Large-scale shell-model study for excitations across the neutron $N=82$ shell gap in ${}^{131–133}\mathrm{Sb}$

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 $(0g_{7/2},1d_{5/2},1d_{3/2},2s_{1/2},0h_{11/2})$ for both protons and neutrons, with two additional neutron orbits $(1f_{7/2},2p_{3/2})$ 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.

Figure 1

Comparison of the calculated energy levels with the experimental data for ${}^{133}\mathrm{Sb}$. Data are taken from Refs. [15, 27, 35].

Figure 2

The calculated levels (opened diamond) of cross-shell excitations in ${}^{133}\mathrm{Sb}$, selected from the lowest configuration each for positive parity and negative parity and the lowest energy state for each spin, are compared with available experimental data [35] (filled square). The three experimental levels (opened square) with error bars are taken from Refs. [27, 28].

Figure 3

Illustration of the effects of monopole corrections (a) $k_{mc}$($\nu h_{11/2},\nu f_{7/2}$) and (b) $k_{mc}$($\nu d_{3/2},\nu f_{7/2}$) on cross-shell excitations in ${}^{133}\mathrm{Sb}$. Experimental data points are taken from Ref. [35].

Figure 4

Comparison of the calculated energy levels with the experimental data in ${}^{132}\mathrm{Sb}$. Data are taken from Refs. [35, 37, 38].

Figure 5

The experimental high-spin states of ${}^{132}\mathrm{Sb}$ above 2.5 MeV observed in Ref. [37] and the description of our shell-model calculation with their configurations.

Figure 6

Comparison of the calculated energy levels with the experimental data in ${}^{131}\mathrm{Sb}$. Data are taken from Refs. [35, 40].

Figure 7

The levels with $\mathrm{\Delta }I=2$ of (a) the $\nu h_{11/2}^{-2}$ multiplet in ${}^{130}\mathrm{Sn}$ and (b) the analogous levels of the $\pi g_{7/2}\nu h_{11/2}^{-2}$ multiplet in ${}^{131}\mathrm{Sb}$, both of experiment [35, 40] and theory.

Figure 8

The calculated levels of cross-shell excitations in ${}^{131}\mathrm{Sb}$, selected from the lowest configuration each for positive and negative parity and the lowest energy state for each spin.

Figure 9

Illustration of the effects of monopole corrections (a) $k_{mc}$($\nu h_{11/2},\nu f_{7/2}$) and (b) $k_{mc}$($\nu d_{3/2},\nu f_{7/2}$) on cross-shell excitations in ${}^{131}\mathrm{Sb}$.

Figure 10

Schematic illustration of transitions among the three positive-parity states $15/2^{+}, 13/2^{+}$, and $11/2^{+}$ in ${}^{133}\mathrm{Sb}$ with the configuration $\pi g_{7/2}\nu \left(h_{11/2}^{-1}{f}_{7/2}\right)$. See text for discussion. Experimental data are taken from Ref. [28].