Energy-weighted sum rule for Gamow-Teller giant resonances in high-spin isomeric states of N=Z nuclei

The sum-rule approach and the shell model are used to estimate the energies of Gamow-Teller (GT) giant resonances in high-spin isomeric (HSI) states in $N=Z$ nuclei. The newly derived energy-weighted sum rules show that the GT resonance energies of HSI states are related to the $\ensuremath{\sigma}\ensuremath{\sigma}\ensuremath{\tau}\ensuremath{\tau}$ and $\ensuremath{\sigma}\ensuremath{\sigma}$ interactions. Comparing the results of the sum-rule approach with those of large-scale shell-model calculations for the $^{52}\mathrm{Fe}({12}^{+})$ and $^{94}\mathrm{Ag}({21}^{+})\phantom{\rule{4pt}{0ex}}N=Z$ high-spin isomers, the deduced ${\ensuremath{\kappa}}_{\ensuremath{\sigma}}$, which is the strength of the $\ensuremath{\sigma}\ensuremath{\sigma}$ residual interaction in a simple residual-interaction model, is 2.5 MeV.