Shell Model Description of $^{102-108}$Sn Isotopes

TL;DR

This paper uses shell model calculations with different interactions to study neutron-deficient Sn isotopes near $^{100}$Sn, comparing results with recent experimental data to test the model's effectiveness in this region.

Contribution

It provides a comparative shell model analysis of $^{102-108}$Sn isotopes using two interactions and different single-particle energy assumptions, testing the model against experimental data.

Findings

Shell model calculations agree fairly well with experimental data.

Different interactions and single-particle energy adjustments impact results.

The study tests the shell model's applicability near the doubly magic $^{100}$Sn.

Abstract

We have performed shell model calculations for neutron deficient even $^{102-108}$Sn and odd $^{103-107}$Sn isotopes in $sdg_{7/2}h_{11/2}$ model space using two different interactions. The first set of interaction is due to Brown {\it et al.} and second is due to Hoska {\it et al}. The calculations have been performed using doubly magic $^{100}$Sn as core and valence neutrons are distributed over the single particle orbits 1$g_{7/2}$, 2$d_{5/2}$, 2$d_{3/2}$, 3$s_{1/2}$ and 1$h_{11/2}$. In more recent experimental work for $^{101}$Sn [Phys. Rev. Lett. {\bf 105} (2010) 162502], the g.s. is predicted as 5/2$^+$ with excited 7/2$^+$ at 172 keV. We have also performed another two set of calculations by taking difference in single particle energies of 2$d_{5/2}$ and 1$g_{7/2}$ orbitals by 172 keV. The present state-of-the-art shell model calculations predicts fair agreements with the experimental data. These calculations serve as a test of nuclear shell model in the region far from stability for unstable Sn isotopes near the doubly magic $^{100}$Sn core.