Seniority isomerism in proton-rich N=82 isotones and its indication to stiffness of the Z=64 core

The ${10}^{+}$ and $27\mathrm{/}{2}^{-}$ isomers of the $Z>64$, $N=82$ nuclei are investigated in the shell model framework. We derive an extended seniority reduction formula for the relevant $E2$ transition strengths. Based on the extended formula, as well as on the approximate degeneracy among the $0h_{11\mathrm{/}2}$, $2s_{1\mathrm{/}2}$ and $1d_{3\mathrm{/}2}$ orbits, we argue that the $B(E2)$ data require the ${}^{146}$Gd core excitation. The energy levels of both parities and the $B(E2)$ values are simultaneously reproduced by a multi-$j$ shell model calculation with the MSDI, if the excitations from $(0g_{7\mathrm{/}2}1d_{5\mathrm{/}2})$ to $(0h_{11\mathrm{/}2}2s_{1\mathrm{/}2}1d_{3\mathrm{/}2})$ are taken into account.