130.9(1) 16.2(17) 4b 23/2− →21/2+148.1(2) 7.8(56) 1b 11/2− →9/2−148.8(1) 9.0(16) 2b 15/2+ →13/2+159.1(2) 9.4(11) 0.67(12)/M1 5a 27/2− →25/2−159.4(1) 37.4(16) 0.67(10)/M1 35/2− →33/2−170.2(2) 3.7(6) 1b 13/2− →11/2−190.1(5) 1.0(5) 0.49(14)/M1 5b 29/2− →27/2−190.7(2) 4.7(7) 1a 15/2− →13/2−204.1(1) 10.4(8) 4a 25/2− →23/2−214.3(1) 7.6(7) 4b 27/2− →25/2−222.4(1) 13.5(22) 2b 15/2+ →11/2+223.1(5) 0.7(4) 5a 31/2− →29/2−225.6(3) 3.3(6) 1a 19/2− →17/2−229.3(1) 9.6(7) 4a 29/2− →27/2−231.3(1) 80.7(141) 1.05(11)/E2 3a 9/2− →5/2−246.4(2) 1.0(6) 5b 33/2− →31/2−252.4(4) 1.1(5) 1a 23/2− →21/2−257.0(3) 10.0(8) 2a 17/2+ →13/2+257.2(1) 12.1(14) 2b 19/2+ →17/2+271.5(2) 50.2(36) 1a 11/2− →7/2−273.9(4) 1.9(5) (31/2+)→29/2−283.5(5) 0.1(3) 5a 27/2− →23/2−318.4(1) 69.6(93) 0.92(12)/E2 1b 13/2− →9/2−319.8(2) 2.3(4) 33/2− → (31/2+)342.9(1) 87.5(43) 0.95(1)/E2 3a 13/2− →9/2−349.6(10) 6.1(7) 5b 29/2− →25/2−

(continued)a The 123 keV DCO ratio is given for the doublet but mainly 27/2− to 25/2− .


Table 2 (continued)

Eγ Iγ RDCO/Assignment Band Jπi → Jπf

361.2(1) 76.2(51) 1a 15/2− →11/2−364.9(1) 60.4(38) 2b 19/2+ →15/2+365.5(4) 7.3(35) 2a 21/2+ →17/2+394.8(1) 47.9(19) 0.90(12)/E2 3a 29/2− →25/2−399.6(1) 75.9(40) 1.08(15)/E2 1b 17/2− →13/2−413.0(8) 0.4(3) 5a 31/2− →29/2−418.5(2) 2.9(5) 4b 27/2− →23/2−421.7(1) 100.0(40) 3a 17/2− →13/2−423.0(11) 0.4(2) 29/2− →25/2−431.7(9) 0.5(3) 5a 27/2− →25/2−434.2(1) 80.6(41) 19/2− →15/2−434.8(1) 73.8(28) 1.03(11)/E2 1a 25/2− →21/2−439.9(1) 20.3(10) 0.90(17)/E2 3a 33/2− →29/2−455.1(1) 94.1(36) 1.01(10)/E2 3a 21/2− →17/2−464.3(1) 68.9(32) 0.94(10)/E2 3a 21/2− →17/2−467.2(3) 6.2(7) 1b 31/2− →27/2−468.0(4) 2.8(5) 5b 33/2− →29/2−487.1(1) 7.2(6) 33/2− → (29/2−)490.3(1) 66.2(32) 1a 23/2− →19/2−512.5(1) 49.0(22) 1.00(12)/E2 1b 25/2− →21/2−516.7(1) 6.8(6) 3a 29/2− →25/2−524.9(1) 8.5(7) 33/2− → (29/2−)531.7(2) 42.2(22) 1a 27/2− →23/2−535.0(3) 2.6(13) 5b 25/2− →23/2−539.3(3) 1.4(3) 33/2− → (31/2+)547.7(1) 20.3(12) 0.98(16)/E2 1b 29/2− →25/2−560.2(2) 11.4(9) 1a 31/2− →27/2−565.8(3) 1.8(4) 1b 33/2− →29/2−567.4(2) 2.6(5) 4b 35/2− →31/2−573.5(5) 0.2(2) 1b 37/2− →33/2−599.6(2) 2.5(4) 33/2− →33/2−622.4(2) 4.0(5) (25/2−)→ (23/2−)623.0(12) 4.7(6) 0.57(33)/E1(I = 1) 33/2− →31/2+623.7(2) 4.0(5) (31/2+)→29/2−643.6(9) 0.8(3) (25/2+)→25/2−654.9(1) 4.0(5) 0.68(21)/E2 29/2− →25/2−657.5(5) 0.8(3) (23/2−)→25/2−662.4(3) 1.4(6) 5a 23/2− →21/2−708.1(2) 2.7(4) (29/2−)→29/2−754.9(1) 13.4(7) 0.92(17)/M1(I = 0) 33/2+ →33/2−842.8(2) 2.1(4) (31/2+)→29/2−848.6(2) 17.2(11) 4a 21/2+ →21/2+920.2(3) 1.2(3) 33/2+ → (31/2+)955.2(4) 2.7(4) 4a 21/2+ →19/2+

1056.3(1) 7.9(7) 0.94(28)/E2 33/2− →29/2−1064.9(3) 0.8(3) 31/2− →25/2−1078.4(2) 2.9(5) 25/2− →21/2−1091.9(2) 2.9(5) (23/2−)→21/2−

(continued on next page)

n theng the

meric

(b)–(c)g. 8(b)sitiontions.t they-,d.9-keVstate


Table 2 (continued)


→ Jπf

1103.0(1) 3.8(5) (29/2−)→25/2−1195.0(1) 14.8(9) 0.91(11)/E2 33/2− →29/2−1213.9(4) 2.0(5) 4a 21/2+ →17/2+1240.7(3) 1.7(3) (29/2−)→25/2−1243.3(1) 4.8(4) (31/2−)→27/2−

Fig. 8. (a) The early total projection spectrum from the delayed/early matrix. Eachγ -ray event in the matrixmust have occurred in delayed coincidence with a 160-keV transition with a time difference betweenγ rays of20–75 ns, (b) a gate on the 305-keV transition, and (c) a gated on the 786-keV transition in this matrix.

state. Fig. 8(a) shows the early total projection of the delayed/early matrix gated o159.5 keV transition. By selective gating on these prompt transitions, and examinicoincidences between them, new bands labelled, 7a and 7b, and 8a and 8b and 9a and9b were established. The partial level scheme for the feeding and decay of the isostate is shown in Fig. 7 and the energies and intensities of theγ -ray transitions belowand above the 24(4) ns isomer are given in Tables 2 and 3, respectively. Figs. 8and 9(a)–(d) show a few selected spectra to illustrate the quality of these data. Fiis a prompt gate on the 305.0-keV transition and Fig. 8(c) on the 786.3-keV transhowing bands 7a and 7b and the fragmented level scheme which feeds these transiFig. 9(a) is a prompt gate on the 194.9- and 225.3-keV transition which reveals thaare in prompt coincidence with a series of transitions of energy 322.4-, 334.3-, 345.2. . . ,390.1-keV and another sequence 657.4-, 679.8-,. . . ,792.0-keV. In addition, the 194.9- an225.3-keV gates are observed to be in strong coincidence with the 412.3- and 175transitions, respectively, which lie below this band and connect it to the isomeric
at 3739 keV. The single-gated spectrum on the 195.5-keV transition reveals that it is notin coincidence with the 226.0- and 382.2-keV transitions implying that this decay path is

ts are


Table 3The energies, intensities and assignments for all of theprompt transitions observed above theKπ = 35/2−isomeric state in181Os in this work, see text for details. If no DCO ratio is given then the spin assignmenbased upon the best estimates according to the most likely multipole combination between the states


→ Jπf

165.6(5) 1.0(5) M1 7a (43/2+)→ (43/2+)175.9(1) 9.1(9) 0.56(4)/E1 7b 37/2+ →35/2−194.9(1) 11.9(15) M1 8a (41/2+)→ (39/2+)225.3(2) 6.6(17) M1 8a (39/2+)→37/2+267.3(1) 39(3) M1 7a (51/2+)→ (49/2+)268.6(1) 14.1(13) M1 7a (43/2+)→ (43/2+)284.6(1) 5.4(5) M1 (57/2+)→ (55/2+)305.0(1) 50(4) M1 7b (41/2+)→ (39/2+)314.3(22) 0.1(1) E1 (53/2+)→ (51/2−)314.5(3) 2.1(6) M1 7b (61/2+)→ (59/2+)315.3(1) 18.8(14) E1 (43/2−)→ (41/2+)322.2(1) 6.8(10) M1 8b (55/2+)→ (53/2+)322.4(1) 24.8(25) M1 (43/2+)→ (41/2+)326.8(1) 1.7(7) M1 (45/2−)→ (43/2−)331.2(1) 0.1(1) M1 9a (47/2+)→ (45/2+)334.3(1) 4.7(9) M1 8a (45/2+)→ (43/2+)340.0(10) 0.1(1) M1 (47/2−)→ (45/2−)345.2(2) 2.3(5) M1 8b (47/2+)→ (45/2+)355.8(1) 10.1(14) M1 8a (49/2+)→ (47/2+)356.2(1) 100(5) M1 7b (45/2+)→ (43/2+)362.5(2) 4.1(9) M1 8b (51/2+)→ (49/2+)362.9(1) 97(5) M1 7a (47/2+)→ (45/2+)372.5(10) 0.1(1) M1 8a (53/2+)→ (51/2+)376.2(1) 94(5) M1 7b (49/2+)→ (47/2+)376.9(10) 0.1(1) M1 8b (55/2+)→ (53/2+)381.9(1) 11.4(16) M1 8a (41/2+)→ (39/2+)390.1(10) 9.1(9) M1 8a (57/2+)→ (55/2+)399.0(1) 22.3(17) E1 (51/2−)→ (49/2+)412.3(1) 90(8) M1 7a (39/2+)→37/2+432.4(1) 13.9(12) M1 7a (55/2+)→ (53/2+)440.2(1) 26.5(23) M1 7b (57/2+)→ (55/2+)446.0(1) 46.6(24) M1 7b (53/2+)→ (51/2+)480.9(1) 45(3) M1 7a (43/2+)→ (41/2+)525.3(1) 9.0(10) M1 7a (59/2+)→ (57/2+)565.2(7) 9.1(12) E2 (33/2−)→ (29/2−)573.2(1) 10.6(10) M1 7b (57/2+)→ (55/2+)591.0(1) 18.6(16) M1 7b (43/2+)→ (41/2+)643.4(9) 0.4(12) E2 7a (51/2+)→ (47/2+)654.1(2) 2.1(4) E2 9b (59/2+)→ (55/2+)657.4(3) 2.3(7) E2 8a (45/2+)→ (41/2+)665.5(1) 0.1(10) E2 9a (47/2+)→ (43/2+)668.1(2) 6.0(8) E2 9a (51/2+)→ (47/2+)677.2(2) 3.9(6) E2 9b (55/2+)→ (51/2+)679.8(3) 2.0(6) E2 8b (47/2+)→ (43/2+)691.3(3) 2.3(6) E2 (49/2−)→ (45/2−)

+ +
696.2(2) 2.6(6) E2 9a (55/2 )→ (51/2 )

nergiessum to

itionss were.9-keV

nfigu-VCO ra-9-keVs

ng on ther the

e onlyto be,hown

itionales. 9(b),ce thenand 9s the


Table 3 (continued)


→ Jπf

700.7(2) 5.9(8) E2 8a (49/2+)→ (45/2+)718.7(2) 7.5(10) E2 8b (51/2+)→ (47/2+)722.6(3) 1.3(3) E2 9b (63/2+)→ (59/2+)735.0(2) 1.5(4) E2 8a (53/2+)→ (49/2+)739.3(3) 1.3(3) E2 9b (67/2+)→ (63/2+)749.3(3) 0.1(6) E2 8b (55/2+)→ (51/2+)755.0(4) 1.2(4) E2 9a (59/2+)→ (55/2+)767.0(3) 1.5(6) E2 8a (57/2+)→ (53/2+)781.9(10) 0.1(1) E2 8b (59/2+)→ (55/2+)786.3(1) 48(3) E2 7a (43/2+)→ (39/2+)792.0(3) 1.7(6) E2 8a (61/2+)→ (57/2+)828.1(5) 1.0(4) E2 9a (63/2+)→ (59/2+)836.3(2) 9.8(15) E2 7b (45/2+)→ (41/2+)839.9(1) 13.3(15) E2 7b (61/2+)→ (57/2+)

1011.4(2) 5.6(9) E2 (55/2+)→ (51/2+)

parallel. The addition of adjacent energies in the lower-energy sequence yields the eof the higher-energy sequence, for example, the 322.4- and 334.3-keV transitionsgive the 657.4-keV transition. Such behaviour is generally associated with high-K bandswith the lower-energy sequence consisting of predominantly magnetic-dipole transand the higher-energy sequence being electric-quadrupole transitions. No DCO ratioestablished for these weak transitions above the isomeric state apart from the 175transition, see below.

The nature of the 159.5- and 175.9-keV transitions is crucial to deduce the corations of bands 7a,7b,8a,8b,9a, and 9b. The DCO ratios for the 159.5- and 175.9-ketransitions are 0.67(10) and 0.54(4), respectively, see Tables 2 and 3. Both of these Dtios are consistent with stretched-dipole transitions which defines the spin of the 373state to be 35/2h and that of the 3914-keV state to be 37/2h. In order to deduce the paritieof these states, the total intensity balance across these states was considered. Gati412.3-keV transition and checking the values of internal conversion required [24] fototal intensity of the 175.9- and 159.5-keV transitions to balance, revealed that thsolution was for the 159.5-keV transition to be an M1 and the 175.9-keV transitionan E1 which establishes the 3739-keV state to haveJπ = 35/2− and the 3914-keV stateJπ = 37/2+. The intensities and internal conversion values used in this analysis are sin Table 4.

The projection of the delayed/early matrices, Fig. 8, revealed the presence of addγ -ray transitions which were not part of bands 8a and 8b. By selectively gating on thestransitions, the prompt coincidence relationships between them were examined. Fig(c) and (d) show spectra for some of these relationships which were used to dedupresence of bands 7a and 7b and 9a and 9b in Fig. 7. Fig. 9(b) is a prompt gate othe 331.2-keV transition and shows the coincidences with the sequence labelled baand 9b in Fig. 7. Fig. 9(c) is a prompt gate on the 668.1-keV transition which show
coincidence with the other members of band 9a and 9b. Fig. 9(d) is a prompt gate on the412.3-keV transition and shows bands 7a and 7b. In this work, we have only been able

d/early

wingg

.9- andte in anccursrtectors

t is

ly


Fig. 9. A few prompt gates to illustrate the quality of the delayed/early data. The gates are from a delayematrix which was gated on the delayed 319- or the delayed 422-keVγ -ray transitions in bands 1b and 3a,respectively, with a time difference betweenγ rays set to be 20–75 ns. (a) The 195- and 225-keV gates shothe high-K bands 8a and 8b. (b) The 331-keV gate showing the high-K bands 9a. (c) The 668-keV gate showinthe high-K bands 9a and 9b. (d) The 412-keV gate showing the high-K bands 7a and 7b.

Table 4Table of intensities and internal conversion coefficients used to determine the multipolarity of the 175159.5-keV transitions. The intensities of the 175.9- and 159.5-keV transitions are from a 412.3-keV gaungatedγ–γ matrix from the thick-target experiment. This calculation assumes that no intensity loss othrough the isomer because the electronics coincidence gate is very long≈ 1 µs (compared with the isomelifetime, 24(4) ns) and the backed target stops all of the recoils within the focus of all of the germanium dein the array. The intensity flow through the isomer reveals that the 159.5- and 175.9-keVγ rays must be M1 andE1 transitions, respectively

Eγ Iγ E1 (1+ αcc) M1 (1+ αcc) Itotal (E1) Itotal (M1)

159.5 25.54± 1.35 1.119 2.54 28.6± 1.5 64.9± 3.4175.9 53.06± 2.71 1.0925 2.17 60.0± 3.1 115.1± 5.9

to place a limit of< 5 ns on the possible lifetime of the 4521-keV state. (This limiadopted from the minimum lifetime obtainable from theEγ -time lifetime analysis withthe large-volume GAMMASPHERE detectors, see Section 3.2.4).

Although DCO ratios for bands 9a and 9b could not be extracted, the only liketransition combination, in the absence of measurable ns lifetimes (> 5 ns), is for the
331.2-keVγ ray to be a magnetic-dipole and the 665.5-keVγ ray to be an electric-quadrupole transition. Several other fragments of bands were also established from these

ed intocere also

ed inht

ch are

d toly backwer decay.roughedlayed8-keVtra,howsteding tohepluso the

likely3.3-keVn was

y pathson

ven inon a

ceulatedm the


delayed/early matrices. For example, a 315.3-keV transition was established to fethe (41/2+) state in band 7b. This 315.3-keVγ ray was also observed to be in coincidenwith 326.8- 340.0- and 691.3-keV transitions, see Fig. 7. Other short sequences weobserved to feed into bands 7a and 7b via a 399.0-keV transition at the (49/2+) level and1011.4-keV at the (51/2+) level. From these spectra and the level scheme presentFig. 7, it can be observed that the high-K structure of181Os is not as regular as migbe expected for an axially-symmetric deformed nucleus. For example, bands 7a, 7b, 9a,9b and the fragments of bands on the left-hand side of Fig. 7 show structures whiquite irregular when compared to those of the more regular band sequences 8a and 8b. Theunusual nature of these bands is discussed more fully in Section 4.

3.2.3. States below the3739keV isomeric stateIn a previous study of181Os [14], the isomeric level at 3739 keV was establishe

decay through a 159.3-keV transition to a state which subsequently decayed directto the 1/2−[521], band 3a, through 754.9- and 1195.0-keV transitions. In this work,have established a much more comprehensive decay scheme following the isomeIn total nine new decay paths were found from this 3578-keV state which feed tha variety of new states to the 1/2−[521] and 7/2−[514] bands, see Fig. 7. This delaylevel scheme was deduced mainly from a matrix which contained only those deevents which were in coincidence with either a delayed 318.6- or a delayed 421.γ -ray transition from bands 1b and 3a, respectively. Representative out-of-beam specwhich illustrate the quality of these data are shown in Figs. 10(a)–(d). Fig. 10(a) sthe out-of-beam double gated 455.1-/421.8-keV spectrum and Fig. 10(b) the double ga395.2-/421.8-keV out-of-beam spectrum. Both spectra show the strong delayed feedthe lower- and higher-spin regions of the 1/2[521] band, respectively. Fig. 10(c) shows tdouble gated 464.4-/318.6-keV combination and Fig. 10(d) the double gated (512.6-547.9-)/318.6-keV combination both of which illustrate the strong delayed feeding tlower- and higher-spin regions of the 7/2[514] band, respectively.

In addition, decays have also been established which feed to the 1875 keVt-bandthrough the 1056.3- and 1243.3-keV transitions. Although the direct link from theKπ =35/2− isomeric state to the 3536-keV state was not established in this work, it isthat an unobserved 42-keV transition exists between these states because the 124γ ray is observed as a delayed decay in the delayed/delayed matrix. A similar situatioestablished in183Os [13], see later. Thet-band subsequently decays into the 9/2+[624]band. The 516.7-keV transition which links the 1/2−[521] band to the 7/2−[514] bandwas also clearly populated in the decay of this isomer, see Fig. 7. The delayed decafrom the isomeric state to the (25/2−) state at 3268 keV, which the 622.4-keV transitidepopulates, were not established in the present work.

The energies, intensities and DCO ratios for these delayed transitions are giTable 2. The delayed DCO ratios were extracted from a matrix which was gatedprompt 175.9-keV transition and only thoseγ rays which were in delayed coincidenwere incremented. The DCO ratios were only extracted for the most strongly-poptransitions in the decay. The spin of the state at 3739 keV was mainly deduced fro
DCO ratios for the 754.9- and 1195.0-keV transitions, see Table 2. The DCOs for the754.9- and 1195.0-keV transitions are consistent with dipole (I = 0) and quadrupole

yed

se twond anible

e spin

ionaldeaser andmplesearlyelayedrompt

s in the176-,


Fig. 10. Delayed spectra showing the decays from theKπ = 35/2− isomeric state at 3739 keV in181Os.(a) Spectrum double gated by the delayed 455/422-keV transitions. (b) Spectrum double gated by the dela395/422-keV transitions. (c) Spectrum double gated by the delayed 464/319-keV transitions. (d) Spectrumdouble gated by the delayed(513+ 548)/319-keV transitions.

(I = 2) assignments, although the uncertainties are large. However, in support, thetransitions decay from the same initial level to a final level, with no parity change aspin difference of two units. The only likely combination, in the absence of any discerhalf-lives (> 5 ns) for the states, is E2 (I = 2) and M1 (I = 0) for the 1195.0- and754.9-keV transitions, respectively. The various connecting transitions established thand parity of the state at 3578 keV to beKπ = 33/2− which is consistent with all of thenew decays established in this work.

3.2.4. Half-life of the3739keV isomeric stateIn order to extract the half-life of the 3739 keV isomeric state, a three-dimens

asymmetric cube was created. This cube consisted ofγ -ray energies on the first- ansecond-axes and the time difference between the twoγ rays on the third axis. Thcalibration of the time axis was 0.28 ns/channel. The lifetime of an isomeric state wobtained from this cube by setting gates on transitions above and below the isomexamining the time difference between them. Fig. 11 shows two representative exaof time differences across the isomeric state at 3739 keV for (a) the 412.3-keVversus the 159.5-keV delayed gates, and (b) 412.3-keV early versus the 754.9-keV dgates. Typical non-linear fits consisting of a convoluted Gaussian (representing the presponse of the germanium detectors) and exponential are shown by the solid linefigure. Half-lives across the 3739 keV isomer were measured in this cube for the
305-, 356-, 376-, 412-, 481- and 786-keV transitions. The standard deviation of thesemeasurements yielded a half-life of 24(4) ns. This value is consistent with the 34(6) ns

. Typicalre. The

time

riousf the

curatee


Fig. 11. Time differences for transitions above and below theKπ = 35/2− isomeric state in181Os, (a) spectrumof the 412 keV early versus 160 keV delayed gates, and (b) 176 keV early versus 160 keV delayed gatesnon-linear fits consisting of a convoluted Gaussian and exponential are shown by the solid lines in the figustandard deviation of these measurements yields a half-life of 24(4) ns.

reported in Ref. [14] where only a few points were available to be fitted with a poorerresolution of 5.75 ns/channel.

In order to check the accuracy of the half-lives extracted with this method, vaknown isomeric states were measured. The half-life extracted for the decay o7/2−[514] state was determined to be 262(6) ns which is consistent with the less ac316(18) ns measured in Ref. [25] at 287 ns/channel. In addition, the lifetime of th
Kπ = 25+ isomeric state, in the neighbouring isotope182Os, was deduced to be 145(8) nswhich is again consistent with the previous measurement of 130(20) ns in Ref. [9].

160-keVe solid

libration

thisitions.layedctedas

e been

andspler

t of theinatedions ingated

. Thesewith

these


Fig. 12. Time differences for transitions above and below theKπ = (21/2+) t-band isomeric state in181Os. Thegate shown is the time difference between the delayed 848- plus 1214-keV transitions and the prompttransition. Typical non-linear fits consisting of a convoluted Gaussian and exponential are shown by thlines in the figure. The standard deviation of these measurements yields a half-life of 7(2) ns. The time cais given by 0.28 ns/channel.

The half-life for the 21/2+ state which thet-band decays to was also measured inwork from a series of spectra gated on the 848.2-, 956.5-, and 1213.5-keV transA typical spectrum gated on the 130.8-keV prompt and 848.2- plus 1213.5-keV deγ -ray transitions is shown in Fig. 12 along with its associated fit. The half-life extrafor this state ist1/2 = 7(2) ns which is shorter than that reported in Ref. [19] where it wdeduced to be 13(2) ns. The calculated hindrance factors reported in Ref. [19] havre-evaluated in Section 4.2.2 with this revised half-life.

In this work, no evidence for higher-lying isomeric states above theKπ = 35/2− isomerwas observed with a half-life> 5 ns.

3.3. Mean lifetimes of the low-K states from the Doppler shift attenuation method(DSAM)

In the present work, the mean lifetimes for two of the collective rotational bin 181Os, bands 2a and 3a, have been established from an analysis of the Dopbroadened transition lineshapes from the thick-target data. In this experiment, mosγ rays studied were from triple- and higher-coincident events and the least contamspectra were produced from those events which were double gated on the transita particular band of interest. In the lineshape analysis this was achieved by usingcoincidence matrices whose gates were the uncontaminated lower-spin transitionslow-spin transitions were emitted from states whose lifetimes were long, comparedthe slowing down time of the recoils in the target and backing, which ensures that
transitions were emitted when the nucleus was at rest and show no Doppler broadenedlineshapes. These are the so-called “stopped” transitions.

eh werewerey eventaxis.

nyenergys wasngles.

entals. [27]ed toectivepowertiononte

r as as occurof thelatedsin a

a totalmpleteaks.ede thenby theof the

n intominedationalighest-omentand.

ndingle

a


In order to fully analyse these lineshapes three gatedγ –γ coincidence matrices wercreated for each band of interest. The first matrix contained only those events whicdetected in the 31.7 (forward) detectors on one of the axes versus those whichdetected in any of the other detectors on the other axis. The second matrix had anfrom a 162.7 (backward) detector on one axis and any other detector on the otherFinally the third gated matrix had any event from the 90 detectors on one axis and aother detector on the other axis. The latter matrix was used to ascertain the preciseof theγ -ray transitions. For each band a sum of the low-spin uncontaminated gatethen produced from each of these matrices for the forward and backward detector a

The transition lineshapes were analysed by the program “LINESHAPE” [26] which isbased on a program written by Gascon, see Ref. [27]. The program calculatesγ -raylineshapes and extracts the lifetimes of the nuclear states by fitting the experimdata. Detailed descriptions of the method and its application are discussed in Refand [28]. In the analysis, both electronic and nuclear stopping powers were uscalculate the slowing down process. For the electronic stopping powers, Ward’s effcharge and Ziegler’s proton stopping powers were used. For the nuclear stoppinga multiple Coulomb scattering formalism was employed [29]. The velocity distribuof the recoiling ions in the target and backing material was calculated in a MCarlo fashion [30]. The Monte Carlo simulation treats the electron stopping powecontinuous slowing down process and assumes that the discrete nuclear collisionat a rate given by the Lindhart cross section [29]. In this process the distributionmagnitude and direction of the velocity, the so-called “velocity profile”, was calcuat fixed time intervals during the slowing-down time and a set ofγ -ray peak shapes waproduced for each time step at eachγ -ray detector angle. These shapes were stored“shape-versus-time” two-dimensional matrix. A time step of 0.01 ps was used andnumber of 5000 histories was calculated for each detector angle which provided a coset of lineshapes ranging from the fully-shifted (at time zero) to the fully-stopped pe

In order to reproduce the lineshapes, theγ -ray yield as a function of time was calculatusing the solution of Bateman’s equation [31]. The final calculated lineshapes werobtained by summing the independent lineshapes at each time interval weightedγ -ray yield. Since the spectra were gated below the states of interest, the lifetimesstates include a time delay contribution from the side feeding which must be takeaccount. The side feeding intensities were obtained from the experimentally deterintensities given in Table 1. In the analysis the program assumes that a set of rottransitions with the same moment of inertia as the band being fitted precedes the hspin transition. This side-feeding cascade, comprising of five levels with a constant mof inertia ( (SF )= 50h2 MeV−1), was assumed to be connected to each level in the bThe side-feeding life-time was controlled by a parameter,Qo(SF ), which was included inthe fit. With this method it was possible to fit the lifetime of a state and the corresposide-feeding quadrupole moments,Qo(SF ), for eachγ -ray transition with an observablineshape, starting from the highest level.

In the analysis the following parameters were simultaneously fitted usingχ2

minimisation technique; (1) the transition quadrupole moment of the state,Qo, (2) the
associated side-feeding quadrupole moment of the modelled state,Qo(SF ), (3) theintensities at each angle of the fitted peak and those of the contaminant stopped peaks near

ath thetisticalvaluehich

dataetime

rmedthianscussed

ote bandsed byn, the

shapes

ouble-.6-keV

d and-keVshape

nt,eragenoteduces a

milar

ascade,

.8-,ates onws the) and


the peak of interest, and (4) the intercept and gradient of a linear background benepeaks. In the program the uncertainties in the lifetimes were determined by a stamethod using the MINOS subroutine [32]. This routine assumes that the lowestof χ2, χ2

min, occurs for the most likely or best fit parameters and the region over wχ2 assumes values smaller thanχ2

min + 1 corresponds to one standard deviation. Thefrom the forward and backward detectors were fitted independently and the final lifwas an arithmetic average of the forward and backward fits.

The extracted deformations of the bands, for which this analysis could be perfo(bands 2a and 3a), were compared with those predicted from a series of Total RouSurface calculations based upon the proposed configurations. This comparison is diin Section 4.1.3. For the other bands in181Os (the high-K bands 7a, 7b, 8a, 8b, 9a and9b and bands 1a, 1b, 2b, 3b, 4a, 4b, 5a, 5b, 6a and 6b) this lineshape analysis could nbe performed. Doppler broadened transition lineshapes were not observed for theseither due to their low population intensity or their resulting spectra being complicatthe presence of many overlapping transitions in a band crossing region. In additiohigh-K bands have smaller Clebsch–Gordan coefficients which means that the linewould only develop at relatively higher spins compared with the lower-K bands.

3.3.1. Band2a DSAM lineshapesThree gated lineshape matrices were created for band 2a, for the 31.7, 162.7 and 90

detector angles, gated on the 364.8-, 463.8-, 547.9- and 586.9-keV transitions. Dgated spectra were produced by setting gates on the 599.7-, 586.9- and 627transitions in these matrices. Fig. 13 shows three transitions in band 1a, in the region overwhich it was possible to perform the lineshape analysis, with the respective forwarbackward fits for the 627.6-keV (a) and (b), the 708.2-keV (c) and (d) and the 802.3(e) and (f) transitions. The fitted parameters extracted from the results of the lineanalysis for the forward and backward fits for band 2a are shown in Table 5.

In Tables 5 and 6, for band 3a, the uncertainty limit shown on the quadrupole momeQo, was from the results of the MINOS routine. The uncertainty on the accepted avvalue is the larger of the two MINOS values used in the averaging. However, it wasthat the uncertainty associated with the electronic and nuclear stopping powers introdminimum possible uncertainty in the lifetime values of≈ 8%. When the uncertainties frothe fitting routines were smaller than this value, a lower limit of 8% was used. A simprocess was adopted for the side-feeding quadrupole moments of the side-feeding cQo(SF ).

3.3.2. Band3a DSAM lineshapesThe lineshape matrices for band 3a were gated on the 231.7-, 343.1-, 395.2-, 421

435.0- and 455.1-keV transitions. Double-gated spectra were produced by setting gthe 231.7-, 343.1-, 421.8-, and 455.1-keV transitions in these matrices. Fig. 14 shorespective forward and backward fits for the 704.8-keV (a) and (b), the 780.9-keV (c
(d) and the 846.3-keV transitions (e) and (f) in band 3a and the fitted parameters are givenin Table 6.

et(f) showhown by

,

e


Fig. 13. The Doppler broadened line shapes observed for band 2a from a double-gated spectrum in the thick-targdata; (a) and (b) show the 627.6-keV lineshape; (c) and (d) show the 708.2-keV lineshape; and (e) andthe 802.3-keV transition lineshape for the forward and backward detectors, respectively. The data are shistograms and the total line shapes by solid lines.

Table 5Summary of the results for the transition quadrupole moments,Qo, and lifetimes,τ , for the states in band 2a9/2[624], (α = +1/2) and those of the side-feeding (SF)

Eγ (keV) Qo (eb) Qo (eb) Qo (eb) τ (ps) Qo(SF) (eb) Qo(SF) (eb) Qo(SF) (eb)Forward Backward Average Average Forward Backward Averag

627.6 7.45+0.60−0.60 8.23+0.66

−0.66 7.84+0.66−0.66 0.42+0.04

−0.04 4.00+2.11−2.11 4.78+0.38

−0.38 4.39+2.11−2.11

708.2 7.78+0.62−0.62 5.83+0.47

−0.47 6.81+0.62−0.62 0.31+0.03

−0.03 4.31+0.34−0.34 5.10+0.41

−0.41 4.71+0.41−0.41

802.3 6.30+0.50−0.50 4.79+0.38

−0.38 5.55+0.50−0.50 0.25+0.02

−0.02 4.07+0.33−0.33 4.84+0.39

−0.39 4.46+0.39−0.39

899.0 5.48+0.93−0.44 4.15+0.33

−0.33 4.82+0.93−0.44 0.18+0.03

−0.02 3.64+0.29−0.29 4.06+0.32

−0.32 3.85+0.32−0.32

4. Discussion

An inconsistency exists in the published literature for the level scheme of181Os. TheTable of Isotopes [33] records the excitation energy of the 13/2+ state in the 9/2+[624]band to be 292.1 keV. In this work, and that described in Ref. [19], the 13/2+ state is
observed at an excitation energy 274-keV. The evidence supporting this is based on thefact that the 136-keV, 13/2+ → 9/2+, γ ray reported in the Table of Isotopes [33] was not

e.

as

,

e

eteshape;ectively.


observed in these data, however, an 118.2-keVγ -ray transition was observed in its placIn addition, the states in this 9/2+[624] band 2a and 2b are connected to bands 4a and 4bwhich are in turn connected to the 7/2−[514] bands 1a and 1b. This condition can only bemet if the 13/2+ → 9/2+ transition in band 2a has energy 118.2 keV and not 136 keVreported in Ref. [33].

Table 6Summary of the results for the transition quadrupole moments,Qo, and lifetimes,τ , for the states in band 3a1/2[521], (α = +1/2) and those of the side-feeding (SF)

Eγ (keV) Qo (eb) Qo (eb) Qo (eb) τ (ps) Qo(SF) (eb) Qo(SF) (eb) Qo(SF) (eb)Forward Backward Average Average Forward Backward Averag

618.5 7.21+0.58−0.58 7.64+0.61

−0.61 7.43+0.61−0.61 0.46+0.03

−0.03 3.58+0.29−0.32 4.79+0.38

−0.38 4.19+0.38−0.38

704.8 7.29+0.58−0.58 8.38+0.67

−0.67 7.84+0.67−0.67 0.22+0.02

−0.02 3.98+0.32−0.32 4.71+0.38

−0.38 4.35+0.38−0.38

780.9 6.88+0.55−0.55 5.14+0.41

−0.41 6.01+0.55−0.55 0.23+0.02

−0.02 4.03+0.32−0.32 3.64+0.29

−0.29 3.84+0.32−0.32

846.3 3.75+0.30−0.30 6.08+0.49

−0.49 4.92+0.49−0.49 0.26+0.03

−0.03 4.70+0.38−0.38 3.86+0.31

−0.31 4.28+0.38−0.38

Fig. 14. The Doppler broadened line shapes observed for band 3a from a double-gated spectrum in the thick-targdata, see text for details; (a) and (b) show the 704.8-keV lineshape; (c) and (d) show the 780.9-keV linand (e) and (f) show the 846.3-keV transition lineshape for the forward and backward detectors, resp
The data are shown by histograms, contaminant peaks by dashed lines and the total line shapes with and withoutcontaminant peaks, by solid lines.

- toe beenarticleder tod shellrmed.

n the

s ofre not

CSM.

d-

ms

d at a.rd

l

presentds 1gs.e


4.1. Cranked shell model and total Routhian surface calculations

The configurations of the low-K bands have previously been discussed for lowmoderate-rotational frequencies in Ref. [19]. In the present work, these bands havextended to higher rotational frequencies, where new crossings to higher quasipconfigurations occur, and in addition, new bands have been established. In orunderstand the configurations of the bands at high rotational frequencies, crankemodel (CSM) and total Routhian surface (TRS) calculations [34] have been perfoAs was discussed in Ref. [19], the total Routhian surface for181Os is quite soft in theγdirection in theβ–γ deformation plane. As a consequence the CSM calculations ipresent work were performed at the deformation(β2, β4)= (0.258,−0.010) for γ = 0.3and γ = −15 from the minimum extracted from the TRS calculations. The resultthese calculations are almost identical to those shown in Fig. 7 in Ref. [19] and areproduced here.

The lowest single-particle neutron configurations around the Fermi surface in thecalculations are the 9/2+[624], 7/2+[633], 7/2−[514] and 1/2−[521] orbits, respectivelyIn this work, it should be noted that a general feature of the bands in181Os is that they arefound to interact or decay to one another. For example, Fig. 1 shows that theKπ = 21/2+band-head state decays strongly to the 9/2+[624] band 2a and 2b and also above the banhead state to the 7/2−[514] band 1a and 1b. Similarly, the 1/2−[521] band 3a decays toband 1b at spin 29/2h and in this work, band 5a was established to decay to band 3a.Likewise, a new transition was established in this work from the 33/2− state in band 1a tothe 29/2− state in band 3a. This mixing of configurations is discussed more fully in terof the softness of the nucleus toγ vibrations in Section 4.2.4.

4.1.1. The configuration of the low-K bandsBands1a, 1b, 1c, 1d

Bands 1a and 1b are known to be based upon the one-quasineutron 7/2−[514]configuration [19]. The bands show near zero signature splitting and are crosserotational frequencyhω = 0.28 MeV with an alignment gain,Ix = 8h, see Fig. 15(a)This gain in alignment may be associated with thet-band crossing although the standaCSM crossing based on the alignment of thei13/2 9/2[624] neutron orbit fits very wel[19]. In the neighbouring nucleus182Os, the alignment gain for thisi13/2 crossing wasmeasured to beIx = 9h at a rotational frequency,hω ≈ 0.26 MeV [36,37] and in183Os,Ix = 9h at hω≈ 0.22 MeV [13]. The extension of bands 1a and 1b, in this work to muchhigher rotational frequencies, reveals that they are again crossed athω ≈ 0.37 MeV withan alignment gain,Ix ≈ 4h, by two other bands, bands 1c and 1d , respectively. It wasnot possible to unambiguously define the spins and parities for these states in thework, however, if the linking transitions are electric quadrupole transitions, then bancand 1d may be the continuations of bands 1a and 1b above their respective band crossinThe experimental Routhians for these bands 1c and 1d , plotted in Figs. 17(b) and thexcitation energy minus arbitrary reference, plotted in 18(b), reveal that bands 1c and 1d ,
are smooth extensions of bands 1a and 1b, respectively and are therefore, consistent withthese ideas.

rsand

nl

,), (b),nd (c)

s [35]the

nseished in6,s 7, 8

nds 2e is to

tononal


Fig. 15. The experimental aligned angular momenta,ix for the rotational bands observed in181Os. (a) bands 1a,1b and 1c, 1d , (b) bands 2a, 2b and (c) bands 3a, 3b and 3c. A reference band with Harris paramete o = 30.0h2/MeV and 1 = 20.0h4/MeV3 was subtracted from each band. Open symbols refer to paritysignature configuration(π,α)= (+,+1/2) or (−,+1/2) and closed symbols(π,α)= (+,−1/2) or (−,−1/2).

In order to deduce how the configurations of the low-K bands evolve as a functioof rotational frequency, the aligned angular momentum,Ix (or alignment), experimentaRouthians,e′ and the excitation energy of the states minus an arbitrary referenceE −0.0085I (I + 1) MeV, have been calculated from these experimental data. Figs. 15(aand (c) show the experimental alignment for bands 1, 2 and 3 and Figs. 16(a), (b), afor bands 4, 5, 6, 7 and 8, respectively. A reference band with Harris parameter o = 30h2/MeV and 1 = 20h4/MeV3 has been subtracted from each band to removecollective rotation. These values are not from the average of the ground-state bands i182Osand184Os ( o = 24h2/MeV and 1 = 110h4/MeV3), as was used in Ref. [19], becauthat average reference over subtracts at the highest rotational frequencies establthis work. The experimental Routhians,e′ are plotted in Figs. 17(a) for bands 3 andFig. 17(b) for bands 1 and 5, Fig. 17(c) for bands 2 and 4, and Fig. 17(d) for bandand 9. The excitation energy minus an arbitrary reference,E − 0.0085I (I + 1) MeV isplotted in Fig. 18(a) for bands 3 and 6, Fig. 18(b) for bands 1 and 5, Fig. 18(c) for baand 4, and Fig. 18(d) for bands 7, 8 and 9. The subtraction of this arbitrary referencremove some dependence of the collective contribution to the angular momentum.

Higher spin band crossings are predicted to occur in bands 1a and 1b at hω = 0.4 MeVbased on the neutron 1/2−[521] crossing, or at 0.48 MeV based on either the proh9/2 or h11/2 crossing [19]. However, without further experimental data at high rotati
frequencies to observe the full alignment gain, the identification of these crossings isdifficult to establish because they are greatly affected by the value of theγ parameter.


Fig. 16. The experimental aligned angular momenta,ix for the rotational bands observed in181Os. (a) bands and4a, 4b, 5a,5b and 5c, (b) bands 6a, 6b, and (c) bands 7a,7b,8a, and 8b, see text for details.

Fig. 17. The experimental Routhians,e′ for (a) bands 3 and 6, (b) bands 1 and 5, (c) bands 2 and 4, and (d) bands7, 8 and 9.

ng

vidence

om thenment

ture

thiss

ich iseits so

hians in


Fig. 18. Excitation energy minus an arbitrary reference,Ex − 0.0085I (I + 1)MeV versusI (I + 1), for (a) bands3 and 6, (b) bands 1 and 5, (c) bands 2 and 4, and (d) bands 7, 8 and 9.

Bands2a, 2bThe low frequency configurations of bands 2a and 2b have been interpreted as bei

based upon each signature of the one-quasineutron 9/2+[624] configuration [19]. The twosequences show a large signature splitting, see Fig. 17(b), which was taken as efor a largeγ deformation (γ = −15) for this configuration. Band 2a upbends athω ≈0.29 MeV and band 2b at hω ≈ 0.32 MeV both with alignment gains ofIx ≈ 6h. Theexperimental crossing frequencies and alignment gains match those predicted frtheoretical CSM calculations [19] for the three-quasiparticle bands based on the aligof the 7/2+[633] quasineutron. Bands based on this 9/2+[624] configuration in183Osshow an alignment gain ofIx ≈ 2h in both signatures sequences. The large signasplitting and delayed alignment gains crossing frequencies, for these bands in183Os, werediscussed to be a result of the blocking effect of the neutroni13/2 orbital [13].

Bands 2a and 2b have been extended to much higher rotational frequencies inwork, see Fig. 1. Above the crossings athω ≈ 0.3 MeV, the alignment of both signaturedisplays a very smooth behaviour with rotational frequency up tohω ≈ 0.65 MeV. Thereis neither evidence for any higher neutron crossings nor the first proton crossing whexpected to occur athω ≈ 0.48 MeV. The lack of crossings in this band may be due to thγsoftness which could possibly be expected to mix all of the various single-particle orbthat particular crossings are washed out, see Section 4.2.4. The experimental RoutFig. 17(c) may give evidence for such an interaction as the states in band 2a, and especiallyband 2b, appear to be perturbed in the rotational frequency range around 0.3 MeV.

Bands3a, 3b and3c
Bands 3a and 3b have been interpreted as being based on the 1/2−[521] configuration
at low spin. The large signature splitting is consistent with this interpretation. The first

elargen com-

heiableendednature

Odsame

e may

i-h showivepossi-

ishd.

bandtent

edd

ossingwever,ds 4ds arelectivegainpling

three-

lective


backbends shown in the alignment plot, Fig. 15(c), are reasoned to be based on thi13/29/2+[624] neutron crossing due to the rotational frequency of the crossing and thealignment gains [19]. These crossings have, however, some unusual features whepared with the 9/2+[624] neutron crossings in bands 1a and 1b. Firstly the crossing inband 3a occurs early athω ≈ 0.22 MeV. Secondly, the crossing in band 3b occurs at theexpected frequency,hω ≈ 0.28 MeV, however, band 3b does not extend much above tcrossing. Band 3b was only weakly populated in the present work due to its apprecsignature splitting. The weak population is consistent with the fact that it was not extto higher-rotational frequencies in the present work, see Fig. 18(a). In contrast, its sigpartner band 3a was extended to much higher rotational frequencies,hω ≈ 0.58 MeV, seeFig. 1. The alignment of band 3a increases slowly above this 9/2+[624] neutron crossingand no further alignment gains were observed, see Fig. 15(c). However, at spin 53/2 a newband, band 3c was observed to feed into band 3a. It was not possible to extract the DCratio for the 912.6-keV transition which links band 3c to band 3a but it might be speculatethat if it is an E2 transition then the two states, at 7204- and 7215-keV, would have thespin 57/2h and parity and would be expected to interact with each other. Indeed, therbe evidence for this interaction in Fig. 15(c) which shows that the 57/2−h state in band 3ais pushed upwards at a rotational frequency ofhω≈ 0.46 MeV. The experimental Routhans, Fig. 17(a) and the excitation energy minus an arbitrary reference, Fig. 18(a) botthat band 3c is a smooth continuation of band 3a and are consistent with these tentatspin and parity assignments. At higher spins the alignment plot Fig. 15(c) shows theble onset of a proton crossing athω≈ 0.5 MeV but more data are required to fully establif this increase in alignment continues and to determine the configuration of this ban

Bands4a and4bBands 4a and 4b have been interpreted at low rotational frequencies, below the

crossing at 0.35 MeV, as at-band. The lack of associated signature splitting is consiswith this idea, see Fig. 16(a). TheKπ = 23/2− configuration of this band was deducto be based upon a deformation-aligned 7/2−[514] quasi-neutron plus two Fermi-alignequasi-neutrons (9/2+[624], 7/2+[633]) whose spins are coupled in parallel to giveK = 8.The crossing observed in this band at 0.35 MeV may be based on a neutron crbecause the rotational frequency is below that of the expected proton crossings. HoFig. 18(c) shows that the excitation energy minus an arbitrary reference, for banaand 4b, is very smooth with increasing rotational frequency and also that these banmore efficient at generating angular momentum compared with, for example, the colrotational bands 2a and 2b. Such behaviour may be more indicative that the smoothin alignment arises from a change in the direction of the angular momentum coumechanism in thet-band rather than the more regular band crossing.

TheKπ = 21/2+ isomeric state at1744keVTheKπ = 21/2+ isomeric state at 1744 keV was deduced to be based on the

quasineutronν(7/2−[514],9/2+[624],5/2−[512]) configuration [19]. In this work, onlyvery tentative evidence was presented for the states which may belong to a col
Kπ = 21/2+ rotational band built upon the isomeric state. The tentative nature of thesetransitions, however, precludes further discussion.

yity in

blysingleeg

ction,ould

these

itd-heads the

andround5itationds 5ch

-

3-t whiches (i.e.,s

ndgeneral


Bands5a, 5b and5cBands 5a and 5b have similarities to bands 4a and 4b, which reflects the fact that the

probably both have a similar three-quasineutron configuration [19]. Note the similarthe alignment properties of bands 4a and 4b with that of bands 5a and 5b in Fig. 16(a).Both bands 4a, 4b, 5a and 5b have non-zero low-spin alignments which presumaindicates that they have a similar low-spin multi-quasiparticle structure based on aneutron coupled to the two Fermi-aligned (9/2+[624],7/2+[633]) quasi-neutrons. Thlowest spin observed in band 5a was 21/2− which could involve the single neutron beinin the 5/2−[512] orbit, giving the three-quasineutron 9/2+[624], 7/2+[633], 5/2−[512]configuration. This configuration involves the single-particle 5/2−[512] neutron orbitwhich may explain the decay of bands 5 to band 3. However, on detailed inspethe low-spin alignment of bands 5 is actually larger than that of bands 3 which wmore likely result from a 1/2−[521] than the 5/2−[512] orbit. In addition, the 5/2−[512]orbital is not predicted to be so low in excitation energy (see Section 4.2). In light offacts, band 5 is likely based on the three-quasineutron 9/2+[624], 7/2+[633], 1/2−[521]configuration. This configuration is consistent with a 17/2− bandhead state becausemight not have been possible with these data to observe bands 5 down to the banstate. More discussion of this point is given in Section 4.1.2 and in the following plotband head of band 5 was taken asKπ = 17/2−.

At higher spins both bands 4 and 5 show evidence for an alignment gain athω =0.35 MeV. Although the full alignment gain was not established for bands 5a and 5b,it is likely based on a band crossing involving either the 1/2−[521] or the 5/2−[512] orbitsince, like that of bands 4a and 4b, all of the other neutron configurations are blockedthe rotational frequency is too low for it to be the first proton crossing expected a0.48 MeV. The experimental Routhians for these bands, Fig. 17(b), show that bandsa, 5band 5c gradually change over the entire frequency range they are observed. The excenergy minus arbitrary reference plot, Fig. 18(b) indicates that the structure of banaand 5b is similar to that of bands 1a and 1b, the data points almost lying on top of eaother in the spin 14–22h region.

Fig. 17(b), shows the experimental Routhian for the states in band 5c. Band 5c hasbeen plotted with the 4173-keV state assigned as spin 41/2. It was not possible to unambiguously define DCO ratios for the 647.7-keV transition which links band 5c to band 5b,however, a lower spin results in band 5c being too highly excited relative to band 5b. Inthis case the 41/2−h states in bands 5b and 5c at excitation energies of 4166- and 417keV, respectively, are very close in energy. These states might be expected to interacshould be observed in Fig. 16(a). Although any effects, of the closeness of these statan interaction) in the alignment plot athω = 0.26 MeV are difficult to establish from thiplot, such an interaction may explain the strong feeding observed from band 5c.

Bands6a and6bThe alignment for bands 6a and 6b are shown in Fig. 16(b). Although the spins a

parities of these states were not unambiguously deduced in the present work, somecomments may still be made. The medium initial alignment ofIx ≈ 6h for these bands
suggests that they have already undergone a band crossing at low rotational frequencies.This initial alignment is probably not based on the 9/2+[624] crossing because the

ilarmineuthiansree plot,

n

ssumesork,caletheingched

r the

ed

saluesal)it

thereticalre

with the

e) forn20(a).


alignment would be expected to be about 9–10h in this case. It is likely that bands 6aand 6b are based upon the configurations which involve the 1/2−[521] orbit becausebands 6a and 6b decay to bands 3a and 3b which suggests that they may share a simunderlying single-particle configuration. However, in order to unambiguously deterconfigurations for these bands, more data would be required. The experimental Rofor these bands, Fig. 17(a), show that bands 6a and 6b gradually change over the entifrequency range they are observed. The excitation energy minus arbitrary referencFig. 18(a) indicates that the structure of bands 6a and 6b are very similar to that of bands 3aand 3b. The data points appear to suggest that band 3a may evolve slowly or mix withincreasing spin into band 6a and band 3b into band 6b. In this scenario there would be ainteraction and exchange of character of the configurations from spins 21/2 to 37/2h.

The configurations of these bands are discussed further in Section 4.2.

4.1.2. |(gK − gR)/Qo| ratios for bands1,2,5 and6In order to validate the configuration assignments for the bands experimental|(gK −

gR)/Qo| values were deduced from theI = 1 to I = 2 γ -ray intensity branchingratios, using the standard prescription, see, for example, Ref. [38]. This approach aQ0 = 7.6 eb from the average of the appropriate low-spin DSAM values in this wsee Tables 5 and 6, andgR = 0.3 [6,39,40]. In order to test how well a given theoreticonfiguration fits the experimental data the intrinsic Nilsson modelg-factor estimates havbeen compared with the experimentalg-factors extracted from the branching ratios forstates in the bands. The theoretical Nilsson intrinsicg-factor estimates are calculated usKgK = Σi(gΛΛ + gΣΣ) for i particles. These calculations make use of the quenintrinsic g-factors which are 60% of the free values,gπfree = +5.59 andgνfree = −3.83.The orbitalg-factors aregπ7 = 1, gν7 = 0. In calculations involving the 9/2+[624] orbit avalue ofgK = 0.06 is often used which is based on the empirical values extracted fo9/2+[624] bands in the neighbouring nuclei, from Ref. [41].

The ratios for the 7/2−[514] bands 1a and 1b are shown in Figs. 19(a). The weightaverage of the experimental values is shown with a solid line. The theoretical|(gK −gR)/Qo| values based on the one quasineutron 7/2[514] orbit (shown as dot-dashed linein Fig. 19(a)) are slightly lower but in reasonable agreement with the experimental vfor bands 1 below the band crossing at spins< 29/2. For this configuration the theoreticgK value (0.33) is almost identical to thegR value (usinggR = 0.3 discussed abovewhich results in a small|(gK − gR)/Qo| ratio. The theoretical calculations for this orbappear to be better suited using thegR =Z/A prescription. These values are shown bylong-dashed lines in Fig. 19(a). The comparison between the experimental and theo|(gK − gR)/Qo| values for the 9/2[624] bands 2 are shown in Fig. 19(b). From the figuit can be seen that the theoretical values (dashed lines) are in excellent agreementexperimental values for this one-quasineutron 9/2+[624] configuration.

Figs. 20(a) and (b) show the comparison of the theoretical and experimental|(gK −gR)/Qo| ratios for bands 4 and 5, respectively. The theoretical values (dashed linthe t-band, band 4 based on the (7/2−[514], 9/2+[624], 7/2+[633]) three-quasineutroconfiguration, are in excellent agreement with the experimental values, see Fig.
This calculation assumedgK = 0.06 for the aligningi13/2 orbits in the configuration asdiscussed above. The theoretical values for band 5 in Fig. 20(b) were calculated based on

odel are

wnr details.


Fig. 19. |(gK − gR)/Qo| values for (a) the 7/2−[514] bands 1 and (b) the 9/2[624] bands 2 in181Os. Theweighted average values are shown by the solid line. The theoretical values based on the Nilsson mshown as broken lines, see text for details.

Fig. 20.|(gK −gR)/Qo| values for (a) bands 4 and (b) bands 5 in181Os. The weighted average values are shoby the solid line. The theoretical values based on the Nilsson model are shown as broken lines, see text fo

the 5/2−[512], 9/2+[624], 7/2+[633] (long-dashed line) and the 1/2−[521], 9/2+[624],7/2+[633] configurations (short-dashed line) and assumedgK = 0.06 for the aligningi13/2orbits. These calculations show that the 1/2−[521], 9/2+[624], 7/2+[633] configuration
is more consistent with the experimental data and this is the configuration we have used inthe paper, see Section 4.2.

rm theide ana

n

rupoles

at


4.1.3. Lifetimes estimated from the TRS calculation deformationsThe mean experimental lifetimes for bands 2a, and 3a in 181Os, from the Dopple

shift attenuation method, have been compared with the lifetimes extracted frodeformations predicted by theoretical TRS calculations. The TRS calculations provestimate of the quadrupole deformation parameter,β2, for a specified configuration asfunction of rotational frequency. The conversion ofβ2 to a quadrupole moment,Qo, inthe limit of smallγ and hexadecapole deformation,β4 is achieved with the transformatio[10,42]

Qo = 0.0126ZA2/3β2(1+ 0.36β2)cos(γ + 30). (2)

Table 7 shows the results of this conversion from the TRS deformation to the quadmoment for a few rotational frequencies for bands 2a and 3a. Fig. 21 shows the resultof a particular TRS calculation for the 9/2[624] neutron orbit, illustrating the predictedγsoftness of this configuration at a rotational frequency ofhω= 0.25 MeV.

Table 7A few examples of the conversion of the TRS(β2, γ ) predictions toQo for bands 2a and 3a, see text for details

Frequency (keV) Band 2a Band 3aTRS(β2, γ )→Qo(eb) TRS(β2, γ )→Qo(eb)

0.250 (0.210,−12.20)→ 6.59 (0.212,−12.50)→ 6.670.289 (0.205,−12.90)→ 6.44 (0.208,−14.10)→ 6.590.329 (0.201,−12.80)→ 6.31 (0.203,−14.40)→ 6.430.369 (0.200,−13.40)→ 6.30 (0.191,−13.10)→ 5.980.409 (0.198,−14.20)→ 6.25 (0.188,−14.20)→ 5.920.449 (0.195,−14.60)→ 6.16 (0.185,−15.70)→ 5.860.489 (0.194,−14.70)→ 6.13 (0.182,−19.00)→ 5.830.529 (0.196,−15.90)→ 6.240.569 (0.191,−16.80)→ 6.09

Fig. 21. Results of TRS calculations for the 9/2+ [624] band 2a in 181Os. These calculations predict th
181Os has a stable axially symmetric deformation characterised by (β2 = 0.230,β4 = −0.03, γ = −0.7). Thecalculation is shown at a rotational frequency ofhω= 0.250 MeV.

d 2losedlot. The

proposed

rupole

imentalted

aratus.s of thes

those,

tes asxial


Fig. 22. The quadrupole moment,Qo, extracted from the forward and backward lineshape fits for (a) banaand 2b, and (b) band 3a, and 3b. Open symbols refer to the fits extracted from the forward detectors and csymbols refer to the backward angles. The largest of the positive and negative errors are shown in the pthick dotted line represents the quadrupole moment extracted from the TRS calculations based on theconfigurations.

Figs. 22(a) and (b) show the respective comparison of the experimental quadmomentsQo, extracted from the DSAM measurement for bands 2a and 3a, with that ofthe TRS calculation based on the corresponding signature of the 9/2[624] and 1/2[521]configurations, respectively. From these figures it can be observed that the experDSAMQo measurements for bands 2a and 3a are in good agreement with those predicfrom the TRS calculation. The average DSAM quadrupole moments are≈ 6–7 eb overthe entire range where they could be measured with the present experimental appRecent measurements based on the recoil-distance method [16] for the deformationlower-spin states in these bands are in good agreement with theQo values extracted in thiwork. One important feature of these low-spin large quadrupole moments, especiallymeasured for band 3a below spin 33/2h is that, despite theγ softness of this configurationthe nuclear shape retains sufficient axially deformed symmetry to allowK to be definedfor these low-spin states. This is consistent with the observation of the isomeric staa consequence of theK selection rule [2] discussed in Section 4.2.2. This low-spin asymmetry in181Os is in contrast to the higher-spin behaviour, see Section 4.2.4.

4.2. Blocked BCS multi-quasiparticle calculations of energies

The experimental DCO ratios and intensity balances, discussed in Section 3.2, revealthe presence of two high-K structures based on theKπ = 37/2+ and Kπ = 41/2+

d on aThese

giesstionsngle-ge one-ies

statesental

n theergiess, see

stateucture.

dicted,

ed ansor this

nt at

band-.

r

e


states and many other intrinsic states and fragments of bands in181Os. In order tocompare these measurements with theory, multi-quasiparticle calculations, basefixed shape Nilsson model plus BCS pairing, have been performed in this work.calculations use the method of Jain et al. [43] with the monopole pairing strengths (Gn =20.8/AMeV andGp = 21.8/AMeV) chosen to reproduce the two-quasiparticle enerin the neighbouring isotopes. The calculations were performed at the deformationε2 =0.222 andε4 = 0.046 [44] taking account of the residual nucleon–nucleon interacempirically based on the Gallagher–Moszkovski coupling rules [45–47]. The siparticle energies near the Fermi surface were adjusted to reproduce the averaquasiproton energies in183

75Re [33,48] and18175Re [49]. The single-particle neutron energ

were adjusted to give the one-quasineutron excitation energies in181Os where known[33]. The results of these calculations predict the existence of many intrinsicin 181Os from low to high spins and Table 8 shows the comparison of the experimresults with the theoretical predictions. (Many of the higher energies, included iconfiguration table, are to provide information for future studies.) The predicted enare in excellent agreement with the experimental cases for most of the stateTable 8.

In the following comparison of the blocked BCS calculations with the experimentalenergies the discussion is limited to those bands which show a well defined band strThis entails that the band must have intra-bandI = 1 and inter-bandI = 2 transitions.For the other states there are in general many competing intrinsic configurations preand their character could not be firmly established in the present experiment.

Kπ = 21/2+ stateThe Kπ = 21/2+ state, experimentally observed at 1744 keV, was assign

ν(7/2−[514],9/2+[624],5/2−[512]) configuration in Ref. [19]. The present calculatioare in excellent agreement with this assignment. The predicted excitation energy fconfiguration is 1781 keV.

Kπ = 23/2− stateTheKπ = 23/2− t-band 4a at 1875 keV was assigned a configuration ofν(7/2−[514],

9/2+[624],7/2+[633]). The predicted excitation energy is also in excellent agreeme1891 keV, see Fig. 1.

Band5Band 5 was deduced to be based upon a 17/2− state from the|(gK − gR)/Qo| analysis

in Section 4.1.2. Unfortunately, this band was not observed down to its deducedhead spin and the lowest-spin state established was 21/2− at 1926 keV, see Fig. 1The predictions from the blocked BCS calculations, Table 8, show that this 17/2− intrinsicthree-quasineutron 1/2−[521], 9/2+[624], 7/2+[633] configuration is predicted to occuat an excitation energy of 1600 keV. Extrapolation of the experimentalγ -ray energies downfrom the 29/2, 25/2 and 23/2 states (see Fig. 1) suggests that the 17/2− bandhead stat
would occur at an excitation energy of about 1890 keV which is in reasonable agreementwith the predictions.

pairingons,

en


Table 8The results of the blocked multi-quasiparticle calculations based on a fixed shape Nilsson model plus BCSup to spin 59/2h, see text for details.EBCS

MQP is the calculated excitation energy and the residual interacti

Eresid., are taken from Ref. [47].Ecalc. is the sum ofEBCSMQP + Eresid. andE is the difference between th

Ecalc. andEexp., whereEexp. is the experimental excitation energy of the bands.π,ν refer to proton and neutroconfigurations, respectively

Kπ EBCSMQP Configuration Eresid. Ecalc. Eexp. E Band

(keV) (keV) (keV) (keV) (keV)

13/2[521]+ 1517 ν7/2[514], π5/2[402],1/2[541] −216 130115/2+ 1716 ν9/2[624],5/2[512],1/2[521] −127 158915/2− 1622 ν9/2[624], π5/2[402],1/2[541] −268 135417/2+ 981 ν7/2[514],9/2[624],1/2[521] −66 91517/2− 1775 ν9/2[624],1/2[521],7/2[633] −175 1600 1890 290 5a, 5b17/2− 1879 ν7/2[514], π9/2[514],1/2[541] −225 165417/2− 2049 ν9/2[624], π7/2[404],1/2[541] +250 229919/2+ 1984 ν9/2[624], π9/2[514],1/2[541] −236 174821/2+ 1818 ν7/2[514],9/2[624],5/2[512] −37 1781 1744 −37 Kπ = 21/2+21/2+ 2430 ν7/2[514], π5/2[402],9/2[514] +309 273923/2− 1877 ν7/2[514],9/2[624],7/2[633] +14 1891 1875 −16 4a, 4b23/2+ 2510 ν7/2[514],9/2[624],7/2[503] −18 249223/2+ 2627 ν7/2[514], π5/2[402],11/2[505] +314 294123/2− 2536 ν9/2[624], π5/2[402],9/2[514] +26 256223/2− 2449 ν7/2[514],9/2[624],1/2[521], −341 2108

π5/2[402],1/2[541]25/2− 2733 ν9/2[624], π5/2[402],11/2[505] +26 275925/2− 2893 ν9/2[624], π9/2[514],7/2[404] −129 2764 2178 −586 6a, 6b27/2− 2862 ν7/2[514],9/2[624],11/2[615] +14 287627/2− 2890 ν7/2[514], π9/2[514],11/2[505] +305 319527/2− 3048 ν9/2[624], π7/2[404],11/2[505] −176 287227/2+ 2811 ν7/2[514],9/2[624],1/2[521], −290 2521

π9/2[514],1/2[541]29/2+ 2995 ν9/2[624], π9/2[514],11/2[505] +58 3053 3091,3053 −38,0 29/2 intrin.31/2− 3362 ν7/2[514],9/2[624],1/2[521], +193 3555 2658 −897 31/2 intrin.

π5/2[402],9/2[514]33/2− 3559 ν7/2[514],9/2[624],1/2[521], +201 3760 3578 −182 Kπ = 33/2−

π5/2[402],11/2[505]35/2+ 3901 ν7/2[514],9/2[624],1/2[521], −26 3875

7/2[633],11/2[615]35/2− 3874 ν7/2[514],9/2[624],1/2[521], −273 3601 3739 138 Kπ = 35/2−

π7/2[404],11/2[505]37/2+ 3821 ν7/2[514],9/2[624],1/2[521], +253 4074 3914 −160 Kπ = 37/2+

π9/2[514],11/2[505]37/2+ 4528 ν7/2[514],9/2[624],7/2[633], +15 4543 3914 629

π5/2[402],9/2[514]39/2+ 4455 ν7/2[514],9/2[624],7/2[633], +20 4475

π5/2[402],11/2[505]39/2+ 4615 ν7/2[514],9/2[624],7/2[633], −201 4414

π9/2[514],7/2[404]41/2+ 4657 ν7/2[514],9/2[624],5/2[512], −65 4349 4521 172

π9/2[514],11/2[505]41/2+ 4770 ν7/2[514],9/2[624],7/2[633], −242 4228 4521 293 Kπ = 41/2+

π7/2[404],11/2[505]43/2− 4717 ν7/2[514],9/2[624],7/2[633], +35 4752

π9/2[514],11/2[505]43/2+ 5350 ν7/2[514],9/2[624],7/2[503], −69 5281

π9/2[514],11/2[505]43/2− 4868 ν7/2[514],9/2[624],1/2[521], −23 4845 4947 102 Kπ = 43/2−

π5/2[402],9/2[514],1/2[541],11/2[505]


e.

itation,

rk we

in thissence

andedV.sed

able. Iny

8 keV


Table 8 (continued)

Kπ EBCSMQP Configuration Eresid. Ecalc. Eexp. E Band

(keV) (keV) (keV) (keV) (keV)

45/2− 5276 ν7/2[514],9/2[624],1/2[521], −470 4806π9/2[514],7/2[404],1/2[541],11/2[505]

47/2− 5702 ν7/2[514],9/2[624],11/2[615], −37 5665π9/2[514],11/2[505]

47/2− 5705 ν7/2[514],9/2[624],5/2[512], –π5/2[402],9/2[514],1/2[541],11/2[505]

47/2− 5827 ν7/2[514],9/2[624],7/2[633], –π5/2[402],7/2[404],1/2[541],11/2[505]

49/2− 6113 ν7/2[514],9/2[624],5/2[512], −640 5473π9/2[514],7/2[404],1/2[541],11/2[505]

49/2+ 6073 ν7/2[514],9/2[624],1/2[521], –π5/2[402],9/2[514],7/2[404],11/2[505]

49/2+ 5764 ν7/2[514],9/2[624],7/2[633], –π5/2[402],9/2[514],1/2[541],11/2[505]

Band6In the present work, band 6 was observed with a 25/2− state at 2178 keV, se

Fig. 1. The nearest predicted configurations are≈ 600 keV too high, see Table 8These predicted values are based on configurations which involve a proton excν9/2+[624],π(5/2+[602],11/2−[505]) and ν9/2+[624], π(9/2−[514],11/2−[505])configurations. This poor agreement might be due to the fact that in the present wohave not observed this band down to its band-head spin.

Kπ = 35/2− stateThe 24(4) ns isomeric state was observed at an excitation energy of 3739 keV

work, in agreement with previous studies [14]. The BCS calculations predict the preof a Kπ = 35/2− state at 3601 keV based on aν(7/2−[514],9/2+[624],1/2−[521])π(7/2+[404],11/2−[505]) configuration. The good agreement in excitation energythe long lifetime of this state are consistent with its high-K nature. This state is establishto decay via a 159.5-keV transition into aKπ = 33/2− state at excitation energy 3578 keA Kπ = 33/2− intrinsic state is predicted from the calculations at 3760 keV baon a ν(7/2−[514],9/2+[624],1/2−[521])π(5/2+[402],11/2−[505]) configuration, seeTable 8. This agreement between the experimental observation and theory is remarkaddition, it should be noted that theKπ = 35/2− andKπ = 33/2− configurations are versimilar, differing only in the change of a single protonπ7/2+[404] → 5/2+[402]. Suchsimilar configurations reinforce the idea that the experimentally observed state at 357is likely of high-K nature. The fact that thisKπ = 35/2− isomer only decays to the 33/2−
state at 3578 keV when there are many path available also reinforces the idea that both ofthese states are high-K.

-

k ev-e ofave

gya sim-hele

is alsod on

yh are

f the

in the

n

cribingem-

ns

Fig. 7asi-

rvedpar-

scle


Kπ = 37/2+ stateThe BCS calculations also predict the presence of states with larger-K values. For exam

ple, aKπ = 37/2+ state based on aν(7/2−[514],9/2+[624],1/2−[521])π(9/2−[514],11/2−[505]) configuration is predicted at 3822 keV, see Table 8. In the present woridence is presented for aKπ = 37/2+ state at 3914 keV and the start of a sequenctransitions built upon it up to spin 49/2h, see Fig. 7. (Similar fragmented sequences hbeen established recently in182Os [12] and183Os [13].) The predicted excitation enerfor this state at 4074 keV, closely matches the experimentally determined value. Inilar manner, to theKπ = 35/2− andKπ = 33/2− configurations, discussed above, tKπ = 37/2+ andKπ = 35/2− configurations are very similar, differing only in a singprotonπ9/2−[514] → 7/2+[404], thus perhaps explaining the presence of the decay.

Kπ = 41/2+ stateTheKπ = 41/2+ intrinsic state at 4521 keV is the only high-K state observed in181Os

where a rotational band (band 8) was fully delineated on top to high spins. This bandthe only high-K rotational band in181Os whose behaviour matches that expected basethe collective rotation of a high-K configuration, i.e., in-bandγ -ray energies regularlincreasing with spin. There are two predicted configurations for this band, whicboth close in energy. Aν(7/2−[514],9/2+[624],5/2−[512])π(9/2−[514],11/2−[505])configuration at 4349 keV and aν(7/2−[514],9/2+[624],7/2+[633])π(7/2+[404],11/2−[505]) configuration at 4228 keV, see Table 8. Although the excitation energy oformer better matches the experimental excitation energy, the intrinsicg-factors appear tofavour the latter configuration, see Section 4.2.3. Directly analogous to the similarityKπ = 35/2− andKπ = 33/2− underlying single-particle configurations and theKπ =37/2+ andKπ = 35/2− configurations, theKπ = 41/2+ single-particle configuratioonly differs from theKπ = 37/2+ configuration by a single neutronν1/2−[521] →5/2−[512] which might explain the relatively unhindered decay half-life (< 5 ns).

In general, the blocked BCS calculations appear to be rather successful in desthe new high-K configurations in181Os. These calculations were also successfullyployed in describing the high-K states in the neighbouring odd-mass isotope,183Os [13].In comparing these neighbouring odd-A isotopes, we note the similarity in the high-Klevel schemes forK 33/2h. Although the underlying multi-quasiparticle configuratioof these states differ;Kπ = 33/2− in 181Os (ν1/2[521],7/2[514],9/2[624]π5/2[402],11/2[505]) and Kπ = 33/2+ in 183Os (ν7/2[503],7/2[514],9/2[624]π1/2[541],9/2[514]), bothK = 33/2 states have a rather fragmented decay pattern, comparewith Fig. 2 of Ref. [13]. In particular, theKπ = 33/2− in 181Os has a decay path to(31/2+) state at 3536 keV which decays to thet-band via an unobserved 42-keV trantion, in this work. A similar decay path was identified in the decay of theKπ = 33/2+ statein 183Os, where theKπ = 33/2+ state decays to an intermediate state via an unobse21-keV transition [13]. The difference in underlying single-particle configurations apently does not affect the overall decay mode of the isomeric state. In181Os, decay pathhave been observed from the 7(2) ns,Kπ = 21/2+ isomeric state to the one-quasiparti9/2[624] band via 956.8-, 848.2- and 1213.5-keV transitions, see Fig. 1. In183Os similar
decays were observed from theKπ = 21/2+,< 3 ns isomeric state to the one-quasiparticle9/2[624] band via 954.1-, 1258.2- and 1445.5-keV transitions [13]. Furthermore, the be-

whichey aretions

resultckeds, themulti-d more

igh-menty

forrvedts, seends 8tionsr

bandthe

e shownrted infor

. All of


haviour at higher spins is also very similar where the expected collective bandsare built upon intrinsic states are only observed for one or two transitions before thcrossed by other intrinsic states, i.e., the yrast intensity only follows the collective rotain these bands for a few states above the bandhead.

Both of these features can presumably be attributed toγ softness in181Os and183Os which may be expected to cause a mixing of the single-particle orbits andin many competing decay paths. Indeed, one significant limitation of these bloBCS calculations is the assumption of fixed axially-symmetric shape. Neverthelespredicted excitation energies show excellent agreement for most of the observedquasiparticle states. The effects of the stability of the nuclear shape are discussefully in Section 4.2.4.

4.2.1. Aligned angular momentum and RouthiansThe aligned angular momenta are shown for bands 7a, 7b, 8a and 8b in Fig. 16(c). The

alignment of bands 8a and 8b demonstrates behaviour which is expected for typical hK bands in this mass region in that they show little signature splitting. The alignof these bands increases smoothly fromhω = 0.1–0.3 MeV with no evidence for anup-bends or bands crossings. This behaviour is similar to that of theKπ = 33/2+ bandin 183Os [13]. In contrast, bands 7a and 7b are more irregular, showing some evidencea small gain in alignment athω = 0.20–0.25 MeV. These features can also be obsein the experimental Routhian and excitation energy minus an arbitrary reference ploFigs. 17(d) and 18(d), respectively. The experimental energies of the states for baaand 8b (Fig. 18(d)) show the expected behaviour for bands built up from collective rotaof a high-K configuration. In comparison, bands 7a and 7b are more irregular. Similairregular behaviour was recently observed for the high-K bands built upon theKπ = 25+isomeric state in182Os [12]. In this case, the alignment increases continuously up theand this was taken as a evidence thatγ vibrations were responsible for generatingangular momentum in addition to the more usual collective rotations.

4.2.2. Reduced hindrance factor calculationsReduced hindrance factors have been calculated for the isomeric states in181Os. The

reduced hindrance factor,fν is defined as,

fν = Tγ

1/2/TW1/2

1/ν, (3)

whereT γ1/2 is the partialγ -ray half-life,T W1/2 is the Weisskopf single-particle estimate,ν isthe degree ofK forbiddenness,ν = K − λ, andλ is the multipolarity of the transitiondepopulating the isomeric state. The hindrance factors, deduced from these data arin Table 9. These factors have been re-evaluated for the new 7(2) ns half-life repothis work for theKπ = 21/2+ isomeric state, see Section 3.2.4. The partial half-livesthe separate decay branches were estimated from the intensities shown in Table 2the reduced hindrance factors for the decays from theKπ = 21/2+ isomeric state in181Oshave values,fν = 12.3–19.2. These reduced hindrance factors are slightly larger in181Os
than those of the correspondingKπ = 23/2+ state decay in183Os [13] wherefν values of 5.6–10 were reported. (The configurations differ by a 5/2−[512] neutron replaced by a

e

ed with

oselyte was

ssumingf the

hereutron

e extentct that

iour. [9],

ofnglexcited


Table 9Reduced hindrance factor calculations for the top panel theKπ = 21/2+ , 7(2) ns, the middle panel thKπ = 35/2− , 24(4) ns, and the lower panel theKπ = 33/2− , < 5 ns isomeric states in181Os, see text fordetails. Theγ -ray intensities are taken from Table 2

Kπi

t1/2 (ns) Eγ (keV) Tpartial1/2 (ns) Multipolarity K ν =K − λ fν

21/2+ 7(2) 848.2 10.19 M1(I = 0) 6 5 12.321/2+ 7(2) 956.5 61.89 M1(I = 1) 6 5 19.221/2+ 7(2) 1214.5 87.6 E2(I = 2) 6 4 12.635/2− 24.4(4) 159.5 < 24.7 M1(I = 1) 1 0 –33/2− < 5 754.9 < 25.0 M1(I = 0) 16 15 < 2.433/2− < 5 1195.0 < 22.6 E2(I = 2) 16 14 < 1.933/2− < 5 599.6 < 133.8 M1(I = 0) 13 12 < 3.233/2− < 5 623.0 < 71.0 M1(I = 0) 8 7 < 7.033/2− < 5 1056.3 < 42.3 E2(I = 2) 6 4 < 8.8

7/2−[503] neutron in183Os.) The larger hindrance factors for the181Os decay may implya more robust conservation of theK quantum number in181Os compared with183Os.

The 33/2−,< 5 ns state at 3578 keV is reasoned to have a high-K value. This is becausits decay pattern is fragmented to many final states in a manner normally associatehigh-K states which are well above the yrast line. In addition, its excitation energy clmatches the theoretical predictions of the blocked BCS codes. The lifetime of the stasmall, see Section 3.2.4, which is consistent with that of other high-K states in the osmiumnuclei, discussed above. Table 9 shows the reduced hindrance factors calculated aa< 5 ns half-life. The hindrance factors for three (754.9-, 1195.0- and 599.6-keV) ofive transitions are of a similar magnitude to those of the decay of theKπ = 33/2+ statein 183Os [13] wherefν ranges from 3.2–4.1. These reduced hindrance factors in181Osare presumably affected by the Coriolis mixing because they decay to the 1/2−[521]and 7/2−[514] one-quasineutron bands in the region of the first band crossing wvarious high-K components would be expected to be mixed into the one-quasinewavefunctions. The other two decays, 623.0-keV to band 5 and 1056.3-keV to thet-band,band 4, have larger hindrance factors and are presumably not affected to the samby Coriolis mixing in the final states. These arguments are also consistent with the faboth bands 5 and 4 have high-K values, 17/2− and 23/2−, respectively.

The new results presented here for181Os are consistent with the systematic behavexpected for the Os nuclei in this region [50]. As concluded by Chowdhury et alit seems likely that the onset ofγ softness is largely responsible for this partial lossconservation of theK quantum number. However, it remains problematic to disentathe influence of level density [51] as the isomers become progressively more highly erelative to the yrast line.

4.2.3. |(gK − gR)/Qo| ratios for the high-K statesExperimental|(gK − gR)/Qo| values have been deduced from theI = 1 toI = 2

γ -ray intensity branching ratios for the states in bands 8a and 8b as outlined in Sec-tion 23. The experimentally determined ratios for thisKπ = 41/2+ band are shown in

eown as

eticals) forly re-

goodecond

sn

nts havel was

are

wer-erably


Fig. 23. |(gK − gR)/Qo| values for theKπ = 41/2+ states in bands 8 in181Os. The weighted averagvalues are shown by the solid line. The theoretical values based on the Nilsson model are shdot-dashed and dashed lines respectively refer to theν7/2[514],9/2[624],5/2[512],π9/2[514]11/2[505]andν7/2[514],9/2[624],7/2[633],π7/2[404]11/2[505], respectively, see Table 8.

Fig. 23 along with the weighted average of the data points (solid line). The theorvalues estimated from the Nilsson model are also shown in the figure (broken linethe two predictedKπ = 41/2+ states. The dot-dashed and dashed lines respectivefer to theν7/2−[514],9/2+[624],5/2−[512]π9/2−[514],11/2−[505] configurationat 4657 keV and theν7/2−[514],9/2+[624],7/2+[633]π7/2+[404],11/2−[505] con-figuration at 4770 keV, see Table 8. Both of these two configurations give a fairlymatch to the experimental excitation energy of the state at 4521 keV. However, the sconfiguration (dashed line) fits the experimental|(gK − gR)/Qo| ratios better, and thiν7/2−[514],9/2+[624],7/2+[633]π7/2+[404],11/2−[505] configuration has beeassigned to theKπ = 41/2+ band 8.

4.2.4. Configuration-constrained potential energy surface calculations for the high-K

statesIn order to address the ideas that the high-spin states in181Os are subject to a significa

γ softness, configuration-constrained potential energy surface (PES) calculationbeen performed using the method of Xu et al. [17]. A Woods–Saxon potentiaused with Lipkin–Nogami pairing and the energy was minimised with respect toβ4 atevery point on theβ2–γ plane. The results of these calculations for theKπ = 33/2−,Kπ = 35/2−, Kπ = 37/2+ andKπ = 41/2+ states are summarised in Table 10 andshown in Figs. 24(a)–(d), respectively.

These calculations differ from the regular TRS calculation performed for the lospin states (discussed in Section 4.1 and shown in Fig. 21) in that they show consid
largerγ softness. Note the small barrier against triaxial (γ ) fluctuations indicated by thewide spacing of the contours around the absolute minima in theγ direction. Figs. 24(a)–

ular

ofthese

cture

y


(d) show that theγ softness is much larger for theKπ = 37/2+ state relative to theKπ = 33/2−, Kπ = 35/2− andKπ = 41/2+ states. This is interesting because a reghigh-K band was established in this work above theKπ = 41/2+ intrinsic state, theKπ =35/2− is isomeric and theKπ = 33/2− configuration shows behaviour representativean intrinsic state in that its fragmented decay feeds many states (implying both ofstates have well definedK values). In contrast, the structure built upon the moreγ -softKπ = 37/2+ configuration is, however, more unusual and more analogous to the struthat was recently established on top of theKπ = 25+ isomer in 182Os. The largeγsoftness predicted for theKπ = 37/2+ configuration in181Os and that of theKπ = 25+configuration in182Os are consistent with their angular momentum being built up bγvibrations or shape fluctuations in addition to collective rotation.

Table 10The results of the configuration constrained potential energy surface calculations for theKπ = 33/2− , Kπ =35/2− ,Kπ = 37/2+ andKπ = 41/2+ states in181Os

Kπi

Configuration (β2, β4, γ ) E (MeV)

33/2− (ν7/2[514],9/2[624],1/2[521],π5/2[402],11/2[505]) (0.207,−0.034,0.7) 4.2835/2− (ν7/2[514],9/2[624],1/2[521],π7/2[404],11/2[505]) (0.214,−0.037,1.6) 4.8037/2+ (ν7/2[514],9/2[624],1/2[521],π9/2[514],11/2[505]) (0.199,−0.024,−5.9) 4.3241/2+ (ν7/2[514],9/2[624],5/2[512],π9/2[514],11/2[505]) (0.211,−0.024,0.8) 4.27

Fig. 24. Configuration constrained potential energy surface calculation for (a) theKπ = 33/2− , ν 7/2[514],9/2[624], 1/2[521], π 5/2[402], 11/2[505], (b) theKπ = 35/2− , ν 7/2[514], 9/2[624], 1/2[521], π 7/2[404],11/2[505], and (c) theKπ = 37/2+ , ν 7/2[514], 9/2[624], 1/2[521], π 9/2[514], 11/2[505], and (d) the
Kπ = 41/2+, ν 7/2[514], 9/2[624], 5/2[512], π 9/2[514], 11/2[505] states in181Os. All figures are plotted forhω= 0.0 MeV and adjacent contours are separated by 200 keV.

oreticals. Thele largeh thosee ideartly

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5. Summary

In summary, this work has greatly extended the known high- and low-K level schemefor 181Os. Configurations for the states have been assigned based on the thecranked-shell model, blocked BCS, and configuration-constrained PES calculationlifetimes for some of the low-K states in the 9/2+[624] and 1/2−[521] collective rotationabands have been measured using the Doppler shift attenuation method (DSAM). Thdeformations deduced from these measurements are found to be consistent witpredicted from theoretical total Routhian surface calculations. The results support ththat for the low-K states the nuclear shape is axially symmetric and theK quantum numbeis well defined and the associatedK-selection rule is upheld. This behaviour apparencontrasts with that of the higher-K states in181Os.

For the higher-K intrinsic states the configurations and excitation energies are fto be in excellent agreement with theoretical multiquasiparticle calculations basthe Nilsson model with BCS pairing. Configuration-constrained potential energy sucalculations suggest that the irregular transition sequence above theKπ = 37/2+ intrinsicbandhead state, the limited excitations observed above the other intrinsic statesobservation of fragmented and non-hindered decays, are due to an appreciableγ softness.

Acknowledgements

D.M.C. acknowledges receipt of an EPSRC Advanced Fellowship AF/100225 anof us (H.M.E., A.M.F., L.K.P., C.S., R.J.W.) acknowledge receipt of EPSRC studentsThe authors would like to thank D.C. Radford for the use of the “Radware” soft[20], W.T. Milner [21] for the use of the “UPAK” software, and H.-Q. Jin for the uof “Jinware”.

References

[1] P.M. Walker, G.D. Dracoulis, Nature 399 (1999) 35.[2] K.E.G. Löbner, Phys. Lett. B 26 (1968) 369.[3] F.G. Kondev, G.D. Dracoulis, A.P. Byrne, M. Dasgupta, T. Kibédi, G.J. Lane, Nucl. Phys. A 601 (1996[4] C. Wheldon, P.M. Walker, R. D’Alarcao, P. Chowdhury, C.J. Pearson, E.H. Seabury, I. Ah

M.P. Carpenter, D.M. Cullen, G. Hackman, R.V.F. Janssens, T.L. Khoo, D. Nisius, P. Reiter, Eur.J. A 5 (1999) 353.

[5] D.M. Cullen, S.L. King, A.T. Reed, J.A. Sampson, P.M. Walker, C. Wheldon, F. Xu, G.D. DracoI.-Y. Lee, A.O. Macchiavelli, R.W. MacLeod, A.N. Wilson, C. Barton, Phys. Rev. C 60 (1999) 064301

[6] C.S. Purry, P.M. Walker, G.D. Dracoulis, T. Kibédi, F.G. Kondev, S. Bayer, A.M. Bruce, A.P. ByW. Gelletly, P.H. Regan, C. Thwaites, O. Burglin, N. Rowley, Nucl. Phys. A 632 (1998) 229.

[7] C. Thwaites, C. Wheldon, A.M. Bruce, P.M. Walker, G.D. Dracoulis, A.P. Byrne, T. Kibédi, F.G. KonC.J. Pearson, C.S. Purry, Phys. Rev. C 66 (2002) 054309.

[8] T. Shizuma, G. Sletten, R.A. Bark, N.L. Gjorup, H.J. Jensen, S. Mitarai, M. Piiparinen, J. WrzesZ. Phys. A 359 (1997) 227.

[9] P. Chowdhury, B. Fabricius, C. Christensen, F. Azgui, S. Bjornholm, J. Borggreen, A. Holm, J. Ped
G. Sletten, M.A. Bentley, D. Howe, A.R. Mokhtar, J.D. Morrison, J.F. Sharpey-Schafer, P.M. Walker,R.M. Lieder, Nucl. Phys. A 485 (1988) 136.

yák,aard,ndorf,

runo,

ieder,

Poland,

man,moto,

ecken,hury,

) 623.sis, OakORNL-

yberg,

ilotte,erence1991,

ee,

hys.

Bayer,


[10] K. Narimatsu, Y.R. Shimizu, T. Shizuma, Nucl. Phys. A 601 (1996) 69.[11] S. Frauendorf, in: Proc. Int. Conf. on the Future of Nuclear Spectroscopy, Crete, 1993, p. 112.[12] L.K. Pattison, D.M. Cullen, J.F. Smith, A.M. Fletcher, P.M. Walker, H.M. El-Masri, Zs. Podol

R.J. Wood, C. Scholey, C. Wheldon, G. Mukherjee, D. Balabanski, M. Djongolov, Th. DalsgH. Thisgaard, G. Sletten, F. Kondev, D. Jenkins, G.J. Lane, I.-Y. Lee, A.O. Macchiavelli, S. FraueD. Almehed, Phys. Rev. Lett., in press.

[13] T. Shizuma, K. Matsuura, Y. Toh, Y. Hayakawa, M. Oshima, Y. Hatsukawa, M. Matsuda, K. FuY. Sasaki, T. Komatsubara, Y.R. Shimizu, Nucl. Phys. A 696 (2001) 337.

[14] Ts. Venkova, T. Morek, H. Schnare, G. Marti, W. Gast, A. Georgiev, K.M. Spohr, T. Kutsarova, R.M. LK. Strahle, T. Rzaca-Urban, K.H. Maier, K.O. Zell, KFA-IKP Annu. Rep., 1990/1991, p. 33.

[15] G. Sletten et al., in: R. Broda (Ed.), Proceedings of XXII Zakopane School on Physics, Zakopane,1–15 May 1987.

[16] Z. Podolyák, S. Al-Garni, R.F. Casten, J.R. Cooper, D.M. Cullen, A. Dewald, R. Krucken, H. NewJ.N. Ocre, C.J. Pearson, C. Ur, R. Venturelli, S. Vincent, C. Wheldon, P.M. Walker, F.R. Xu, A. YamaN.V. Zamfir, Phys. Rev. C 66 (2002) 011304(R).

[17] F.R. Xu, P.M. Walker, J.A. Sheikh, R. Wyss, Phys. Lett. B 435 (1998) 257.[18] I.Y. Lee, Nucl. Phys. A 520 (1990) 641c.[19] T. Kutsarova, R.M. Lieder, H. Schnare, G. Hebbinghaus, D. Balabanski, W. Gast, A. Kramer-Fl

M.A. Bentley, P. Fallon, D. Howe, A.R. Mokhtar, J.F. Sharpey-Schafer, P. Walker, P. ChowdB. Fabricius, G. Sletten, S. Frauendorf, Nucl. Phys. A 587 (1995) 111.

[20] D.C. Radford, Nucl. Instrum. Methods Phys. Res. A 361 (1995) 297.[21] W.T. Milner, UPAK: the Oak Ridge data analysis package, private communication.[22] K.S. Krane, R.M. Steffen, R.M. Wheeler, Nucl. Data Tables 11 (1973) 351.[23] L.P. Ekström, A. Nordlund, Nucl. Instrum. Methods A 313 (1992) 421.[24] R.S. Hagar, E.C. Seltzer, Nucl. Data A 4 (1968) 1.[25] H. Kawakami, M. Ishihara, N. Yoshikawa, K. Ishii, H. Kusakari, M. Sakai, J. Phys. Soc. Jpn. 36 (1974[26] J.C. Wells, N.R. Johnson, Lineshape: a computer program for Doppler-broadened lineshape analy

Ridge National Laboratory Physics Division Progress Report for period ending September 30, 1991,6689, p. 44.

[27] J. Gascon, C.-H. Yu, G.B. Hagemann, M.C. Carpenter, J.M. Espino, Y. Iwata, T. Komatsubara, J. NS. Ogaza, G. Sletten, P.O. Tjøm, D.C. Radford, Nucl. Phys. A 513 (1990) 344.

[28] C.-H. Yu, F.K. McGowan, I.Y. Lee, J.D. Garrett, W.B. Gao, H.Q. Jin, N.R. Johnson, J. Lewis, S. PL.L. Riedinger, J.C. Wells, H. Xie, in: J.X. Saladin, et al. (Eds.), Proceedings of the International Confon High Spin Physics and Gamma-Soft Nuclei, Pittsburgh, PA, 1990, World Scientific, Singapore,p. 133.

[29] J. Lindhard, M. Scharff, H.E. Schiott, Matt. Fys. Medd. K. Dan. Vidensk. Selsk. 33 (1963) 14.[30] W.M. Currie, Nucl. Instrum. Methods 73 (1969) 173.[31] T.K. Alexander, J.S. Forster, Adv. Nucl. Phys. 10 (1979) 197.[32] F. James, M. Roos, Comput. Phys. Commun. 10 (1975) 343.[33] R.B. Firestone, in: V.S. Shirley (Ed.), Tables of Isotopes, 8th Edition, Wiley, 1996.[34] W. Nazarewicz, R. Wyss, A. Johnson, Nucl. Phys. A 503 (1989) 285.[35] S.M. Harris, Phys. Rev. 138 (1965) B509.[36] C. Fahlander, G. Dracoulis, Nucl. Phys. A 375 (1982) 263.[37] R.M. Lieder, G. Sletten, J. Borggreen, J. Pedersen, Nucl. Phys. A 375 (1982) 291.[38] D.M. Cullen, A.T. Reed, D.E. Appelbe, A.N. Wilson, E.S. Paul, R.M. Clark, P. Fallon, I.Y. L

A.O. Macchiavelli, R.W. MacLeod, Nucl. Phys. A 638 (1998) 662.[39] P.M. Walker, G.D. Dracoulis, A.P. Byrne, B. Fabricius, T. Kibédi, A.E. Stuchbury, N. Rowley, Nucl. P

A 586 (1994) 397.[40] E. Hagn, E. Zech, Z. Phys. A 295 (1980) 345.[41] C. Wheldon, G.D. Dracoulis, R.T. Newman, P.M. Walker, C.J. Pearson, A.P. Byrne, A.M. Baxter, S.

T. Kibédi, T.R. McGoram, S.M. Mullins, F.R. Xu, Nucl. Phys. A 699 (2002) 415.[42] P. Ring, A. Hayashi, K. Hara, H. Emling, E. Grosse, Phys. Lett. B 110 (1982) 423.
[43] K. Jain, O. Burglin, G.D. Dracoulis, B. Fabricius, N. Rowley, P.M. Walker, Nucl. Phys. A 591 (1995) 61.[44] R. Bengtsson, S. Frauendorf, F.R. May, At. Data Nucl. Data Tables 35 (1986) 15.

arson,

, Nucl.


[45] C.J. Gallagher, S.A. Moszkowski, Phys. Rev. 111 (1958) 1282.[46] K. Jain, P.M. Walker, N. Rowley, Phys. Lett. B 322 (1994) 27.[47] F. Kondev, Ph.D. thesis, Australian National University, 1997.[48] C.S. Purry, P.M. Walker, G.D. Dracoulis, S. Bayer, A.P. Byrne, T. Kibédi, F.G. Kondev, C.J. Pe

J.A. Sheikh, F.R. Xu, Nucl. Phys. A 672 (2000) 54.[49] C.J. Pearson, P.M. Walker, C.S. Purry, G.D. Dracoulis, S. Bayer, A.P. Byrne, T. Kibédi, F.G. Kondev

Phys. A 674 (2000) 301.[50] P.M. Walker, J. Phys. G 16 (1990) L233.
[51] P.M. Walker, D.M. Cullen, C.S. Purry, D.E. Appelbe, A.P. Byrne, G.D. Dracoulis, T. Kibédi, F.G. Kondev,
I.Y. Lee, A.O. Macchiavelli, A.T. Reed, P.H. Regan, F. Xu, Phys. Lett. B 408 (1997) 42.

high-spin states, lifetime measurements and isomers in os

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