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

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 ($0g_{\frac{7}{2}}, 1d_{\frac{5}{2}}$) and a large space ($0g_{\frac{7}{2}}, 1d_{\frac{5}{2}}, 0h_{\frac{11}{2}}, 2s_{\frac{1}{2}}, 2s_{\frac{1}{2}}$). 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 ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$.