High-spin levels based on the 11/2- isomer in 135Ba

Abstract.High-spin states in the 135Ba nucleus have been studied with the reaction 130Te(9Be, 4n) at a beam energy of 45 MeV. The level scheme based on the h11/2 isomer has been expanded with spins up to 35/2 ℏ. At low spins, the yrast collective structure built on the ν h11/2-1 multiplet may show a transitional shape with γ > 30° according to the systematical behavior observed in neighboring nuclei as well as the calculations of the triaxial rotor-plus-particle model. The configurations for several high-spin states have been discussed from a systematical comparison with neighboring isotones.

The odd-A 135 Ba nucleus with Z = 56 and N = 79 lies in the A = 135 transitional region with the neutron number approaching the closed shell at N = 82. In this region, the nuclei have a small quadrupole deformation parameter ε 2 and a soft γ-deformation. Their level structures should exhibit complex characteristics as the existence of a competition between the collective motion and the single-particle motion. In previous publications, the high-spin levels of many nuclei in this region, such as in 133 Ba [1], 135 La [2], 136 La [3], 137 La [4], 135 Ce [5], 136 Ce [6], 137 Ce [7] and 138 Ce [8], have been extensively researched. Several interesting phenomena, for example, the shape coexistence of prolate and oblate deformations, the oblate rotational bands, the high-spin structures based on isomers and the excitation levels with multi-quasiparticle configurations were observed. The odd-A 135 Ba nucleus like other N = 79 isotones in this region is expected to have a stronger single-particle property and a weaker collectivity than those of N < 79 isotopes as its neutron number is closer to the closed shell at N = 82. Previous experimental studies of the other N = 79 odd-A isotones in 137 Ce [7], 139 Nd [9], 141 Sm [10] and 143 Gd [10] showed the existence of a sequence of levels with weak collectivity based on the 11/2 − isomer state at low-spin states from which a prolate-oblate transition in each isotope can be determined. At high-spin states, some systematical levels a e-mail: chexl02@mails.tsinghua.edu.cn with multi-quasiparticle configurations [7,10] have been assigned and an oblate collective rotational band has been observed [7]. In order to systematically understand the nuclear structural character in this region, it is interesting to study of the high-spin states of 135 Ba. In previous works, some lower-spin levels have been reported by the ( 9 Be, xn) reaction [11], the β-decay [12] and the (n, γ) reaction [12]. In this letter, we briefly report on the experimental investigation of new high-spin levels above the 11/2 − isomer in 135 Ba.
High-spin states in 135 Ba were populated via the 130 Te ( 9 Be, 4n) fusion-evaporation reaction. An isotopically enriched 130 Te target of thickness 2.34 mg/cm 2 evaporated on a natural aurum backing of 20 mg/cm 2 was bombarded by a beam of 9 Be ions accelerated by the HI-13 accelerator at the China Institute of Atomic Energy (CIAE). An array of fourteen Compton-suppressed Ge detectors was employed to measure the in-beam γ-rays. The resolutions of the Ge detectors are between 1.8 and 2.2 keV at 1.333 MeV γ-ray energy. The γ-γ coincidence data were measured at a beam energy of 45 MeV. Approximately 7.7 × 10 7 coincidence events were collected, from which a γ-γ coincidence matrix was built. The γ-ray energies and efficiencies were calibrated with 152 Eu source. In order to determine the multipolarity of γ-ray transitions, four detectors near 90 • with respect to the beam axis were sorted against the other ten detectors at 45 • (four), 55 • (one), 125 • (one) and 135 • (four) to produce a two-dimensional  angular-correlation matrix from which it was possible to extract the average directional correlation of the orientedstate (DCO) intensity ratios. The γ-γ coincidence data were analyzed with the Radware software package [13]. The level scheme of 135 Ba deduced from the present study is shown in fig. 1. It was constructed from the γγ coincidence, the relative transition intensities, and the DCO ratio analysis. The transition intensities are represented by the width of the arrows. Four yrast levels at 0, 268.2, 950.5 and 2002.6 keV along with two linking transitions, 682.3 and 1052.1 keV, reported in ref. [11], were confirmed. We did not observe the 268.2 keV γ-transition from the 268.2 keV level to the ground state as it belongs to an M 4(E5) transition and is too weak to be observed. All the other levels and transitions in fig. 1 were newly identified in our work, including 20 levels and 24 transitions. As example, fig. 2 shows two representative coincidence γ-ray spectra by gating on the 682.3 keV (a), and the 204.0 keV (b) γ-transitions, respectively, from which the stronger coincidence γ-peaks in 135 Ba can been seen.
The spin and parity (I π ) assignments for the levels are based on the previous works [11,12], the DCO ratios and the systematical comparison with the levels of neighboring N = 79 isotones 137 Ce [7], 141 Sm [10] and 143 Gd [10]. Figure 3 shows a plot of the observed DCO ratios for some transitions of 135 Ba in the present work. The DCO ratios for some weak transitions cannot be obtained because of the poor statistics of the γ-peaks. Generally, a quadrupole (∆I = 2, E2) transition is adopted if a DCO ratio is around 1.2, and a dipole (∆I = 1) transition is assumed if a DCO ratio is around 0.85. However, in a dipole (∆I = 1) transition, one cannot distinguish between E1 and M 1 transitions using this method. The I π of the ground state of 135 Ba has been assigned as 3/2 + and the 268.2 keV level was assigned as 11/2 − [11, 12] with a long half-life of T 1/2 = 28.7 h [12]. In ref. [11], the I π of 950.5 and 2002.6 keV levels was tentatively assigned as 15/2 − and 19/2 − , respectively. From our DCO ratio values, we confirmed these assignments because both the 682.3 and 1052.1 keV γ-transitions belong to the E2 multipolarity. According to the observed DCO ratios and the systematical comparison with neighboring nuclei, we assigned or tentatively assigned the I π 's of other high-spin levels, as shown in fig. 1. At the lower-spin states from 11/2 − at 268.2 keV to 19/2 − at 2133.9 keV, there are odd-parity levels connected by the quadrupole transitions. Above the 21/2 − state, the levels divide into two groups of even-parity states (left part) and odd-parity states (right part) connected mainly by the dipole transitions. At high spins, we did not observe a collective oblate rotational band in 135 Ba, as reported in 137 Ce [7]. The reason may be that a higher incident energy beam is needed in order to populate higher-spin states.
The level structure of 135 Ba exhibits complex characteristics. It is difficult to determine all the level configurations. However, some important features can been discussed based on the systematics and model calculations. At lower-spin states, the 11/2 − isomer state at 268.2 keV can be explained by the h 11/2 neutron hole coupled to the even-even nucleus core. The 15/2 − state at 950.5 keV may belong to a member of the νh −1 11/2 × 2 + multiplet and the 19/2 − state at 2002.6 keV may belong to a member of the νh −1 11/2 × 4 + multiplet. Another 13/2 − state of the member of the νh −1 11/2 × 2 + multiplet was not observed in the present work. This νh −1 11/2 level family has been systematically observed in the neighboring isotones 137 Ce [7], 139 Nd [9], 141 Sm [10] and 143 Gd [10] also. Shape transition is a very interesting phenomenon in the A = 135 transitional region. The prolate-oblate shape transition at low-spin states was reported in the neighboring Ce [7,14] and Nd [9] isotopes between N = 77 and N = 79. That is, in an isotopic chain the nucleus has a prolate shape with γ < 30 • at N ≤ 77 and it has an oblate shape with γ ≥ 30 • at N ≥ 79. It indicated that the sequence of the 13/2 − and 15 − levels of the νh −1 11/2 multiplet is a signature of a prolate or an oblate shape: when the 15 − state lies up on the 13/2 − state, the nucleus has a prolate shape, whereas when the level inversion of the 13/2 − state and 15/2 − state occurs, the nucleus has an oblate shape. Although the 13/2 − state member in 135 Ba has not been identified in the present work, we still strongly suggest that at low-spin states 135 Ba has a triaxial shape with γ > 30 • in the oblate side based on the systematic behavior observed in the neighboring nuclei. As in 133 Ba [1] the h 11/2 collective structure is expected to have a prolate deformation, the prolate-oblate transition may occur between N = 77 and N = 79 in Ba isotopes also. In order to further understand the structural characteristics at the low-spin states in 135 Ba, we have performed calculations using the triaxial rotor-plus-particle model with a variable moment of inertia (VMI) [15][16][17]. In the calculations, the adjustable parameters are ε 2 , γ and the Coriolis attenuation factor χ. By varying the ε 2 , γ and χ values, and by carefully comparing the calculated levels with the corresponding experimental ones, we determined these values used in the calculations as follows: ε 2 = 0.09, ε 4 = 0.0, γ = 33.6 • and χ = 0.73. Other parameters were taken as standard. The results of our calculations and a comparison with experimental data are shown in fig. 4. Generally, the agreement between the theoretical and experimental results is quite good. The calculations predict that the 13/2 − state should lie above the 15/2 − state. One needs to observe it in further experiments. As expected, the calculations indicate that the 135 Ba nucleus at low spins has a triaxial shape with γ > 30 • . This might give a support to our above suggestion of the prolate-oblate shape transition in Ba isotopes.
Although determining the configurations of all the levels observed in 135 Ba is difficult, the configurations for some levels may be discussed based on a systematical comparison with neighboring isotopes and isotones. The 11/2 × 6 + configuration. These levels can be seen in the neighboring nuclei 137 Ce [7] also. Now we discuss the even-parity levels at the highspin states in fig. 1. By systematically comparing with the assigned configurations of some levels in the nuclei 137 Ce [7], 141 Sm [10] and 143 Gd [10], three-quasiparticle configurations for some states may be suggested as shown in fig. 5 configuration. The 29/2 + state at 4182 keV and the 31/2 + state at 4696 keV may be two members of the νh −1 11/2 πh 11/2 g −1 7/2 × 2 + multiplet. From fig. 5 one can see that the level energies of these three-quasiparticle states are quite similar in 135 Ba and 137 Ce, and generally decrease with increasing Z number. The high-spin evenparity levels above the 31/2 + state at 4696 keV, may have five-quasiparticle configurations, and the odd-parity levels above the 23/2 − state at 2740 keV at the right side in fig. 1 may have tree-quasiparticle configurations also. But detailed configurations for these levels cannot be determined by the present work.
In summary, high-spin states in the 135 Ba nucleus have been studied. The level scheme based on the h 11/2 isomer has been expanded with spins up to 35/2h. At low spins, the yrast collective structure built on the νh −1 11/2 multiplet shows a transitional shape with γ > 30 • according to the systematical comparison with neighboring nuclei and the calculations of the triaxial rotor-plus-particle model. The prolate-oblate transition may occur between N = 77 and N = 79 in Ba isotopes. The configurations for several high-spin states have been discussed from a systematical comparison with neighboring nuclei. The identification of the proper configurations of the high-spin states in 135 Ba needs more experimental and theoretical work, in particular, on electromagnetic transition probabilities.