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

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.

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