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

• Received 6 June 2000

DOI:https://doi.org/10.1103/PhysRevC.62.054304