Structure of positive-parity yrast band in 80 Br

Nuclear Physics A 678 (2000) 258–274 www.elsevier.nl/locate/npe

Structure of positive-parity yrast band in 80Br I. Ray a , P. Banerjee a,∗ , S. Bhattacharya a , M. Saha-Sarkar a , S. Muralithar b , R.P. Singh b , R.K. Bhowmik b a Saha Institute of Nuclear Physics, Calcutta 700 064, India b Nuclear Science Centre, Post Box 10502, New Delhi 110 067, India

Received 4 April 2000; revised 31 May 2000; accepted 13 June 2000

Abstract The states of the positive-parity yrast band in 80 Br have been investigated using the 76 Ge(7 Li, 3nγ ) reaction at a beam energy of 32 MeV. The band has been extended up to 4450 keV with a spin of (14+ ). Unambiguous spin assignments are made for states up to 2944.0 keV and γ -ray multipole mixing ratios are determined for several 1J = 1 transitions. Lifetimes studies for the 10+ , 11+ and 12+ states provide an estimate of the quadrupole deformation in this band. Cranking model analysis of the experimental data reveals a signature inversion at a spin of 12 h¯ and a probable neutron alignment at hω ¯ ≈ 0.7 MeV. The results are discussed within the framework of the systematics of similar bands in the lighter Br isotopes and the cranked-shell model. In addition, a new positiveparity and two negative-parity sequences have been identified.  2000 Elsevier Science B.V. All rights reserved. PACS: 27.50.+e; 21.10.Re; 21.10.Tg Keywords: NUCLEAR REACTION 76 Ge(7 Li, 3n); Enriched targets; E = 32 MeV; Measured Eγ , Iγ , γ − γ − t; DCO ratios; Doppler shifts; 80 Br; Deduced levels; J π ; B(E2); band structure; Comparison with cranked-shell model calculations

1. Introduction The studies of the positive-parity yrast bands in the odd-odd bromine isotopes have revealed several interesting features [1–6]. In all cases, these bands have been found to be based on a 4+ isomer (with half-lives T1/2 = 49.5 m, 1.3 s and 120 µs for 74 Br, 76 Br and 78 Br, respectively [2]) and interpreted in terms of a two quasiparticle configuration (νg9/2 )⊗(πg9/2 ) and collective excitations. Large prolate deformations of β2 ∼ 0.3–0.4 have been reported [3,4] for this band in the lighter 74,76 Br nuclei from lifetime studies. Similar deformations are also reported for several other doubly-odd nuclei in this mass region [7,8]. However, a systematic study of the properties of the nuclei in this (74,76,78Br)

∗ Corresponding author: [email protected]

0375-9474/00/$ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 0 ) 0 0 3 3 5 - 3

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mass region indicates that the deformation is maximum for nuclei with neutron number N near 40 and decreases as N decreases or increases [3,4,8–10]. A signature inversion has been observed to occur at a spin of about 9 h¯ in this band in 74,76,78Br, in support of earlier particle–rotor calculations for 76 Br [11]. This phenomenon has also been observed in the Rb and Y isotopes [8]. The inversion point shifts to somewhat higher spins as N increases. Also, the bands appear to have almost constant kinematic and dynamic moments of inertia, indicating no change in shape, up to fairly high rotational frequencies. The B(E2) values have been found to remain constant (as in 74 Br [3]) or even decrease (as in 76 Br [4]) at high spin. The reason for this effect in 76 Br is not fully understood. The relatively neutron-rich 80,82 Br have not been studied in much detail. Previously, states up to 2944 keV and 2243 keV have been reported in 80 Br and 82 Br, respectively, populated mostly in deuteron- and alpha-induced reactions [12–14]. There is no lifetime information for the excited states in 80,82 Br. Most of the interesting features mentioned earlier have not been identified in these two nuclei. An attempt is made in the present work to provide further experimental data on 80 Br in order to obtain a better understanding of the structure of the lowest positive-parity band in this nucleus.

2. Experimental methods Excited states of 80 Br were populated in the 76 Ge(7 Li, 3nγ ) reaction at a beam energy of 32 MeV at the 15UD Pelletron Accelerator at Nuclear Science Centre (NSC), New Delhi. The target consisted of isotopically enriched (99%) 76 Ge with a thickness of 1 mg/cm2 , evaporated on a 10 mg/cm2 gold foil. Two or higher fold γ γ -coincidence data were collected using the gamma detector array at NSC comprising of twelve Comptonsuppressed HPGe detectors besides fourteen BGO elements, at least one of which was required to fire in order to validate a coincidence event. Gated energy spectra with a dispersion of 0.5 keV per channel were generated from a 4096 × 4096 matrix, obtained from a sorting of the raw data of all the twelve detectors. These spectra were used for the assignment of the γ -rays in the level scheme. The directional correlation of γ -rays deexciting oriented states (DCO ratios) and the Doppler shift attenuation (DSA) data, for spin assignments and lifetime studies, respectively, were obtained from other matrices as described in Ref. [10]. The DCO ratios (RDCO ), defined as RDCO =

Iγ at 153◦ gated by γG at 99◦ Iγ at 99◦ gated by γG at 153◦

(Iγ is the intensity of the γ -ray of interest, obtained in coincidence with γG ) were compared with the theoretical DCO ratios for assignment of spin and determining multipole mixing ratios (δ). A width of σ = 0.3J (J is the level spin) was used for the presumed Gaussian distribution of the magnetic substate population. Gates on stretched E2 transitions yield RDCO -values close to unity for quadrupole γ -rays, or 1J = 0 nonstretched pure dipole transitions and values ranging from 0 to 2, depending on the E2/M1 multipole mixing ratios δ for 1J = 1 transitions. However, the usual way of setting

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gates on stretched E2 transitions was not feasible in all cases due to their low intensities. Gates were set in several cases on strong 1J = 1 transitions with small δ-values and in some cases on a 1J = 0 pure dipole transition. A gate on a 1J = 1 predominantly dipole transition yields RDCO ≈ 1 for 1J = 1 transitions with small δ and values close to 2 for stretched E2 γ -rays. A gate on 1J = 0 pure dipole transition gives RDCO ≈ 1 for stretched E2 transitions and values close to 0.5 for 1J = 1 predominantly dipole γ -rays. Lifetimes of excited states in 80 Br were determined from the DSA data using the centroid-shift method [10]. The effects of the feedings from the higher lying levels and from the continuum (direct feeding) were taken into account. The direct feeding times to the different excited states were taken to be similar to those which were previously determined for 79 Br [10], populated in the same experiment. Accordingly, direct feeding times of 0.15, 0.12 and 0.08 ps were used for estimating the lifetimes of the 1588.0, 2256.9 and 2944.0 keV states, respectively. Discrete feeding times were estimated directly from the observed shifts in the energies of the transitions feeding the levels of interest. Other details of the DSA and DCO analyses have been reported earlier [10]. The relative intensities of the transitions were measured from the coincidence data at 99◦ to the beam direction. In several cases, these are expressed as relative intensities at 55◦ by using the Ak /A0 (k = 2, 4) values reported previously from the reaction 78 Se(α, pn) at 27 MeV [14]. The Ak /A0 values are not expected to be significantly different for the reaction used in the present work. For the E2 transitions, where the Ak /A0 values are not known, A2 /A0 = 0.3 and A4 /A0 = 0 were used to deduce the relative intensities at 55◦ . 3. Experimental results The experimental results for γ -ray intensities, DCO ratios and spin assignments are summarised in Table 1 and the level lifetimes, transition probabilities, quadrupole moments and quadrupole deformations are listed in Table 2. The resulting level scheme is shown in Fig. 1. Most of the states have been grouped into several bands which are identified by band numbers as indicated. A few low-lying states above 85.8 keV reported earlier [14] but weakly populated in present work, are not shown in this figure. The ground state with spin 1+ and the 37.1 keV 2− state, adopted in the literature [12], are however included in Fig. 1 although the low-energy transitions (with large γ -ray internal conversion coefficients) populating these states were not observed. 3.1. The positive-parity yrast band (bands 1a and 1b) The main decay path of the nucleus was found to follow through the positive-parity yrast band. Bands 1a and 1b (Fig. 1) are identified as the α = 0 and α = 1 signature partners of this band, respectively, built upon the 331.1 keV state with spin J π = 5+ and a half-life of 0.7 ns [14]. States up to 2944.0 keV have been adopted in the literature [12] for this band. The addition of two new transitions of energy 1348 and 1506 keV has extended the band up to 4450 keV. A weak 687 keV transition has been placed in the level scheme connecting the 2944.0 and 2256.9 keV states. Fig. 2a shows the sum of the spectra gated by the low-lying

Table 1 Energies, relative intensities, DCO ratios, multipolarities and spin assignments in 80 Br RDCO

Gated (keV)

Multipolarity/ δ(E2/M1)

Jiπ → Jfπ

Bande

615.3

26.2f 271.4 167.5

– 8.3 ± 1.2h 85.9 ± 7.0

6+ → 5+ 6+ → 5− 8+ → 7+

1a → 1b 1a → 3 1a → 1b

1588.0

<1 22.8 ± 2.5

E2i −0.12+0.08 −0.05

8+ → 6+ 10+ → 9+

1a 1a → 1b

972.6

21.5 ± 2.7

E2

10+ → 8+

1a

687 1356.0 1506

<1 15.6 ± 2.5 2.1 ± 0.6

– 167.5 972.6 245.3 – 245.3 167.5 167.5 1356.0 – 972.6 –

M1g E1 −0.02 ± 0.04

258.0 447.1

– 1.05 ± 0.13 0.56 ± 0.05 0.56 ± 0.03 – 0.53 ± 0.07 0.80 ± 0.09 1.61 ± 0.16 0.94 ± 0.21 – 1.06 ± 0.24 –

– E2 (E2)k

12+j → 11+ 12+ → 10+ (14+ )k → 12+

1a → 1b 1a 1a

245.3 90.6

95.1 ± 7.6 100 ± 8

5+ → 5− 7+ → 6+

1b → 3 1b → 1a

1140.9

<1 52.4 ± 5.2

E2i −0.15 ± 0.04

7+ → 5+ 9+ → 8+

1b 1b → 1a

2256.9

693.1 668.9

<1 18.5 ± 3.0

E2i −0.04 ± 0.05

9+ → 7+ 11+ → 10+

1b 1b → 1a

3605

1116.0 1348

5.2 ± 1.3 3.0 ± 0.7

972.6 245.3 972.6 – 245.3 167.5 – 245.3 972.6 – –

1J = 0, E1 −0.07+0.05 −0.08

116.8 525.6

1.04 ± 0.07 0.52 ± 0.03 0.49 ± 0.06 – 0.46 ± 0.04 0.84 ± 0.07 – 0.57 ± 0.08 0.52 ± 0.11 – –

E2i (E2)k

11+ → 9+ (13+ )k → 11+

1b 1a

Band 1a 357.2

2944.0 4450 Band 1b 331.1 447.8

261

Irel c

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Eγ b (keV)

Ex a (keV)

262

Table 1 — continued RDCO

Gated (keV)

Multipolarity/ δ(E2/M1)

Jiπ → Jfπ

Bande

2796.7

918.8 1086.3 467.4 860.7 795.1

7.0 ± 1.3h 7.4 ± 1.5 2.7 ± 0.6h 20.9 ± 3.1h 9.8 ± 1.8h

0.55 ± 0.09 1.01 ± 0.17 '1 0.95 ± 0.12 1.09 ± 0.16

245.3 245.3 167.5 167.5 525.6

E2/M1 E2 or 1J = 0 (E2/M1) E2/M1 E2/M1

(7+ , 9+ ) → 8+ (7+ , 9+ ) → 7+ + (8 , 10+ ) → (7+ , 9+ ) (8+ , 10+ ) → 9+ + (9 , 11+ ) → (8+ , 10+ )

2 → 1a 2 → 1b 2 2 → 1b 2

Band 3 85.8 379.9 774.3

48.8f 294.1 394.4

20.5 ± 2.4h 15.6 ± 1.9h

6− → 5− 7− → 6−

3 3

1851.2

11.7 ± 2.0 9.9 ± 1.9

1076.9 1076.9 294.1 1076.9 688.4

E2/M1 E2/M1

688.4 1076.9

0.71 ± 0.10 1.15 ± 0.17 1.43 ± 0.18 1.10 ± 0.21 0.94 ± 0.23

E2i E2

7− → 5− 9− → 7−

3 3

355.9 824.2 1180.0 960.6 1063.8

4.0 ± 0.9h 2.8 ± 0.7h 3.6 ± 0.9h 1.9 ± 0.7h 2.7 ± 0.9h

1.02 ± 0.30 1.08 ± 0.32 0.86 ± 0.24 – 0.99 ± 0.25

688.4 355.9 688.4 – 1076.9

E2 or 1J = 0 (E2) E2 or 1J = 0 – E2 or 1J = 0

(5− , 7− ) → 7−

4→3 4 4→3 4 4→3

Band 2 1534.1 2001.6

Band 4 1130.2 1954.3 2915.0

Eγ b (keV)

(7− , 9− ) → (5− , 7− ) (7− , 9− ) → 7−

(9− , 11− )j → (7− , 9− ) (9− , 11− ) → 9−

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Irel c

Ex a (keV)

Table 1 — continued Eγ b (keV)

Irel c

RDCO

Gated (keV)

Multipolarity/ δ(E2/M1)

Jiπ → Jfπ

Bande

Other states 2379 3212 3658

1238 955 714

6.1 ± 1.3h 7.9 ± 1.6h 4.1 ± 0.9h

– – –

– – –

– – –

– → 9+ – → 11+ – → 12+

– → 1b – → 1b – → 1a

a The errors in E are < 0.5 keV for all states up to 3 MeV and 6 1 keV for the higher energy states. x b The γ -ray energies are accurate to ±0.1 keV for transitions with I > 10 and increases to ±1 keV for the weakest ones. rel c Deduced relative γ -ray intensities at 55◦ to the beam direction unless indicated otherwise (see text). d Gating transitions for determining R DCO . e The band labels refer to Fig. 1. f Reported in Ref. [14]. Low energy transition with large γ -ray internal conversion coefficient; not observed in this work. g Reported in Ref. [14]. h Measured intensities at 99◦ to the beam direction.

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Ex a (keV)

i Multipolarity from the cross-over nature of the transition (see text). j J π assignment based on R DCO for other transition from the same level. k From systematics of the band in neighbouring odd–odd Br nuclei.

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Fig. 1. Partial level scheme for 80 Br obtained in this work. The labels 1a, 1b, 2, 3 and 4 identify the bands. The inset shows an expanded view of the lower part of positive-parity yrast band. Energies are given in keV and the relative intensities of the transitions are proportional to the widths of the arrows. Low energy, highly-converted transitions, reported previously, between the three lowest levels and the 357.2 and 331.1 keV states are not shown as these were not observed.

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Table 2 Mean lifetimes (τ ), B(E2) and B(M1), transition quadrupole moments (Qt ) and quadrupole deformations (β2 ) for the positive-parity band in 80 Br. Transition probabilities for 1I = 1 transitions are calculated using the present E2/M1 mixing ratios Ex (keV)

Jiπ → Jfπ

τ (ps)

B(E2) (W.u.)

1588.0

10+ → 8+

20.3+7.7 −5.4

2256.9

10+ → 9+ 11+ → 9+

1.1+0.4 −0.3 0.5 ± 0.2

2944.0

11+ → 10+ 12+ → 10+

0.9+0.3 −0.2

14.9 ± 11.7 10.2+6.8 −2.9 0.7 ± 1.2 9.7+2.7 −2.4

B(M1) (mW.u.)

163.7 ± 52.1 165.3 ± 66.0 –

Qt (eb)

β2

1.25+0.22 −0.18

0.17+0.03 −0.02

0.87+0.26 −0.13

0.12+0.03 −0.02

0.83 ± 0.11

0.12+0.01 −0.02

90.6 and 167.5 keV transitions in this band. Figs. 2b and 2c provide the spectra gated by the 668.9 and 1356.0 keV γ -rays, respectively. The successive inband transitions with energy 90.6, 167.5, 525.6, 447.1 and 668.9 keV are all found to be predominantly dipole in nature with small negative multipole-mixing ratio δ from the present DCO analysis. The lowest transition in this chain with energy 26.2 keV (not observed in this work) is previously assigned M1 multipolarity [14]. The cross-over transitions are taken to be of stretched E2 character. The RDCO values for the strong 972.6 and 1356.0 keV cross-over transitions are consistent with their stretched E2 nature. These arguments provide firm spin assignments for states up to 2944.0 keV. Tentative spin assignments are made for the states at 3605 and 4450 keV on the basis of systematics of similar bands in neighbouring odd–odd nuclei. Lifetimes have been estimated for three states in this band. These are 1.1+0.4 −0.3 , 0.5 ± 0.2 + (1588.0 keV), 11+ (2256.9 keV) and 12+ (2944.0 keV) states, ps for the 10 and 0.9+0.3 −0.2 respectively. The Doppler-shifted γ -ray spectra used in estimating these lifetimes are shown in Fig. 3. Direct feeding times, as stated in Section 2, were used. Discrete feeding times were estimated in all cases except for the weak 1348 (3605 → 2256.9 keV) and 1506 keV (4450 → 2944.0 keV) transitions. Effective lifetimes of 1.0 and 0.5 ps were assumed for the 3605 and 4450 keV states, respectively, based on the systematics of the level lifetimes in the band and their respective direct feedings. However, the 1348 and 1506 keV feedings have small contributions (< 15%) to the total population of the relevant states and even large errors in these discrete feeding times are not significantly reflected in the lifetime results. The deduced B(E2) value for the 972.6 keV, 10+ → 8+ transition of 20.3+7.7 −5.4 W.u. for the 1588.0 keV state. The corresponds to a quadrupole deformation of 0.17+0.03 −0.02 + + + + 1116.0 keV, 11 →9 and 1356.0 keV, 12 →10 transitions however have B(E2) values smaller by a factor of about two. The spectrum in Fig. 2a also shows several other transitions. Based on their coincidence relationships, five of these transitions with energy 467.4, 795.1, 860.7, 918.8 and 1086.3 keV have been assigned to the level scheme to form a new sequence of states at 1534.1, 2001.6 and 2796.7 keV (band 2 in Fig. 1). Tentative spin assignments are proposed

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Fig. 2. Partial gated spectra for bands 1a and 1b with gates on (a) 90.6 + 167.5 keV, (b) 668.9 keV and (c) 1356.0 keV. The γ -ray lines marked with their energies in keV belong to 80 Br, unless otherwise indicated.

for this sequence as shown in Fig. 1 on the basis of the DCO results. Three other states at 2379, 3212 and 3658 keV are found to decay strongly to the yrast band. However, transitions among these three states were not observed. 3.2. Negative-parity bands (bands 3 and 4) Two new negative-parity sequences have been identified. The first (band 3) is built on the previously reported 85.8 keV 5− isomer [14] and is observed up to 1851.2 keV. The

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Fig. 3. Partial γ -ray spectra showing the Doppler-shifted lines with energies (a) 972.6, (b) 668.9 and (c) 1356.0 keV, gated by lower lying transitions. The upper (lower) spectra correspond to 99◦ (153◦ ) data.

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Fig. 4. Partial gated spectra for bands 3 and 4 with gates on (a) 294.1 + 394.4 keV, (b) 1180.0 keV and (c) 1076.9 keV.

other sequence (band 4), based on the 1130.2 keV level, is populated up to 2915.0 keV. Apart from the 294.1 and 394.4 keV transitions, which were previously reported [14], all the γ -rays assigned to these two sequences are new. The placements of the γ -rays in the two bands are supported by the gated spectra shown in Fig. 4. Spin assignments are based on the present DCO analysis (Table 1) and the previously reported J π = 5− [14] for the 85.8 keV level. Firm spin assignments are proposed for the states of band 3 based on the 688.4 keV cross-over transition which is taken to be E2 in character. Gated by this transition, the RDCO for 1076.9 keV γ -ray was found to be consistent with its stretched E2 nature. Tentative spins, as indicated in Fig. 1, are proposed for band 4.

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4. Discussion 4.1. Positive-parity yrast band (bands 1a and 1b) The positive-parity yrast band in 80 Br is previously reported to be based on the intrinsic configuration (πg9/2 ⊗ νg9/2 ) [14], same as that for the lighter Br isotopes. The bandhead appears to be at 331.1 keV with J π = 5+ and it decays to the 85.8 keV, 5− level via the 245.3 keV E1 transition. Hence, the 5+ bandhead in 80 Br is shortlived (T1/2 = 0.7 ± 0.2 ns [14]) compared to the 4+ isomeric bandhead states for the positive-parity yrast bands in the lighter 74,76,78 Br nuclei. The kinematic and dynamic moments of inertia, J (1) and J (2) , respectively, for the α = 0 (band 1a) and α = 1 (band 1b) signature bands in 80 Br, obtained from a cranking-model analysis of the present data, are plotted in Fig. 5. The plots for J (1) and J (2) for the positiveparity yrast bands in 74,76,78Br [2,5,6] are also included in this figure for comparison. Each graph, including the one for 80 Br, indicates a similar pattern for J (1) . The J (1) values are large at low rotational frequencies and then converge to approximately the rigid body value of ∼ 20 h¯ 2 /MeV for hω ¯ > 0.4 MeV. The dynamic moment of inertia values also lie close to the rigid body value up to fairly high frequencies (h¯ ω ∼ 0.6 MeV) and provide a strong evidence for quasirigid rotation. The tendency for the J (2) values to increase at higher h¯ ω, observed in some odd–odd Br nuclei, indicates the onset of nucleon alignments. In 76 Br, for example, the increase in the J (2) values have been interpreted to correspond to a g9/2 neutron alignment at hω ¯ ∼ 0.82 MeV and a g9/2 proton alignment at hω ¯ ∼ 1.09 MeV [5].

Fig. 5. Kinematic and dynamic moments of inertia for the positive-parity yrast band in 80 Br obtained from cranked-shell model analysis of the present experimental data. Calculations were done using K = 4. The filled circles correspond to α = 0 and open circles to α = 1 band. The previous results for 74,76,78 Br are included for comparison.

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The rise in the J (2) value at hω ¯ ∼ 0.75 MeV in 78 Br has also been tentatively attributed to a neutron alignment [6]. A similar neutron alignment may be responsible for the increase in the J (2) value at h¯ ω ∼ 0.7 MeV (Fig. 5) observed in the present work in 80 Br, although a knowledge of the band up to higher spins is necessary for an unambiguous interpretation. The B(E2) values inferred from the measured lifetimes (Table 1) show that the positiveparity yrast band in 80 Br is moderately deformed compared to the lighter Br nuclei [3,4]. A similar trend of decreasing quadrupole deformations with increase in neutron number has also been reported in the doubly-odd Rb isotopes [8]. The three N = 45 isotones 80 Br, 82 Rb and 84 Y all appear to have a similar quadrupole deformation of 0.15–0.20. The excitation energy of the band-head in the Br isotopes increases gradually from 13.8 keV for 74 Br to 331.1 keV for 80 Br, possibly due to the decreasing deformation. However, as noted in Section 3.1, the B(E2) values in 80 Br appear to decrease with spin within the band. A similar behaviour has been reported in 76 Br [4] where the B(E2) values decrease even before the onset of the first neutron alignment which occurs at h¯ ω = 0.82 MeV. The Fig. 6 shows a plot of [E(J ) − E(J − 1)]/2J vs. J for bands 1a and 1b. A large signature splitting is observed for states with J π > 8+ . At low spins, the normalised energy differences corresponding to the even-spin states (filled circles) lie lower compared to the odd-spin states (open circles). There appears to be a reversal of this pattern at high spins with the J π = (13+ ) state lying lower compared to the 12+ and (14+ ) states. This reversal in the phase of the staggering (signature inversion) occurs at 12 h¯ in 80 Br. The signature inversion has been predicted from a two noninteracting-quasi-particle-plus-rotor model calculations [11] to occur at 9 h¯ , the maximum spin that can be obtained from the (πg9/2 ⊗ νg9/2 ) intrinsic configuration and reflects the transition from single-particle excitations at low spins to more collective motion at higher spins. Experimentally, the inversion has been observed at 9 h¯ in 74 Br [1], 11 h¯ in 76,78 Br [6] and at 12 h¯ in 80 Br

Fig. 6. Signature splitting in the positive-parity yrast band in 80 Br.

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from the present work. Similar phase reversals have also been observed at 9 h¯ in 76,78 Rb, 10 h¯ in 80 Rb and at 11 h¯ in 82 Rb [8]. Döring et al. [8] have recently reported that the shift of the inversion point to higher spins as N increases in the odd–odd Rb chain seems to be correlated with the quadrupole deformation, which decreases from β2 ≈ 0.38 for 76,78 Rb to ≈ 0.2 for 82 Rb. In the case of the odd–odd Br isotopes also, the inversion point shifts from 9 h¯ in 74 Br to 12 h¯ in 80 Br while the average nuclear quadrupole deformation decreases from 0.37 for 74 Br [3] to 0.15 for 80 Br. It may be noted however, that the residual protonneutron interaction has also been shown to be important in the A ∼ 120 mass region for reproducing the observed signature inversion [15]. Apart from the particle–rotor approach, cranked-shell-model calculations have also been successful in reproducing both the magnitude of the signature splitting and the frequency at which the inversion occurs in several odd–odd nuclei in this mass region [5,6]. These calculations predict a triaxial shape for the nuclei. Similar calculations have been performed for 80 Br in this work. A modified harmonic oscillator potential was used [16]. The calculated quasiparticle Routhians for the deformation (β2 , γ ) = (0.22, +26◦) are shown in Figs. 7a and 7b. The labels in the figures follow the convention of identifying the lowest unique-parity Routhians for proton (neutron) as a (A) and b (B) for α = +1/2 and α = −1/2, respectively. The deformation parameters used in calculating the Routhians are found to reproduce the experimental kinematic moment of inertia reasonably well for both the signature bands (Fig. 7c). The alignment of the first pair of g9/2 neutrons and protons, predicted to occur at h¯ ω ∼ 0.58 MeV and ∼ 0.40 MeV, respectively, from the quasiparticle Routhians, are not observed experimentally due to the Pauli blocking by the g9/2 valence nucleon. The second g9/2 neutron alignment is predicted to occur at h¯ ω ∼ 0.7 MeV. The observed upbend in the experimental J (2) plot at the same frequency may therefore be attributed to the second g9/2 neutron alignment. Calculated and experimental signature splitting is shown in Fig. 7d. The splitting and the inversion are both well reproduced for aA–aB. These calculations suggest a probable triaxial shape for the positive-parity yrast band in 80 Br although it may be noted, as pointed out in Ref. [6], that signature inversion observed at relatively low spins in odd–odd nuclei may not be sufficient evidence for triaxiality.

4.2. Negative-parity bands (bands 3 and 4)

The nature of the negative-parity sequences is not well understood. The negative-parity band 3 is built upon the 85.8 keV, 5− state. In a recent deformed Hartree–Fock calculation [17] for 80 Br, this state is predicted to have the configuration πg ⊗ ν(pf ) with K π = 1− . This configuration is similar to those for the negative-parity bands in 76 Br. Band 4, observed up to 2915.0 keV, decays strongly to the states of band 3, suggesting overlap in the configurations of the two sequences.

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Fig. 7. Results of CSM calculations for 80 Br. The symbols a (A) and b (B) correspond to the Routhians for proton (neutron) for α = +1/2 and α = −1/2 bands, respectively. Plots (a) and (b) show the calculated quasiparticle Routhians for deformations (β2 , γ ) = (0.22, 26◦ ). Solid lines correspond to Routhians with (π, α) = (+, + 12 ), dotted lines to (+, − 12 ), dashed lines to (−, + 12 ) and dot-dashed lines to (−, − 12 ). Plot (c) shows the calculated and experimental kinematic moment of inertia for the two signature bands. Filled circles (experimental data) and solid line (calculation) correspond to the α = 0 band and open circles (experimental data) and the dotted line (calculation) to the α = 1 band. Plot (d) shows the experimental and calculated signature splitting.

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5. Conclusion The properties of the positive-parity yrast band in 80 Br has been studied in the 76 Ge(7 Li, 3nγ ) reaction at 32 MeV. The band has been extended up to 4450 keV with J π = (14+ ). Firm spin assignments were made for states up to 12+ from DCO studies. Lifetime measurements for three states show that the band is moderately deformed compared to similar sequences in the lighter Br nuclei. The band is based on the intrinsic configuration (πg9/2 ⊗ νg9/2 ). The kinematic and the dynamic moments of inertia remain almost constant at ∼ 20 h¯ 2 /MeV which is close to the rigid body value, up to a rotational frequency of 0.7 MeV. An upbend in the J (2) value at this frequency is probably due to a νg9/2 alignment. The band shows a large signature splitting above spin 8+ and a signature inversion at 12 h. ¯ The shift of the inversion point to a higher spin for 80 Br, relative to the lighter Br isotopes, may be attributed to the decrease in quadrupole deformation, as in the case of the odd–odd Rb nuclei. CSM calculations performed with (β2 , γ ) = (0.22, +26◦) show a fair agreement between experiment and theory for both signature splitting and the crossing frequency. In addition, another sequence of positive-parity states, with tentative spin assignments, have been identified. Two new negative-parity bands have also been observed up to 1851.2 and 2915.0 keV.

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