Construction of shell-model interactions for Z >~ 50, N >~ 82 nuclei: Predictions for A=133-134 beta - decays.

Abstract

Two-shell-model interactions are constructed in the model space of the five proton and six neutron orbits just above the double shell closure at $^{132}\mathrm{Sn}$. One interaction uses the two-body matrix elements calculated by Kuo and Herling for use near $^{208}\mathrm{Pb}$. For the other, the proton-proton two-body matrix elements are replaced with effective ones of Kruse and Wildenthal and selected proton-neutron matrix elements were varied in order to better reproduce the known energy spectra of $^{134}\mathrm{Sb}$. The main difficulty in this construction is the determination of the neutron single-particle energies. This determination was done by comparison of theoretical and experimental (d,p) spectroscopic factors for the N=83, Z=54, 56, and 58 isotones. The \ensuremath{\Delta}J\ensuremath{\ne}0 first-forbidden ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ decays of $^{133}\mathrm{Sn}$(7/${2}^{\mathrm{\ensuremath{-}}}$), $^{134}\mathrm{Sn}$(${0}^{+}$), $^{134}\mathrm{Sb}$(${0}^{\mathrm{\ensuremath{-}}}$), and $^{134}\mathrm{Sb}$(${7}^{\mathrm{\ensuremath{-}}}$) were considered in order to exemplify the application of these interactions.