Isomerism and persistence of the $N=82$ shell closure in the neutron-rich ${}^{132}\mathrm{Sn}$ region

The occurrence of seniority isomers in semimagic nuclei is a clear indication for shell closure. By performing large-scale shell-model calculations in a model space that allows excitations across the $N=82$ neutron and $Z=50$ proton shell gaps, we investigate the isomerism along the $N=82$ isotonic chain. The calculation describes well the properties of the experimentally observed $8^{+}$ isomeric state and the other low-lying states in ${}^{126}\mathrm{Pd},{}^{128}\mathrm{Pd}$, and ${}^{130}\mathrm{Cd}$. We further predict energy levels and $E2$ transitions for ${}^{126}\mathrm{Ru}$ and ${}^{124}\mathrm{Mo}$ as their structure information is necessary for a complete understanding of the seniority picture. Our results, together with other existing evidence, support the conclusion that the shell closure persists at the neutron number $N=82$ in the neutron-rich region.

Figure 1

Comparison of calculated results with experimentally known energy levels for (a) ${}^{126}\mathrm{Pd}$, (b) ${}^{128}\mathrm{Pd}$ (both data taken from Ref. [8]), and (c) ${}^{130}\mathrm{Cd}$ (data taken from Ref. [7]).

Figure 2

(a) Experimental yrast $2^{+}–8^{+}$ states in the $N=50$ isotones from Refs. [16, 17] and (b) those in the $N=82$ isotones from Ref. [8] with the results of the shell-model calculation.

Figure 3

Calculated $B(E2;8^{+}\to 6^{+})$ values for ${}^{128}\mathrm{Pd}$ and ${}^{130}\mathrm{Cd}$ as functions of the $J=8,T=1$ matrix element of the Hamiltonian.

Figure 4

(a) Experimental $B(E2;8^{+}\to 6^{+})$ values in the $N=50$ isotones from Refs. [16, 17] and (b) those in the $N=82$ isotones from Ref. [8] with the results of the shell-model calculation.