High spin band structure of 85 - APS Link Manager - American ...

PHYSICAL REVIEW C 90, 024315 (2014)

High spin band structure of 85 38 Sr47 S. Kumar, Naveen Kumar, S. Mandal, and S. C. Pancholi* Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India

P. C. Srivastava† and A. K. Jain Department of Physics, Indian Institute of Technology, Roorkee 247667, India

R. Palit, S. Saha, J. Sethi, B. S. Naidu, R. Donthi, and P. K. Joshi Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai 400005, India

T. Trivedi Department of Pure and Applied Physics, Guru Ghasidas University, Bilaspur, Chhattisgarh 495009, India

S. Muralithar, R. P. Singh, R. Kumar, A. Dhal,‡ and R. K. Bhowmik Inter-University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi 110067, India (Received 8 April 2014; revised manuscript received 23 June 2014; published 20 August 2014) High spin states in the 85 Sr nucleus were populated in the reaction 76 Ge(13 C,4n) at a beam energy of 45 MeV. The γ -γ and γ -γ -γ coincidence measurements have been utilized to establish the level scheme of 85 Sr up to I π = 35/2− . Nearly 50 new γ rays and about 25 new levels were identified and most of the previously known levels confirmed. The spin-parity assignment of the levels was made by using the directional correlations of the oriented nuclei ratios and polarization asymmetry measurements. The shell-model calculations have been performed by using two recent interactions, JUN45 and jj44b, for a detailed comparison between theoretical results and the experimental data obtained in the present work. The shell-model results are in good agreements with the experimental data and are able to explain the various features such as the odd-even staggering well. Tilted axis cranking calculations were also performed to understand the magnetic rotation (MR) phenomenon at higher spins. One of the positive-parity I = 1 bands has been assigned a three-quasiparticle (3qp) configuration, which appears to behave like a MR band. A negative-parity band populated up to I π = 35/2− was also assigned a 3qp configuration at low spin and a five-quasiparticle configuration at high spin; however, it does not exhibit the expected MR features, in contrast to a similar band in the 83 Kr nucleus. DOI: 10.1103/PhysRevC.90.024315

PACS number(s): 21.10.Re, 21.60.Ev, 23.20.Lv, 27.50.+e

I. INTRODUCTION

The phenomenon of high-spin magnetic rotation (MR) is well established in the mass regions A ≈ 60, 80, 110, 130, and 190 [1,2]. In 1995, Tabor and Döring [3] listed a group of negative-parity I = 1 bands in the mass A = 80 region, whose properties resembled the I = 1 “shears bands.” The first experimental confirmation for a MR band in the A = 80 mass region came in 1999, when two odd-odd isotopes of Rb were shown to display the characteristic feature of decreasing B(M1) values with increasing spin for one band each in 82,84 Rb [4,5]. These studies have been extended further by observing the MR phenomenon in 79 Br [6]. Later, the possibility of MR bands was also reported in odd-even 83,85 Rb [7] and confirmed [8]. In 2005, the hybrid version of the tilted axis cranking (TAC) model [9] was used to

* Present address: Inter-University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi-110067, India. † Formerly at Instituto de Ciencias Nucleares, UNAM, 04510 México, D.F., Mexico. ‡ Present address: Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 76100, Rehovot, Israel.

0556-2813/2014/90(2)/024315(14)

establish the MR phenomenon in the negative-parity I = 1 bands based on oblate shapes in odd-A 79,81,83 Kr isotopes [10]. These calculations pointed out that 83 Kr was probably the best candidate of MR among the three nuclei and probably the best example of a MR band in the A ≈ 80 region. The observed MR bands and their features are tabulated in the updated and the old version of the table of MR bands [1]. In the present paper, we focus upon the N = 47 odd-A nucleus 85 Sr. Other N = 47 isotones such as 83 Kr, 87 Zr, and 89 Mo have been experimentally studied in the past [11–16], and their high spin structure is known [11,17,18]. Since these nuclei have only three neutron holes in the N = 50 closed shell, a spherical shell structure is expected to dominate with little or no evidence of collectivity [13,17,19]. Under these conditions, one would expect a phenomenon such as MR to dominate. Indeed, as stated above, 83 Kr has been shown to be a good example of a MR band in the A = 80 mass region [10]. The other interesting phenomena in this mass region include superdeformation [20,21], loss of collectivity [22,23], band termination [24], chiral rotation [25], and shape-related effects [3,26,27]. Excited states in the 85 Sr nucleus were previously investigated via the 82,84 Kr(α,xn) reaction [28] and the 76 Ge(12 C,3n) reaction [29,30]. Some lifetimes and electromagnetic

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©2014 American Physical Society

S. KUMAR et al.


TABLE I. Level excitation energy Ex , initial and final spin and parity of the levels, Jiπ and Jfπ , measured Eγ , relative γ -ray intensity, RDCO , polarization asymmetry () ratios, and assigned multipolarity for γ transitions in 85 Sr (Mult.). Ex 1111.6(3) 2400.1(3) 3080.0(4) 4845.0(6) 231.2(3) 1221.1(4) 1261.8(4) 1658.1(3)

1850.3(3) 2525.6(4) 2840.1(4)

3071.6(4)

3384.0(4)

3511.6(4)

3965.8(5) 4491.5(5) 5091.2(6) 5749.7(8) 6360.8(9) 4779.6(5) 4969.0(5)

5181.0(5)

5422.9(5)

6007.9(6) 6466.7(8) 5036.5(5) 5703.5(7) 6203.5(9) 2102.1(3)

Jiπ → Jfπ

Eγ

Iγ

RDCO

Mult.

13/2+ → 9/2+ 17/2+ → 13/2+ 21/2+ → 17/2+ 25/2+ → 21/2+ 7/2+ → 9/2+ 11/2+ → 9/2+ 9/2+ → 7/2+ 9/2+ → 9/2+ 11/2+ → 9/2+ 11/2+ → 7/2+ 11/2+ → 9/2+ 13/2+ → 13/2+ 13/2+ → 9/2+ 15/2+ → 11/2+ 15/2+ → 13/2+ 17/2+ → 17/2+ 17/2+ → 13/2+ 17/2+ → 13/2+ 17/2+ → 17/2+ 17/2+ → 15/2+ 17/2+ → 17/2+ 17/2+ → 13/2+ 19/2+ → 17/2+ 19/2+ → 17/2+ 19/2+ → 15/2+ 19/2+ → 17/2+ 21/2+ → 19/2+ 21/2+ → 21/2+ 21/2+ → 17/2+ 23/2+ → 21/2+ 25/2+ → 23/2+ 27/2+ → 25/2+ 29/2+ → 27/2+ (31/2+ ) → 29/2+ (21/2+ ) → 21/2+ (21/2+ ) → 21/2+ 23/2(+) → (21/2+ ) 23/2(+) → 23/2+ 23/2(+) → 21/2+ 23/2(+) → 21/2+ 25/2+ → (23/2+ ) 25/2+ → 25/2+ 25/2+ → 25/2+ 25/2+ → 23/2+ 25/2+ → 21/2+ 27/2+ → 25/2+ 27/2+ → 25/2+ 27/2+ → 25/2+ 29/2+ → 27/2+ 31/2(+) → 29/2+ 25/2+ → 23/2+ 27/2(+) → 25/2+ (29/2+ ) → 27/2(+) 13/2− → 11/2+ 13/2− → 11/2+ 13/2− → 13/2+

1111.6(3) 1288.8(3) 679.7(3) 1765.0(5) 231.2(3) 1221.0(5) 1030.6(7) 1261.8(6) 396.2(5) 1426.8(3) 1658.0(3) 738.8(4) 1850.4(5) 1304.6(5) 1414.0(5) 440.0 (3) 989.6 (5) 1728.4(5) 231.6 (7) 546.0 (5) 671.6(5) 1221.2(5) 312.3(3) 543.9(5) 858.3(5) 983.9(3) 127.7(3) 431.6 (3) 1111.9 (5) 454.2(3) 525.7(3) 599.7(5) 658.5(5) 611.1(5) 1268.4(5) 1698.9(5) 189.2(5) 1003.2(5) 1457.4(5) 1889.0(5) 212.0(4) 336.0(5) 689.5(5) 1215.2(5) 1669.4(5) 241.9(3) 386.4(5) 931.4(3) 585.0(3) 458.8(5) 1070.7(3) 667.0(5) 500.0(5) 444.0(3) 881.0(5) 990.4(3)

100.0(8) 70.4(11) 9.82(23) 1.8(3) 7.8(6) 1.9(3) 0.81(22) 0.66(23) 0.62(18) 6.9(7) 10.0(4) 5.9(3) 4.2(4) 1.62(18) 2.36(18) 3.20(21) 1.16(23) 4.8(3) 0.40(14) 2.1(5) 5.8(4) 2.22(17) 4.3(5) 3.6(4) 0.62(23) 4.5(5) 5.4(3) 3.1(4) 30.1(21) 26.1(14) 15.4(9) 9.6(9) 1.67(23) 0.35(9) 0.46(14) 0.41(12) 0.34(11) 0.20(10) 0.83(21) 1.4(3) 1.14(9) 0.73(19) 0.20(10) 3.6(5) 0.26(8) 3.7(4) 0.77(18) 1.88(16) 4.4(3) 3.6(5) 4.0(3) 1.4(3) 1.3(3) 14.0(7) 1.0(2) 20.6(6)

1.90(13)b 0.96(7)a 1.17(8)a 0.87(15)a 2.17(8)b 0.64(16)b 1.07(8)b

0.081(6) 0.078(6) 0.162(13) 0.06(4) −0.049(22) −0.010(17) −0.09(5)

E2 E2 E2 E2 M1 M1

0.55(6)f 2.2(3)b 0.48(5)b 1.25(9)a

−0.037(29) 0.090(12) 0.009(7) 0.074(16)

M1 + E2 E2 M1 + E2 E2

0.54(11)d 1.04(8)c

−0.058(16) 0.099(26)

M1 E2

0.93(11)a

0.049(20)

E2

0.78(7)d 1.02(9)c 1.08(15)d 0.56(5)a 0.68(12)c 2.4(6)d 0.27(3)c 1.09(18)a 0.84(7)e 1.01(7)a 0.49(3)a 0.48(3)a 0.97(11)d 0.86(7)d

0.106(21) −0.028(22) 0.011(19) −0.078(22) −0.014(12)

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0.48(17)a 0.71(10)e 0.78(11)e

−0.060(15)

E2 + M1 M1(+E2) (E2) M1 + E2 M1 + E2 Q M1 + E2

0.160(21) 0.072(7) −0.044(5) −0.039(7) −0.033(9) −0.046(14)

E2 E2 M1 M1 M1 M1

0.047(24)

D+Q D+Q E2 + M1

0.41(7)d

−0.010(16)

M1

1.1(4)d 1.01(18)d 0.57(9)d 0.58(6)d 0.64(6)d 0.96(12)d 0.60(14)d

−0.035(21)

M1 D M1 + E2 M1 D M1 D

1.08(7)b 1.04(21)b 1.97(14)b

0.099(3) 0.014(22) −0.075(5)

−0.193(35) −0.030(21) −0.013(9)

E1 E1 E1 (J = 0)

HIGH SPIN BAND STRUCTURE OF 85 38 Sr47

PHYSICAL REVIEW C 90, 024315 (2014) TABLE I. (Continued.)

Ex 2367.0(4) 2661.0(4) 2861.1(4) 3027.8(4)

3227.2(4) 3396.5(4) 4361.3(5) 4793.2(5)

5006.8(7) 5699.4(5) 5939.4(5) 6626.2(6) 7221.8(8) 7554.9(8)

Jiπ → Jfπ 17/2− 15/2− 15/2− 17/2− 17/2− 19/2− 19/2− 19/2− 21/2− 21/2− 23/2− 23/2− 25/2− 25/2− 25/2− (25/2− ) 27/2− 27/2− 29/2− 29/2− 31/2− 31/2− 33/2− 35/2−

→ → → → → → → → → → → → → → → → → → → → → → → →

13/2− 13/2− 13/2+ 15/2− 17/2− 17/2− 17/2+ 17/2− 17/2− 19/2− 21/2− 19/2− 23/2− 21/2− 21/2− 21/2− 25/2− 23/2− 27/2− 25/2− 29/2− 27/2− 31/2− 33/2−

Eγ

Iγ

RDCO

264.9(3) 558.2(5) 810.8(3) 200.0(2) 494.2(3) 166.6(3) 627.8(3) 660.4(5) 860.2(3) 368.5(3) 964.6(3) 1334.0(5) 432.0(5) 1396.6(3) 1566.0(5) 1779.6(5) 906.3(5) 1338.0(5) 240.0(5) 1146.3(3) 686.8(3) 926.8(5) 595.6(5) 333.1(3)

33.7(9) 1.52(17) 1.56(12) 1.81(23) 3.8(4) 3.5(3) 10.5(9) 14.8(6) 8.3(5) 27.7(9) 6.3(6) 2.2(6) 3.0(3) 12.7(8) 0.52(23) 0.78(19) 2.2(3) 2.0(7) 2.1(5) 8.8(4) 4.3(6) 0.50(17) 4.1(7) 2.6(3)

1.49(8)a 0.69(17)b

0.179(17)

Mult. E2 D

0.046(20) 1.44(15)b 0.99(12)b 0.97(12)a 0.51(4)a 0.32(12)a 0.94(8)a 0.51(4)a 0.85(6)b 0.66(11)f 0.91(8)b 2.16(18)b

0.089(12) −0.023(6) 0.090(9) −0.032(6) −0.037(8) 0.041(38) −0.060(20) 0.043(11)

D+Q E2 + M1 Q E1 M1 + E2 E2 M1 M1 + E2 E2 M1 + E2 E2

1.11(12)b 1.1(3)b 1.34(15)b 1.81(14)b 0.84(6)b

0.189(20) −0.084(13) 0.015(12) −0.088(56) 0.087(12) −0.054(8)

(E2) M1 + E2 E2 M1 + E2 E2 M1 + E2

1.02(7)b 1.22(11)b

−0.084(23) −0.066(17)

M1 + E2 M1 + E2

0.171(13)

a

Gate on 1111.6-keV quadrupole (Q) transition. Gate on 368.5-keV dipole (D) Transition c Gate on 1288.8-keV quadrupole transition. d Gate on 454.2-keV dipole transition. e Gate on 679.7-keV quadrupole transition. f Gate on 264.9 keV. b

transition probabilities were measured by Arnell et al. [28], Zhovliev et al. [30], Bucurescu et al. [31], Ekström et al. [32], and Lühmann et al. [33] by using the recoil distance method and the Doppler shift attenuation method (DSAM). The Nuclear Data Sheets for A = 85 [34,35] summarize the available information on the low spin states in the nucleus 85 Sr. However, the overall available information on 85 Sr is scarce and incomplete. A knowledge of high spin data on this nucleus will help in developing a systematic understanding of the existence of MR bands in N = 47 isotones. Therefore, the high spin states in 85 Sr were populated by the 76 Ge(13 C,4n) fusion-evaporation reaction at beam energies of the 52 and 45 MeV and reinvestigated by means of more comprehensive γ -γ and γ -γ -γ coincidence measurements. The results of the experiment performed at a beam energy of 52 MeV are reported in Ref. [36]. We report in this paper the results of the experiment performed at a beam energy of 45 MeV and compare these with the results of shell-model calculations based on the new effective interactions (JUN45 and jj44b) for the f5/2 pg9/2 model space. The hybrid version of the TAC model [9] has also been used to interpret the I = 1 band structures in 85 Sr. In analogy to 83 Kr [10], we expected a MR feature also in 85 Sr for a negative-parity band based on −1 1 ⊗ (p1/2 /f5/2 )1 ] ⊗ νg9/2 configuration. However, to the π [g9/2

our surprise, we have not found any evidence of MR in this configuration. II. EXPERIMENTAL METHODS

High spin states in 85 Sr were populated by the reaction Ge(13 C,4n)85 Sr using a 13 C beam of 45 MeV from the Pelletron accelerator at the Tata Institute of Fundamental Research (TIFR), Mumbai. The 76 Ge target had a thickness of 850 μg/cm2 with 7.6 mg/cm2 181 Ta backing. The de-exciting γ rays were detected using the Indian National Gamma Array (INGA), which at the time of the experiment consisted of 15 Compton-suppressed clover high-purity germanium detectors. The clover detectors were arranged in a spherical geometry with 3, 2, 2, 4, 2, and 2 clovers placed at 157◦ , 140◦ , 115◦ , 90◦ , 65◦ , and 40◦ with respect to the beam direction, respectively. The target-to-detector distance was 25 cm. The data were collected in the list mode using a PCI-PXI digital data acquisition (DDAQ) system using a Pixie-16 Module by XIA LLC Software [37,38]. This system has a provision for the digitization of 96 channels of 24 clover detectors with 100-MHz sampling rates. Time-stamped data were collected when at least two clovers in Compton-suppressed mode fired in coincidence. A time window of 200 ns was set for this coincidence between the fast triggers of individual 76

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channels, and the coincidence trigger was kept open for 4 μs. A total of about 2.9 × 109 twofold and higher fold coincidence events were recorded. The data were sorted using the in-house program MARCOS (Multi-pARameter timestamped-based COincidence Search) and analyzed by using DAMM software [39] for asymmetric matrices to generate the gated spectrum. The coincidence events were sorted into twodimensional (γ -γ ) matrices and three-dimensional (γ -γ -γ ) coincidence cubes with a 200-ns coincidence time window and were analyzed with the RADWARE software package [40]. An asymmetric matrix was created by the events detected in the clover detectors at 157◦ on one axis and 90◦ on the other axis, to obtain information on multipolarities of γ -ray transitions from the directional correlations of the oriented nuclei (DCO) ratios [41]. The following relation was used for the calculation of the DCO ratios: intensity of γ1 observed at 157◦ gated on γ2 at 90◦ RDCO = . intensity of γ1 observed at 90◦ gated on γ2 at 157◦ (1) The DCO ratios for a particular γ -ray transition were obtained by setting gates on stretched transitions of known multipolarity in the asymmetric matrix. When gating on stretched quadrupole transitions, the expected RDCO value is 1.0 for the stretched quadrupole transitions and 0.52 for the pure stretched dipole transitions. If the gate is set on a pure stretched dipole transition, then the expected RDCO value is 1.92 for the stretched quadrupole transitions and 1.0 for the pure stretched dipole transitions. 1000

The electromagnetic character (electric or magnetic) of transitions was determined from a measurement of the linear polarization of the γ -ray transitions using the integrated polarization direction correlation method [42–44] for the clovers placed at 90◦ angle. In this method the experimental asymmetry of Compton-scattered polarized photons is defined as =

a(Eγ )N⊥ − N , a(Eγ )N⊥ + N

(2)

where N⊥ and N denote the number of coincidence counts between the segments of the clover detector in directions perpendicular and parallel to the emission plane, respectively. a(Eγ ) denotes the correction due to the asymmetry in the response of the perpendicular and parallel clover segments. The correction was obtained from unpolarized γ rays using a 152 Eu source placed at the target position under the same experimental conditions. It is defined as a(Eγ ) =

N (unpolarized) . N⊥ (unpolarized)

(3)

The experimentally determined value of a(Eγ ) was 1.023(3) in the γ -ray energy range of 300 to 2000 keV [38]. The results of the linear polarization asymmetry are given in Table I and the figure given in the Supplemental Material [45]. Figure 1 shows the N⊥ and N counts for the 627.8- and 1111.6-keV γ rays, which have electric multipole character, and the 454.2 and 525.7-keV γ rays, which have magnetic multipole character. In the present geometry, = 0.078(6) [with RDCO = 0.97(6), gated on the stretched quadrupole 1600 M

(b)

800

E

(a)

1200

600 800

Counts

400 400

200

4000

610

620

630

430 650 1000

640 E

(c)

800

3000

440

450

460

470

M

(d)

600 2000 400 1000

200

0

0 1090

1100

1110

1120

510

520

530

540

550

Energy(keV) FIG. 1. (Color online) Spectra showing the N⊥ (dashed red histogram) and N (black histogram) counts for the 627.8-, 454.2-, 1111.6-, and 525.7-keV γ transitions labeled as (a), (b), (c), and (d), respectively. The letters E and M represent electric and magnetic multipole character. The N⊥ (dashed red histogram) and N (black histogram) denote the number of coincidence counts between the segments of the clover detector in directions perpendicular and parallel to the emission plane, respectively 024315-4



85 38

6204 29/2

500.0 5704 27/2 (

)

5036

25/2

1070.7

686.8 926.8

29/2

5939

23/2

27/2

Band 1 336.0

4845

4793

25/2

1765.0

23/2

858.3 17/2

1111.9 983.9

440.0

15/2

3080

17/2

21/2

546.0

671.6

989.6

627.8 17/2

2400

2661

660.4

2367

1221.2 1304.6

1850

881.0

738.8 11/2

1221

1112

493.2

2861 200.0 558.2

17/2 15/2

21/2

860.2 17/2

13/2

444.0

1288.8

1414.0

3227 19/2 166.6

264.9

2102

810.8 13/2

21/2 368.5

3028

679.7

2526

1779.6

1566.0

964.6 1334.0 3397

431.6

3072 312.3 231.6

(25/2 )

432.0

1396.6

1889.0

1698.9

5007

25/2

4361

1457.4

543.9

1728.4

27/2

1338.0 1146.3 906.3

21/2 127.7 19/2

2840

29/2 240.0

5699

1268.4

454.2 3512 3384

31/2

1669.4

525.7 3966

595.6

5181 241.9 25/2 4969 212.0 23/2 ( ) 189.2 689.5 (21/2 ) 1003.2 1215.2

599.7

33/2

6626

386.4

25/2 931.4

4492

7222

585.0

667.0 27/2

35/2 333.1

458.8

5423

658.5 5091

(29/2 ) 6008

5750

7555

31/2 ( )

6467

(31/2 ) 611.1

Sr47

Band 3

Band 2 6361

Band 4

990.4

11/2

1658 1262

396.2 9/2

13/2 1426.8

1850.4 1221.0

1111.6

1658.0 1261.8

1030.6 7/2

231 0

9/2

231.2

FIG. 2. The partial level scheme of 85 Sr obtained in the present work.

transition] is obtained for the 1288.8-keV E2 stretched transition, = −0.03(2) [with RDCO = 0.50(2), gated on the stretched quadrupole transition] for 454.2- and 525.7-keV M1 stretched transitions, = 0.089(12) [with RDCO = 0.51(4), gated on the stretched quadrupole transition] for the 627.8-keV E1 stretched transition, = −0.075(5) [with RDCO = 1.97(14), gated on the stretched dipole transition] for the 990.4-keV E1 (J = 0) unstretched transition, and = 0.17(2) [with RDCO = 0.99(12), gated on the stretched quadrupole transition] for the 494.2-keV E2 (J = 0) unstretched transition.

polarization asymmetries. In earlier work [31], the highest known level was 3396.5 keV (I π = 21/2− ). The spin and parity of the levels located below I π = 21/2− , therefore, have been verified in the present work and found to be in agreement with those from the previous works [28–35]. The high spin part of the 85 Sr level scheme, as shown in Fig. 2, consists of four sequences of γ rays, labeled as bands 1 to 4. Some typical examples of coincidence γ -ray spectra are presented in Figs. 3–7. The cascade of 1111.6–1288.8–679.7– 1765.0 keV γ rays belongs to band 1. The 1765.0-keV γ ray of this band has been observed in the present work, as shown in Fig. 3(b) and Fig. 4(b).

III. MEASUREMENTS AND RESULTS

The level scheme of 85 Sr has been extended up to 7.5 MeV excitation energy and spin I π = 35/2− as shown in Fig. 2. The experimentally measured γ -ray energies, intensities, RDCO values, polarization asymmetry (), and multipolarities assigned in the present work are listed in Table I. A. γ -γ and γ -γ -γ coincidence measurement

In the present work, the new γ rays were placed in the nucleus 85 Sr on the basis of γ -γ and γ -γ -γ coincidences utilizing previously known γ -ray transitions. Spins and parities of the levels were assigned on the basis of the multipolarity of γ -ray transitions obtained from the value of RDCO and

B. Band 2 and band 3

The positive-parity high spin states grouped into bands 2 and 3 are shown in Fig. 2. All the levels up to a maximum spin of I π = (31/2+ ) have been established in the present work. Previously, the 127.7-, 312.3-, 454.2-, 525.7- and 599.7-keV γ rays were known, but their placements have been modified in the present work. The spectra in coincidence with both 127.7- and 454.2-keV γ -ray transitions [see Fig. 3(a)] show a 1728.4-keV γ ray which is not seen in coincidence with either 1111.6- or 1288.8-keV γ -ray transitions [Fig. 3(b)]. Thus, the new 1728.4-keV γ ray is in coincidence with the 1111.6-, 454.2-, and 525.7-keV γ rays but in anticoincidence

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525.7

0

400

1000

679.7

454.2

368.5

127.7

500

241.9

600

800

600

1200

1400

1600

1800

1600

1800

2000

(b)

1111.9

400

525.7 599.7 627.8

200

1850.4

1414.0

1304.6

1728.4

1288.8

983.9

*

1070.7

858.3

*

100

Counts

386.4 440.0 458.8 500.0

200

931.4

241.9

300

543.9 585.0 599.7 611.1 658.5 671.6 689.5 738.8

400

(a)

1215.2 1221.2

500

1111.6, 1111.9

312.3

600

*

1889.0

1765.0

1396.6

1215.2

1146.3

1070.7

906.3 931.4 964.6 983.9

* *

658.5

585.0

100

440.0

200

312.3 336.0

212.0

300

0 200

400

800

600

1000

1200

1400

2000

Energy (keV)

1111.6

200

400

600

800

1000

1850.4

1414.0

1728.4

1800

1600

1288.8

1400

2000

(b)

* *

1889.0

*

1765.0

599.7

454.2

50

1288.8

1200

431.6 336.0

100

241.9

150

1304.6

1215.2

**

200

212.0

Counts

0

1070.7

**

931.4 *

2000

(a)

1221.2

671.6 738.8 689.5

4000

599.7

6000

127.7

8000

231.6 241.9

10000

454.2 525.7 546.0

FIG. 3. Typical γ -γ -γ coincidence spectra showing the γ -ray peaks of band 1, band 2, and band 3. The spectrum in (a) is taken in coincidence with the 127.7- and 454.2-keV cascade in band 2. The spectrum in (b) is taken in coincidence with 1111.6- and 1288.8-keV intense ground-state cascades. The contaminant transitions are marked with an asterisk (*).

0 200

400

600

800

1000

1200

1400

1600

1800

2000

Energy(keV) FIG. 4. The γ -ray spectra in coincidence with the 312.3-keV transition (a) and in coincidence with both the 1111.6- and 679.7-keV transitions (b) showing γ rays connecting bands 1 and 2. The contaminant transitions are marked with an asterisk (*). 024315-6


1850.4 1889.0

1288.8

1215.2 1221.2

1070.7

931.4

738.8

671.6

983.9

679.7

212.0 312.3 336.0 386.4 440.0 458.8 525.7

*

1728.4 1765.0

Counts

2000

189.2

127.7

454.2

6000

(a)

1111.6, 1111.9

241.9

8000

4000


0 200

400

800

600

1000

1200

1400

1600

1800

2000

1800

2000

100

1288.8

458.8

585.0

50

1111.6

679.7

212.0

(b)

0 200

400

800

600

1000

1200

1400

1600

Energy (keV)

264.9

FIG. 5. (a) The γ -ray spectra in coincidence with the 585.0-keV γ -ray and illustrating the γ rays of band 3 and connecting bands 3 and 2. (b) The γ -ray spectra in coincidence with both 241.9- and 1889.0-keV γ -rays transitions and representing the γ rays connecting bands 3 and 1.

(a)

444.0

300

400

500

600

700

1100

1200

1426.8

1396.6

906.3

1334.0 1338.0

1261.8

1221.0

1288.8

1146.3 1030.6

1000

1000

(b)

1.0

0

900

1658.0

2.0

800

964.6

990.4

200 1111.6

100

881.0

860.2

0

810.8

738.8

686.8

627.8

558.2

595.6

494.2

432.0

396.2

333.1

5

Counts (10 )

1.0

240.0

200.0

166.6

2.0

368.5

231.2

3.0

660.4

4.0

1300

1400

1500

1600

1700

1800

1900

2000

Energy (keV) FIG. 6. The sum-gated γ -ray spectrum in coincidence with 264.9-, 368.5-, and 444.0-keV γ -ray transitions illustrating the γ rays of band 4. The lower and the higher energy parts of the spectrum are shown in (a) and (b), respectively. 024315-7

S. KUMAR et al.


368.5

150

1658.0

1426.8

1288.8

1111.6

990.4

595.6 627.8 660.4 686.8

444.0 494.2

333.1

264.9

0 400

400

600

800

1000 990.4

1600

1800

2000

(b)

1779.6

1658.0

1566.0

1426.8

881.0

100

1221.0

200

1400

231.2

300

1200 1111.6

200

444.0

Counts

166.6 200.0 231.2

100

50

(a)

0 200

400

600

800

1000

1200

1400

1600

1800

2000

Energy(keV) FIG. 7. The γ -ray spectra in coincidence with both 1146.3- and 1396.6-keV γ -ray transitions (a) and in coincidence with both 860.2- and 264.9-keV γ -ray transitions (b) showing γ -ray transitions of negative-parity states.

with the 1288.8-keV γ ray [Fig. 3(b)]. On the basis of this argument, we have established the 2840.1-keV level, which decays to the 1111.6-keV level by the 1728.4-keV γ ray and to the 2400.1-keV level by the 440.0-keV γ ray. Figure 3(a) also shows the 738.8- and 1221.2-keV γ rays, which are again in anticoincidence with the 1288.8-keV γ ray, which confirms the existence of the 1850.3- and 3071.6-keV levels. The placement is further supported by the observation of 1850.4-, 546.0-, and 671.6-keV γ rays. Similarly, the 543.3-, 312.3-, 858.3-, and 983.9-keV γ rays [shown in Fig. 3(a)] help us to establish the 3384.0-keV level. The placing of 2525.8-keV levels was confirmed with two depopulating transitions of 1304.3 and 1414.0 keV. The spectrum gated on the 312.3-keV transition [see Fig. 4(a)] shows all γ -ray transitions for levels placed below the 3071.6-keV level. The levels of 3511.6, 3965.8, 4491.5, 5091.2, 5749.7, and 6360.8 keV were placed above the 3384.0-keV level, with the emission of 127.7-, 454.2-, 525.7-, 599.7-, 658.5-, and 611.1-keV γ rays, respectively. The cascade of these γ rays constitutes band 2. The level 3511.6 keV also feeds the 3080.0-keV level by the 431.6-keV γ ray, as shown in Fig. 4(b). Figure 4 also helps to confirm the placement of 1111.9and 983.9-keV transitions, as these γ rays are not seen in coincidence with the gate of 312.3 keV [see Fig. 4(a)] and both 679.7 and 1111.6 keV [see Fig. 4(b)]. On the other hand, these γ rays are clearly in coincidence with both 1111.6 and 1288.8 keV, as shown in Fig. 3(b).

The gate of the 585.0-keV γ ray [Fig. 5(a)] exhibits γ rays of 127.7, 189.0, 212.0, 241.9, 454.2, 458.8, and 1215.2 keV along with other γ rays belonging to the positive-parity states and the ground band (1111.6–1288.8–679.7–1765.0 keV). The 1215.2-keV transition is not seen in coincidence with both 679.7 and 1111.6 [see Fig. 4(b)] nor both 241.9 and 1889.0 [see Fig. 5(b)]. But it is seen in coincidence with 1111.6-, 1288.8-, 241.9-, 454.2-, and 458.8-keV γ rays. Thus, the coincidence and anticoincidence relationships of 1215.2 keV justify the presence of the 4969.0- and 5181.0-keV levels. In addition, the 1889.0-keV γ ray as shown in coincidence spectra [see Fig. 3(b), Fig. 4(b), and Fig. 5(a)] also supports the placement of the above levels. The spectra shown in Fig. 4(b) and Fig. 5 as well as the above arguments lead to the placement of the 4969.0-, 5181.0-, 5422.9-, 6007.9-, and 6466.7-keV levels. The placement of these levels was also assisted by the observation of the other γ rays connected to band 3 such as those at 931.4, 386.4, 1669.4 keV, etc. The spin and parity for band 3 is assigned on the basis of RDCO and polarization asymmetry measurements. C. Band 4

The level scheme comprising the negative-parity states is shown in the right-hand portion of Fig. 2. Figure 6 represents all γ -rays on basis of those the negative-parity states were established. The seven new levels located above the

024315-8



3396.5-keV level constitute a highly staggered band consisting of 964.6-, 432.0-, 1396.6-, 906.3-, 1338.0-, 240.0-, 1146.3-, 686.8-, 926.8-, 595.6-, and 333.1-keV γ rays. All these γ rays have been observed to be in coincidence with the 368.5-keV γ -ray which depopulates the already known 3396.5-keV level. Figure 7 supports the placement of these levels as the γ rays placed above 3396.5-keV level, which are in anticoincidence with both 860.2- and 264.9-keV γ rays [see Fig. 7(b)] and are in coincidence with both 1288.8- and 1111.6-keV γ rays [see Fig. 3(b)]. RDCO and polarization asymmetry values were used to assign the spin and parity for the levels of band 4. In the earlier works [28,31], there was a controversy associated with the placement of the 860.2-keV γ ray; this has been resolved in the present work. We have observed that the 860.2-keV γ ray is in coincidence with all the γ -rays placed below the 2367.0-keV level [see Fig. 7(b)], but not in coincidence with the γ ray placed above the 3396.5-keV level, as shown in Fig. 7(a). Thus, the 860.2-keV γ ray is emitted from a new level at 3227.2 keV to the level which decays by emitting the 264.9-keV γ ray. Also, the placement of the 166.6-keV γ -ray and the 494.2-keV γ -ray has been confirmed in the present work. This placement is supported by the 558.2-, 810.8-, and 200.0-keV γ rays (unplaced in Arnell et al. [28]), which are in coincidence with both 1146.3- and 1396.6-keV γ rays, as shown in Fig. 7(a), but in anticoincidence with both 264.9- and 860.2-keV γ rays, as shown in Fig. 7(b). IV. DISCUSSION

The level scheme of 85 Sr as shown in Fig. 2 is markedly different from that of 83 Sr [21]. Whereas 83 Sr exhibits a well-developed rotational band structure, which is a sign of deformation and collectivity, the level scheme of 85 Sr represents a mixed character. We, therefore, rely on a comparison with the odd-A, N = 47 isotones 83 Kr [11], 87 Zr [13,18], and 89 Mo [16,17] to assign the configuration of levels in 85 Sr. A. Shell-model interpretation

To interpret the experimental data, shell-model calculations have been carried out in the 28–50 valence shell composed of the orbitals 1p3/2 , 0f5/2 , 1p1/2 , and 0g9/2 . The calculations have been performed with two recently derived effective shell-model interactions by Honma et al. (JUN45) [46] and Brown and Lisetskiy (jj44b) [47]. The single-particle energies employed in conjunction with the JUN45 interaction are −9.8280, −8.7087, −7.8388, and −6.2617 MeV for the p3/2 , f5/2 , p1/2 , and g9/2 orbitals, respectively. In the case of the jj44b interaction [47] the single-particle energies are −9.6566, −9.2859, −8.2695, and −5.8944 MeV for the p3/2 , f5/2 , p1/2 , and g9/2 orbitals, respectively. The results shown in this work were obtained by using the m-scheme code ANTOINE [48]. Figure 8 shows a comparison of the experimental positiveparity level energies of 85 Sr with the predictions of the shell-model calculations obtained by using the JUN45 and jj44b interactions. It is evident that the shell-model calculations provide a good agreement with the experimental data. The 7/2+ 1 level observed at 231 keV is predicted at 372 and

404 keV by JUN45 and jj44b interactions, respectively. For nearly all the levels a one-to-one correspondence between the spin-parities of the observed levels and the calculated levels can be established; this supports the model space chosen by us for the calculations. Figure 9 shows a comparison of the experimental and the calculated energies of 85 Sr for the negative-parity states. In this figure, we have also plotted the calculated results for − − − − − 1/2− 1 , 3/21 , 5/21 , 7/21 , 9/21 , and 11/21 levels. However, we have shown only those negative-parity levels which have been observed in the present experiment. The experimentally observed 13/2− 1 at 2102 keV is predicted at 2234 and 1819 keV by the JUN45 and jj44b interactions, respectively. Both the calculations predict nearly the same order of energy levels as − in the experiment from 15/2− 1 to 35/21 . We have assigned the calculated energy levels obtained by using the JUN45 interaction with the experimentally observed bands 2, 3, and 4 in Fig. 10. The assignments are solely based on the sequences of observed and predicted levels. While bands 2 and 3 are positive-parity bands, band 4 is a negative-parity band. The agreement for band 2 and band 4 is quite good. However, band 3 is reproduced rather poorly. We have listed the wave functions for the positive- and the negative-parity levels in Tables II and III, respectively (see these tables in the Supplemental Material [45]). Both −3 the interactions used in our calculations predict ν(g9/2 ) as the dominant neutron component in the wave functions of 9/2+ to 27/2+ states. On the other hand, the dominant proton component from the JUN45 interaction oscillates between 0 2 (πg9/2 ) to (πg9/2 ) for the different signature partner members of the sequence shown in Table II. The calculations based on 2 jj44b predict the component to be predominantly (πg9/2 )⊗ −3 (νg9/2 ). A similar pattern is seen in the negative-parity band 4, whose dominant components of wave functions for various levels are listed in Table III. The two signature partner levels have been grouped together and a pattern in their wave functions is evident. While the unfavored signature −3 1 partner levels have a component (πg9/2 ) ⊗ (νg9/2 ), the favored −2 0 signature partner levels have a (πg9/2 ) ⊗ (νg9/2 ) component for the JUN45 interaction, implying a larger alignment for an oblate shape. This may be directly linked to the large signature splitting observed in band 4 (Fig. 11). This odd-even splitting in the energy levels and B(M1)/B(E2) ratios for the negative-parity band 4 is plotted in Fig. 11. The agreement between the experimental and the calculated results is quite remarkable for the JUN45 interaction. The B(M1)/B(E2) ratios are overestimated by a factor of 10. If we divide the calculated values by 10, they come very close to the measured values. The shell-model wave functions can be clearly distinguished for the two signature partner members of band 4, as shown in Table III. While the 15/2− , 19/2− ,..., 31/2− states have an extra proton in the g9/2 orbital, the 13/2− , 17/2− ,..., 25/2− states have an extra neutron in the g9/2 orbital. The 29/2− and 33/2− levels, however, acquire a structure similar to the 31/2− and 35/2− levels and we can see from Fig. 11 that the signature splitting does disappear around spin 31/2− . Band 4 is expected to have an oblate shape,

024315-9

S. KUMAR et al.

PHYSICAL REVIEW C 90, 024315 (2014) 85

31/2

+

Sr positive parity 31/2+

6811

6668

31/2+

6074

29/2

+

29/2

+

5758

29/2+

5667

+

5471

27/2+

5906

31/2(+)

6467

+

(31/2 )

6361

+

6204

29/2+

6069

(+)

6008

31/2

+

5957

+

5750

29/2

+

5884

27/2

+

5613

29/2+

5474

29/2 29/2

29/2

27/2(+)

5704

27/2+

5423

5368

5181

27/2+ 25/2+

25/2+

5221 5036

5174

27/2+

27/2+

5091

27/2+

5077

+

4956

25/2+ 23/2(+)

5037 4969

25/2+

5031

25/2+ + (21/2 )

25/2+

4903

4845 4780

25/2

+

4723

4492

23/2+

4485

+

4420

21/2+

4005

23/2+

3795 3653

27/2

25/2

23/2+

4833

25/2+

4540

25/2+

4490

25/2+

25/2 23/2

+

4043

21/2

+

4008

19/2+

23/2+

3966

3640 +

3512

21/2+

21/2+

3528

21/2

17/2+

3256

19/2+

3384

21/2

+

3293

21/2+

3170

21/2+

3080

19/2+

3250

17/2+

3072

17/2+

2987

+

2840

17/2+

2849

15/2+

15/2+

2610

2526

17/2+

2400 17/2+

2249

13/2+

1963

+

1764

11/2+

1462

9/2+

1262

13/2+

938

7/2+

404

17/2

+

15/2

+

3011 2807

17/2

+

2267

13/2

+

2244

11/2

+

1709

9/2+

1610

11/2+

1433

13/2+

971

7/2+

372

17/2

13/2

1850 11/2

11/2+

1658

9/2+

1262

11/2+

1221

13/2+

1112

7/2 9/2+

+

+

231

9/2+

JUN45

FIG. 8. Comparison of the experimental positive-parity level scheme of 85 Sr with the results of the shell-model calculations using interactions shown in the figure.

9/2+

EXPT.

jj44b

which is supported by the Struntinsky calculations which minimize the deformation at 2 = 0.11,γ = 58o . The extra proton in the g9/2 orbital is deformation aligned while the

extra neutron in the g9/2 orbital is rotational aligned for an oblate shape. The states having more rotation alignment lie lower in energy.

024315-10



Sr negative parity

35/2-

33/2

27/2

7555

33/2-

7222

-

6964 31/2-

6626

-

5751

-

29/2-

5939

-

5699

27/2

4600

25/2-

4372

-

3983

21/2-

3195

19/2-

4793

23/2-

-

5754

27/2

-

5552

25/2-

4686

-

4272

23/2-

3970

21/2-

3177

21/2-

2974

19/2

-

2741

17/2

-

2579

15/2-

2389

17/2

-

2303

11/2

-

1924

13/2

-

1819

25/2

21/2-

3397

3003

-

21/2

3227

2825

19/2-

3028

2759

-

17/2 15/2

-

2595

11/2-

2533

17/2-

2503

17/2-

2367

13/2-

2234

13/2-

2102

9/2-

1738

-

1564

3/2-

1009

5/2-

798

-

333

1/2

29/2

4361

-

7/2

6652

5007

25/2

21/2

31/2-

5347

-

-

6964

6341

-

23/2

-

33/2

(25/2-)

25/2

8092

7446

31/2-

29/2

35/2-

35/2-

JUN45

2861

17/2

15/2-

2661

EXPT.

FIG. 9. Comparison of the experimental negative-parity level scheme of interactions shown in the figure.

024315-11

9/2-

1151

7/2-

860

3/2-

479

5/2-

206

1/2-

10

jj44b 85

Sr with the results of the shell-model calculations using

S. KUMAR et al.


85

Sr

35/2 7.555

35/2- 7.446

33/2 7.222 33/2 6.964

7 +

31/2 6.668 (+) 31/2 6.467

(31/2+) 6.361 +

Energy (MeV)

31/2 6.074

6

+

5.750

29/2

5.667

+

5.221

29/2

+

5.091

+

4.492

27/2

27/2

29/2+ 5.758 27/2+ 5.423 25/2+ 5.181 (+) 23/2 4.969 (21/2+) 4.780

5 25/2

4

31/2 6.341

+ 29/2 6.008

+

31/2- 6.626

29/2- 5.939 27/2 5.699

+ 27/2 5.368

25/2+ 5.036 + 23/2 4.833

29/2- 5.751 27/2 5.347

25/2 4.793

+

25/2 4.490

23/2 4.361

23/2+ 3.966

23/2+ 4.043

21/2+ 3.512

21/2+ 3.528

+ 21/2 4.008

25/2- 4.372 23/2- 3.983

21/2- 3.397 19/2- 3.028

3

21/2 3.195

19/2- 2.825

EXPT.

JUN45

EXPT.

Band 2

2

JUN45

Band 3

EXPT.

JUN45

Band 4

FIG. 10. (Color online) Comparison of the experimental and theoretical (with JUN45) energies for different bands. B. TAC calculations π

+

The 3384-keV I = 19/2 level marks the beginning of a new set of levels belonging to band 2 mostly connected by

[(E(I)-E(I-1)) / 2I ]

50

30 20 10 0

10

12

10

12

14

16

18

20

14

16

18

20

2

B(M1)/B(E2)[ µN /eb ]

Expt JUN95 jj44b

40

100

10

1

I(h)

FIG. 11. (Color online) Comparison of signature splitting and B(M1)/B(E2) for negative-parity band 4 with shell-model calculations. The theoretical B(M1)/B(E2) values divided by a factor of 10 are also shown to provide comparison with experimental B(M1)/B(E2) values.

M1 transitions as also seen in 89 Mo [16]. This implies that a new configuration has taken over at this point. We propose that the positive-parity levels connected by the dipole transitions in 85 Sr may have a three-quasiparticle (3qp) configuration −1 2 π (g9/2 ) ⊗ (νg9/2 ). If we choose the (πg9/2 )2 × (νg9/2 )−3 configuration as suggested by the shell model, the TAC calculation generates higher angular momentum values. We, therefore, restrict the TAC calculations to the 3qp configuration −1 2 π (g9/2 ) ⊗ νg9/2 . The calculations based on this configuration result in a minimum at 2 = 0.11,γ = 60o . We took the pairing gap as p = 0.951 and n = 1.270 MeV, which is 80% of the oe value. The plot of I() versus ω (see Fig. 12) shows that the results of TAC calculations match the experimental data at lower spins and also lead to strong magnetic dipole transitions. The experimental B(M1) values were calculated from the lifetime measurements [30]. It can be seen that the measured B(M1) strength is consistent with the TAC calculation (see the lower panel of Fig. 12). However, the measured values have large error bars and do not show a definite fall with increase in spin. New measurements are, therefore, needed to confirm this. This suggests that band 2 may have a MR character. However, it is also evident that the five-quasiparticle (5qp) configuration (πg9/2 )2 × (νg9/2 )−3 would certainly play an important role at higher rotational frequency, as is also evident from a rise in the B(M1) values. Such a rise suggests an opening of the n-p blades, which may close again. In view of the systematics for N = 47 isotones, we have −1 1 chosen the 3qp configuration π [g9/2 ⊗ (p1/2 /f5/2 )1 ] ⊗ (νg9/2 ) to describe the behavior of the negative-parity band 4 by using the TAC model. A self-consistency in the deformation

024315-12



FIG. 12. Plot showing the angular momentum I () as a function of rotational frequency ω for the positive-parity band 2 at 3384 keV.

parameters was achieved for a minimum at 2 = 0.11,γ = 58◦ in the Nilsson-Struntinsky minimization. The results of the TAC calculation are plotted in Fig. 13, where the total angular momentum I() versus the rotational frequency (ω) is plotted. It is seen that the observed behavior of I () versus ω before the backbending is very well reproduced by the calculations.

However, the post-backbending data are not available; yet it is clear (Fig. 13) that a 5qp configuration may contribute at higher angular momenta. We have found a minimum at 2 = −3 1 ⊗ (p1/2 /f5/2 )1 ] ⊗ (νg9/2 ) 0.105,γ = 58o for the 5qp π [g9/2 configuration. This is in accordance with the wave functions calculated from the shell model. Note that the deformation has not changed at all in going from 3qp to 5qp. The 5qp results of the TAC calculation are plotted as a dot-dashed line in Fig. 13. It appears to give the correct angular momentum and trend as suggested by the available experimental data. It is interesting that the same configuration in 83 Kr leads to a MR band. The only change in going from 83 Kr to 85 Sr is the deformation parameter 2 , which decreases from 0.18 to 0.11. One would expect a strong MR behavior in 85 Sr due to the smaller deformation. However, this does not appear to be the case. The shell-model calculation for 85 Sr also predicts a flat trend for the B(M1) values in this band. A strong signature splitting suggests a large Coriolis effect, which may lead to a behavior different from the expected MR behavior. The comparison of the excitation energy, both measured as well as calculated, as a function of angular momentum, i.e., E versus I (see the Supplemental Material [45]), reinforces the configuration assignment for band 2 and band 4. In brief, we conclude that the calculations based on the TAC model are also able to explain the observed salient features of the bands in 85 Sr and generally support the results obtained from the shell model.

V. SUMMARY

The previously known level scheme of 85 Sr has been substantially extended for both the positive- and the negativeparity levels. The spin and parity of different levels up to a spin of 35/2 and excitation energy ≈7.5 MeV have been established through RDCO and polarization measurements. The experimental results have been compared with the large-scale shell-model calculations without any truncation in the 28–50 model space (1p3/2 , 0f5/2 , 1p1/2 , and 0g9/2 ) with the JUN45 and the jj44b interactions. The shell-model results give a reasonably good agreement with the observed data. However, the results for the negative-parity states are in better agreement with the experimental data. The configuration assignments based on the shell-model calculations for the positive-parity and the negative-parity bands are reasonably supported by the TAC calculations. The positive parity sequence, although very short, seems to satisfy the criteria of magnetic rotation. However, the negative-parity sequence, band 4, does not satisfy the MR band criteria. Based on the shell-model and the TAC calculations, a reasonably good understanding of the observed behavior in 85 Sr from low to high spins has been obtained.

ACKNOWLEDGMENTS FIG. 13. Plot showing the angular momentum I () as a function of rotational frequency ω for the negative-parity band 4 at 2102.0 keV.

The authors thank the staff at TIFR-BARC Pelltron Linac accelerator, target laboratory staff at IUAC, New Delhi. Financial support from the Department of Science and Technology

024315-13

S. KUMAR et al.


(DST, Government of India) for providing funds for the INGA project (No. IR/S2/PF-03/2003-I) is gratefully acknowledged. The authors also thank the CSIR and DAE (Government

of India) for financial supports at various stages. All the shell-model calculations were performed at the Kan Balam computational facility of DGCTIC-UNAM, México.

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