Large-scale shell-model study for excitations across the neutron N=82 shell gap in Sb131–133

The cross-shell excitations in the mass-130 region are determined by the behavior of the single-particle (or single-hole) states around the doubly magic nucleus $^{132}\mathrm{Sn}$ and the size of the energy gaps at $N=82$ and/or $Z=50$. The present work reports on the results from large-scale shell-model calculations with the extended paring plus quadrupole-quadrupole force, usually with additions of monopole corrections (the EPQQM model). This paper applies the EPQQM model to the northwestern quadrant of $^{132}\mathrm{Sn}$. The model space includes the orbits of $(0{g}_{7/2},1{d}_{5/2},1{d}_{3/2},2{s}_{1/2},0{h}_{11/2})$ for both protons and neutrons, with two additional neutron orbits $(1{f}_{7/2},2{p}_{3/2})$ above the $N=82$ shell gap, allowing cross-shell excitations. It is found that the experimentally known low-lying levels for $^{133}\mathrm{Sb}, ^{132}\mathrm{Sb}$, and $^{131}\mathrm{Sb}$ can be well described. The highly excited states above 4.0 MeV are clearly explained as excitations across the neutron $N=82$ shell gap. The monopole effects in these nuclei are carefully examined. In contrast to the already studied northeastern and southwestern quadrants around $^{132}\mathrm{Sn}$ by the EPQQM model, the description of the current Sb data does not request particular monopole corrections. Experiments to further explore the cross-shell excitations in the Sb isotopes are called for.