Shell-model calculations of nuclei around mass 130

Shell-model calculations are performed for even-even, odd-mass, and doubly-odd nuclei of Sn, Sb, Te, I, Xe, Cs, and Ba isotopes around mass 130 using the single-particle space made up of valence nucleons occupying the $0g_{7/2},1d_{5/2},2s_{1/2},0h_{11/2}$, and $1d_{3/2}$ orbitals. The calculated energies and electromagnetic transitions are compared with the experimental data. In addition, several typical isomers in this region are investigated.

Figure 1

Comparison between the spectra in which the number of levels $\left(L_c\right)$ for diagonalization is limited to $500 \left(L_c=500\right)$ and $1000 \left(L_c=1000\right)$ for $({\mathrm{a})}^{135}\mathrm{Ba},({\mathrm{b})}^{136}\mathrm{Ba}$, and $({\mathrm{c})}^{132}\mathrm{Ba}$.

Figure 2

Comparison between the experimental spectra (expt.) and the shell-model results (SM) for Sn isotopes. The experimental data are taken from Refs. [22, 23, 24, 25, 26, 27, 28, 29, 36].

Figure 3

Comparison between the experimental spectra (expt.) and the SM results (SM) for Sb isotopes. The experimental data are taken from Refs. [22, 23, 24, 25, 29, 39, 40, 41, 42, 47].

Figure 4

Comparison between the experimental spectra (expt.) and the SM results (SM) for Te isotopes. The experimental data are taken from Refs. [23, 24, 25, 29, 39, 40, 48, 49, 50, 51, 52, 53].

Figure 5

Comparison between the experimental spectra (expt.) and the SM results (SM) for I isotopes. The experimental data are taken from Refs. [24, 25, 29, 39, 40, 48, 49, 60, 61, 65].

Figure 6

Comparison between the experimental spectra (expt.) and the SM results (SM) for Xe isotopes. The experimental data are taken from Refs. [25, 29, 39, 40, 48, 49, 60, 66, 74, 75].

Figure 7

Comparison between the experimental spectra (expt.) and the SM results (SM) for Cs isotopes. The experimental data are taken from Refs. [29, 39, 40, 48, 49, 60, 66, 76, 77, 78, 79].

Figure 8

Comparison between the experimental spectra (expt.) and the SM results (SM) for Ba isotopes. The experimental data are taken from Refs. [9, 29, 40, 48, 49, 60, 66, 77, 80, 81, 82, 83].

Figure 9

Comparison between the experimental spectra (expt.) and the SM results (SM) for ${}^{130}\mathrm{Sn},{}^{134}\mathrm{Te}$, and ${}^{132}\mathrm{Sb}$. The experimental data are taken from Refs. [25, 29, 40, 49].

Figure 10

Comparison between the experimental energy levels (expt.) and two kinds of calculated results for ${}^{132}\mathrm{Sb}$ using phenomenological neutron-proton two-body interactions: the shell-model results (SM) with only the QQ interaction and the SM results including multipole interactions [SM(multipole)].

Figure 11

Comparison between the experimental energy levels (expt.) and the calculated results (SM) with modified interactions for ${}^{135}\mathrm{Cs}$. The experimental data are taken from Refs. [29, 60, 76].

Figure 12

Experimental and theoretical $B(E2;I\to I-2)$ values (in W.u.) in ${}^{131}\mathrm{Sb}$. The filled circles in red and diamonds in blue represent the experimental data (expt.) and the theoretical results (SM), respectively. The experimental data are taken from Ref. [39].

Figure 13

Energy $\left(E\right)$ versus spin $\left(I\right)$ diagram for calculated energies with assumed configurations [$\pi g_{7/2}\nu {\left(h_{11/2}^{-2}\right)}_{J^{+}}$] for ${}^{131}\mathrm{Sb}$.

Figure 14

Experimental and theoretical $B(E2;I\to I-2)$ values (in W.u.) in ${}^{136}\mathrm{Xe}$. The filled circles in red and diamonds in blue represent the experimental value (expt.) and the theoretical results in the full SM calculation [SM(full)], respectively. The squares in green indicate single-$j$ results [SM(single-$j$)]. The experimental data are taken from Ref. [66].

Figure 15

The expectation numbers of proton pairs in each state calculated by the PTSM for ${}^{136}\mathrm{Xe}$. $S,D,G,{\left(g_{7/2}\right)}_{6+}^2$ and ${\left(g_{7/2}{d}_{5/2}\right)}_{6+}$ represent the proton $S$ pair, $D$ pair, $G$ pair, ${\left(g_{7/2}\right)}_{6+}^2$ pair, and ${\left(g_{7/2}{d}_{5/2}\right)}_{6+}$ pair, respectively.

Figure 16

Experimental and theoretical $B(E2;I\to I-2)$ values (in W.u.) in ${}^{126}\mathrm{Sn}$. The filled circles in red and diamonds in blue represent the experimental data (expt.) and the theoretical results in the full SM calculation [SM (full)], respectively. The squares in green indicate single-$j$ results [SM (single-$j$)]. The experimental data are taken from Ref. [36].