Pair-truncated shell-model analysis for doubly-odd nuclei around mass 130

Low-lying states for doubly-odd nuclei in the mass $A\sim 130$ region are investigated using a pair-truncated shell model. Energy levels of the low-lying states for doubly-odd nuclei, ${}^{132}$Cs, ${}^{130}$Cs, ${}^{134}$La, and ${}^{132}$La, are reproduced very well along with the electromagnetic transitions. The analysis of the wave functions reveals band structure for doublet bands built on the $\nu h_{11/2}\otimes \pi h_{11/2}$ configuration, showing various angular-momentum configurations of the unpaired neutron and the unpaired proton, weakly coupled with the quadrupole collective excitations of the even-even part of the nucleus.

Figure 1

Comparison between experimental energy spectra (expt.) and those of the PTSM (PTSM) for (a) ${}^{132}$Xe, (b) ${}^{130}$Xe, (c) ${}^{134}$Ba, and (d) ${}^{132}$Ba. The level sequences on the left represent the yrast states, and the level sequences on the right represent the $2_2^{+}$, $3_1^{+}$, $4_2^{+}$, $5_1^{+}$, $6_2^{+}$, and $0_2^{+}$ states. The experimental data are taken from Refs. [37, 38, 39, 40, 41, 42, 43].

Figure 2

Comparison of experimental energy levels (expt.) based on the $\nu h_{11/2}\otimes \pi h_{11/2}$ configuration with PTSM results (PTSM) for ${}^{132}$Cs. In the right panel, two level sequences of $\Delta I=1$ on the right represent the yrast band, and two level sequences of $\Delta I=1$ in the middle, the yrare band. Two levels on the left denote the third lowest-energy states for each total spin $I$. The experimental data are taken from Refs. [44, 45, 46].

Figure 3

Same as Fig. 2, but for ${}^{130}$Cs. The experimental data are taken from Refs. [5, 7, 47, 48].

Figure 4

Same as Fig. 2, but for ${}^{134}$La. The experimental data are taken from Refs. [3, 49].

Figure 5

Same as Fig. 2, but for ${}^{132}$La. The experimental data are taken from Refs. [4, 9, 44, 50].

Figure 6

Comparison between experimental $B\left(M1\right)/B\left(E2\right)$ ratios of yrast states and those in PTSM for (a) ${}^{132}$Cs, (b) ${}^{130}$Cs, (c) ${}^{134}$La, and (d) ${}^{132}$La. The experimental data are taken from Refs. [3, 4, 6, 7].

Figure 7

Theoretical $B(E2;I\to I-2)$ values for (a) ${}^{132}$Cs, (b) ${}^{130}$Cs, (c) ${}^{134}$La and (d) ${}^{132}$La. The filled circles, open squares, open circles and filled squares represent the transitions between yrast states, between yrare states, from yrast to yrare states and from yrare to yrast states, respectively. Solid lines indicate the transitions between the odd-spin states, and the dotted line indicates the transitions between even-spin states. In the lower panel for each nucleus, the yrast states with spin $I$ and the yrare states with spin $I-2$ are connected by solid or dotted lines.

Figure 8

Theoretical $B(M1;I\to I-1)$ values for (a) ${}^{132}$Cs, (b) ${}^{130}$Cs, (c) ${}^{134}$La, and (d) ${}^{132}$La. The filled circles, open squares, open circles, and filled squares represent the transitions between yrast states, between yrare states, from yrast to yrare states, and from yrare to yrast states, respectively. In the lower panel for each nucleus, the yrast states with spin $I$ and the yrare states with spin $I-1$ are connected by solid lines.

Figure 9

Partial level scheme of ${}^{134}$La suggested by the PTSM calculation. The green arrows indicate $E2$ transitions [$B\left(E2\right)\ge 0.02e^2{b}^2$], and the orange arrows denote $M1$ transitions [$B\left(M1\right)\ge 0.40{\mu }_N^2$]. The numerals on the right side of the $E2$ transitions denote the $B\left(E2\right)$ values (in ${10}^{-2}{e}^2{b}^2$), and those beneath the $M1$ transitions denote the $B\left(M1\right)$ values (in ${\mu }_N^2$). Schematic illustrations of the chopsticks configurations are presented below each $\Delta I=2E2$ band. The red and the blue arrows indicate the angular momenta of the neutron and the proton for the bandhead state, respectively. Six $\Delta I=2E2$ bands have the configurations shown by the schematic illustrations below.

Figure 10

Comparison of experimental energy levels (expt.) with the PTSM results (PTSM) for ${}^{132}$Cs. For the PTSM results, two level sequences of $\Delta I=2$ on the left represent the negative-parity states arising from the unpaired positive-parity neutron, and four level sequences of $\Delta I=2$ in the middle represent the negative-parity states arising from the unpaired positive-parity proton. The level sequences on the right denote the positive-parity states arising from the unpaired nucleons with positive-parity. The experimental data are taken from Refs. [44, 45, 46].

Figure 11

Same as Fig. 10, but for ${}^{130}$Cs. The experimental data are taken from Refs. [5, 7, 47, 48].

Figure 12

Same as Fig. 10, but for ${}^{134}$La. The experimental data are taken from Refs. [3, 49].

Figure 13

Same as Fig. 10, but for ${}^{132}$La. The experimental data are taken from Refs. [4, 9, 44, 50].

Figure 14

Band scheme predicted by the PTSM calculation in weak-coupling limit. The vertical arrows from top to bottom indicate $E2$ transitions, and the horizontal arrows from right to left indicate $M1$ transitions. Schematic illustrations of the chopsticks configurations are presented below the band scheme.