Structure analysis for hole-nuclei close to ${}^{132}$Sn by a large-scale shell-model calculation

The structure of neutron-rich nuclei with a few holes in respect of the doubly magic nucleus ${}^{132}$Sn is investigated by means of large-scale shell-model calculations. For a considerably large model space, including orbitals allowing both neutron and proton core excitations, an effective interaction for the extended pairing-plus-quadrupole model with monopole corrections is tested through detailed comparison between the calculation and experimental data. By using the experimental energy of the core-excited $21/2^{+}$ level in ${}^{131}$In as a benchmark, monopole corrections are determined that describe the size of the neutron $N=82$ shell gap. The level spectra, up to 5 MeV of excitation in ${}^{131}$In, ${}^{131}$Sn, ${}^{130}$In, ${}^{130}$Cd, and ${}^{130}$Sn, are well described and clearly explained by couplings of single-hole orbitals and by core excitations.

Figure 1

The experimental energy levels in ${}^{131}$In taken from [36] and the results of shell-model calculation.

Figure 2

Effects of the proposed monopole corrections in the ${}^{131}$In calculation.

Figure 3

The experimental energy levels in ${}^{131}$Sn taken from [36] and the results of shell model calculation. The four experimental levels (blue color marked with star) are the latest experimental energy levels [9].

Figure 4

Comparison of the high-spin part of the calculated energy levels (black dots) with experimental data [4] (red squares) in ${}^{131}$Sn.

Figure 5

The experimental energy levels in ${}^{130}$In taken from [36] and the results of the shell-model calculation.

Figure 6

The members of the $\pi g_{9/2}^{-1}\nu h_{11/2}^{-1}$ multiplet predicted by the shell-model calculation for ${}^{130}$In.

Figure 7

The experimental energy levels in ${}^{130}$Cd taken from [36] and the results of the shell-model calculation.

Figure 8

The experimental energy levels in ${}^{130}$Sn taken from [36] and the results of the shell-model calculation.