Construction of shell-model interactions forZ≳50,N≳82 nuclei: Predictions forA=133–134β−decays

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 ΔJ≠0 first-forbidden ${\mathrm{\beta }}^{\mathrm{-}}$ decays of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Sn}$(7/$2^{\mathrm{-}}$), ${}_{}{}^{134}{}_{}{}^{}\mathrm{Sn}$($0^{+}$), ${}_{}{}^{134}{}_{}{}^{}\mathrm{Sb}$($0^{\mathrm{-}}$), and ${}_{}{}^{134}{}_{}{}^{}\mathrm{Sb}$($7^{\mathrm{-}}$) were considered in order to exemplify the application of these interactions.