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 $\sigma \sigma \tau \tau$ and $\sigma \sigma$ interactions. Comparing the results of the sum-rule approach with those of large-scale shell-model calculations for the ${}^{52}\mathrm{Fe}\left({12}^{+}\right)$ and ${}^{94}\mathrm{Ag}\left({21}^{+}\right)N=Z$ high-spin isomers, the deduced ${\kappa }_{\sigma }$, which is the strength of the $\sigma \sigma$ residual interaction in a simple residual-interaction model, is 2.5 MeV.

Figure 1

(top) Gamow-Teller transition strength distributions from the ${}^{52}\mathrm{Fe}\left({12}^{+}\right)$ initial state calculated by the shell model in the full $pf$-shell-model space with the GXPF1J [32] effective interaction. Transition strengths are averaged by a Lorentzian weighting function with a width of 0.5 MeV. The excitation energy is defined from the initial state. The quenching factor is not adapted. (bottom) Same as the top but for the isoscalar $M1$ transitions from the ${}^{52}\mathrm{Fe}\left({12}^{+}\right)$ state.

Figure 2

Same as Fig. 1 but for the transitions from the ${}^{94}\mathrm{Ag}\left({21}^{+}\right)$ initial state. In the shell-model calculation, the $(2p_{1/2},1g_{9/2},1g_{7/2},2d_{5/2})$ shell-model space and a modified PIGD5G3 [33] interaction are employed.