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The $10^+$ and $27/2^-$ isomers of the $Z>64$, $N=82$ nuclei are investigatedin the shell model framework. We derive an extended seniority reduction formulafor the relevant $E2$ transition strengths. Based on the extended formula, aswell as on the approximate degeneracy among the $0h_{11/2}$, $2s_{1/2}$ and$1d_{3/2}$ orbits, we argue that the $B(E2)$ data require the $^{146}$Gd coreexcitation. The energy levels of both parities and the $B(E2)$ values aresimultaneously reproduced by a multi-$j$ shell model calculation with the MSDI,if the excitations from $(0g_{7/2}1d_{5/2})$ to $(0h_{11/2}2s_{1/2}1d_{3/2})$are taken into account.Comment: To be published in Phys. Rev. C, Revtex 25 pages with 9 Postscript  figure

physical review. c. nuclear physics/physical review. c, nuclear physics

Seniority isomerism in proton-rich<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>82</mml:mn><mml:mn /></mml:math>isotones and its indication to stiffness of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>64</mml:mn><mml:mn /></mml:math>core

Seniority isomerism in proton-richN=82isotones and its indication to stiffness of theZ=64core