ЯДЕРНАЯ ФИЗИКА, 2014, том 77, № 11, с. 1399-1407
= ЯДРА ^^
HIGH-SPIN STRUCTURES OF 86,87,88>89y ISOTOPES
© 2014 P. C. Srivastava1)*, Vikas Kumar1), M. J. Ermamatov2)
Received March 17, 2014
In the present paper nuclear structure properties of 86>87>88>89y isotopes have been investigated using large-scale shell-model calculations within the full f5/2pg9/2 model space. The calculations have been performed with JUN45 and jj44b effective interactions that have been proposed for use in the f5/2, p3/2, pi/2, g9/2 model space for both protons and neutrons. Reasonable agreement between experimental and calculated values are obtained. This work will add more information to the previous study by the projected shell model [Eur. Phys. J. A 48, 138 (2012)], where full-fledged shell-model calculations were proposed for these nuclei.
DOI: 10.7868/S0044002714100122
1. INTRODUCTION
The neutron-rich nuclei with Z = 28—40 recently attracted much theoretical and experimental affords [1 — 12]. Many fascinating phenomena have been observed in this region. The nuclei Sr, Y, and Zr are close to subshell closure, thus they are expected to exhibit single-particle characteristics. The other important features in this region are existence of high-spin isomers and shape transitions as higher j orbitals are occupied. Recently structure of Sr and Zr isotopes near and at the magic number N = 50 shell via g-factor and life-time measurements have been investigated. The Zr isotopes are changing structure from 80Zr (super-deformed) with high occupancy of ng9/2 orbit to less-deformed 90Zr with substantial ng9/2 orbit occupancy. Recent experimental study claims the evolution of collectivity and shape coexistence for Sr isotopes.
The high-spin states in 86Y using heavy-ion fusion—evaporation reactions have been studied in [13]. The corresponding structures were interpreted by shell-model with truncation. For 88Y the high-spin states up to an excitation energy of 8.6 MeV and spin and parity of have been reported in [14]. In another experiment high-spin states up to spin 21h were investigated through fusion—evaporation reaction 82 Se(nB, 5n) [15]. The excited states of87Y up to 33/2(-) at MeV with in-beam 7-ray spectroscopy were reported in [16]. In this work majority
'-'Department of Physics, Indian Institute of Technology,
Roorkee.
2)Institute of Nuclear Physics, Academy of Sciences of
Uzbekistan, Ulughbek, Tashkent.
E-mail: pcsrifph@iitr.ac.in
of the observed high-spin states are explained on the basis of v = 3 and v = 5 configurations. Previously this nucleus was experimentally studied in [17—19], and excited states up to ^4.6 MeV were observed. The experimental results up to 31/2+ h for 89Y are reported in [20] by using in-beam 7-ray spectroscopy. Cheal et al. used laser spectroscopy method to study isomeric states of yttrium isotopes [21]. In this work nuclear charge radius differences, magnetic dipole and electric quadrupole moments have been obtained. Recently, theoretical results of positive-parity yrast bands of odd 79-89Y isotopes using projected shell model (PSM) were reported in [22]. In this work it is mentioned that the results of large-scale shell-model calculation in this mass region is limited due to involvement of g9/2 orbital which generates large configuration space. Thus, results of modern shellmodel calculations are desired for these nuclei.
In the present paper, we reported systematic study of shell-model results for 86>87>88>89Y isotopes. The main motivation of the present study is to explain recently available experimental data for these isotopes.
The result of the present work is organized as follows: Model space and Hamiltonian are given in Section 2. In Sections 3—5, energy levels and transition probabilities, quadrupole moments, occupancy are compared with the available experimental data. Finally, concluding remarks are drawn in Section 6.
2. MODEL SPACE AND HAMILTONIANS
The present shell-model (SM) calculations have been carried out with two recently available effective SM interactions, JUN45 and jj44b, that have been proposed for the 1p3/2, O/5/2, lpi/2, and 0g9/2 single-particle orbits. JUN45, which was recently developed
by Honma et al. [23], is a realistic interaction based on the Bonn-C potential fitting 400 experimental binding and excitation energy data with mass numbers A = 63—96. Since the present model space is not sufficient to describe collectivity in these regions, data have not been used while fitting in the middle of the shell along the N = Z line. For JUN45, the data are mostly fitted to develop this interaction closure to N = 50. This interaction is not successful in explaining data for Ni and Cu isotopes, possibly due to the missing 0f7/2 orbit in the present model space. The jj44b interaction due to Brown et al. [24] was developed by fitting 600 binding energies and excitation energies with Z = 28—30 and N = 48—50. Instead of 45 as in JUN45, here 30 linear combinations of good JtAYT two-body matrix elements (TBME) varied, with the rms deviation of about 250 keV from experiment. For the JUN45 interaction, the single-particle energies are taken to be —9.8280, —8.7087, —7.8388, and —6.2617 MeV for the p3/2, f5/2, p1/2, and g9/2 orbits, respectively. Similarly, for the jj44b interaction, the single-particle energies are taken to be —9.6566, —9.2859, —8.2695, and —5.8944 MeV for theP3/2, f5/2, P1/2, and g9/2 orbits, respectively.
All calculations in the present paper are carried out at TLAPOA computational facility at ICN, UNAM, Mexico using the shell-model code ANTOINE [25]. In case of79 Se for positive parity maximal dimension is 59 791 822.
3. RESULT OF Y ISOTOPES
The shell-model results for 86-89Y with two different interactions are shown in Figs. 1—4.
3.1. 86Y
Previously shell-model calculation in f5/2pg9/2 space for this isotope with truncation by allowing up to two particle excitation from f5/2 and p3/2 to p1/2 and g9/2 is reported in [13]. The signature
splitting and magnetic rotation of 86Y using self-consistent tilted axis cranking calculations based on relativistic mean-field theory to investigate the dipole structures have been studied by Li et al. [26]. In the present study we performed shell-model calculation in f5/2pg9/2 space, this will add more information in the previous study [13] where truncated shell-model results are reported.
The JUN45 predicts the same sequence of the first four levels as in the experiment, however 7- level is much higher than in the experiment. This level is better predicted by jj44b, but the other two levels are lower than in the experiment. All the calculated
levels up to 17- have lower values in both calculations than in the experiment. Then the value of 18- comes very close to the experimental one. The 19- is a little bit lower in JUN45 calculation and in jj44b the calculated value of this level becomes -300 keV larger as compared to the experimental one.
The 8+ level at 218 keV is predicted to be 181 and 74 keV by JUN45 and jj44b calculations, respectively. Then the sequence of two 1+ levels are the same in jj44b calculation. However for jj44b, the value of the second 1+ level in this calculation is lower than in the experiment and that of the first level is higher. In JUN45 both levels are located higher than in the experiment. A very good agreement is given by both calculations starting from 9+ until 15+. Then both calculations start to differ from the experiment. For the ground state 4-, the JUN45 interaction predicting n(pi/2) ® v(g-f2) (-30%) configuration,
while jj44b as n^) ® v(f-/12) (-17%).
3.2. 87Y
Both calculations predict correct ground state. In the jj44b calculation the sequence of the next four negative parity levels are the same as in the experiment, though the values of these levels are lower than the experimental ones. The 13/2- level is lower than in the experiment, while 11/2- is higher than in the experiment, but the difference in 15/2-experimental and calculated values is only 3 keV. The 23/2- levels which appear in the calculation have not been measured in the experiment. Then the values of the next 25/2- level are -300 keV lower than in the experiment. Last four 27/2-, 29/2-, 31/2-, and 33/2- levels are in good agreement with the experimental data.
In JUN45 calculation the 3/2- and 5/2- levels are interchanged as compared to the experiment. The 1/2- level is much closer to the experiment than in jj44b calculation.
Positive parity levels start from 9/2+ in the experiment and in both calculations. In jj44b it starts from a lower value than in the experiment. The 7/2+ level appearing in both calculations has not been measured in the experiment. Then 5/2+ and 13/2+ levels are lower than in the experiment in jj44b calculation, while they are higher in the JUN45 calculation. Better agreement with the experiment in higher spins gives JUN45 calculation. The structure of the ground state 1/2- is a single-particle character (n(p/)). The
JUN45 and jj44b interactions predict -41% and -22% probability, respectively.
Fig. 1. Comparison of shell-model results with experimental data for86 Y with different interactions.
86'
Y
5993_ 5777
886_ 844"
272 _ 218-
- 17«
- 16«
- (15+)
- (14*)
-(13+)
- (12+)
11(+)
- (10+)
(9+) 1+
(8+)
302 243
Expt.
- 18(-)
- 17(-)
- 15(-)
- 12(-) -11«
-11(-) - 10(-)
9(-)
(7-) 2-
(5-)
10+ 1+
1+ 9+
5352_16+ 5377-16-
13+ 3138
JUN45
17+ 16+
158
75
jj44b
11- 10-
7511
19
7216
7154
19-
6812
6785
6782
6779
18
18-
18
6412
6408
18
6004
6001
17-
17-
5811
17
5477
5430
5319
5137
16-
4710
4523
15
4345
15
4251
4191
14
4153
4104
15
15
4010
3877
3823
3828
14
14
3622
14-
3454
3189
3170
3133
3090
13-
13
2939
13-
2819
2788
2758
12-
12
2566
2567
2521
12
12-
2466
2351
2329
2259
2042
2022
1987
1976
1971
11
11
1887
1804
1696
1325
1268
1230
10
1149
1097
998
986
929
7-
852
721
9
513
419
37
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