Shell-model studies for theSn132region. I. Few proton cases

Abstract

The Brueckner $G$ matrix from the Reid soft-core potential is taken for the leading contribution of the effective two-proton interaction in the $^{132}\mathrm{Sn}$ region. Phenomenological two-body pairing and multipole forces are added to adjust for all neglected effect. Two model spaces are selected; a small space ($0{g}_{\frac{7}{2}}, 1{d}_{\frac{5}{2}}$) and a large space ($0{g}_{\frac{7}{2}}, 1{d}_{\frac{5}{2}}, 0{h}_{\frac{11}{2}}, 2{s}_{\frac{1}{2}}, 2{s}_{\frac{1}{2}}$). For each space the strengths of the phenomenological terms are adjusted to fit the $^{134}\mathrm{Te}$ spectrum. It is found that both of the total interactions have a high statistical correlation with the bare $G$ matrix. The total effective interactions are then used without further adjustment in shell model calculations to obtain good predictions for the spectra of $^{135}\mathrm{I}$, $^{136}\mathrm{Xe}$, and $^{137}\mathrm{Cs}$.NUCLEAR STRUCTURE Shell-model structure of $^{132}\mathrm{Sn}$ core plus valence protons: shell-model effective interactions consisting of Brueckner reaction matrix plus phenomenological multipole corrections.