Pairing Energies of the High-Spin Isomers in N=83 Isotones

High-spin isomers in $N$=83 isotones have been systematically studied. Excitation energies of these isomers locate between 8.5 and 9.0 MeV. Their spins and parities are 49/2$^+$ and 27$^+$ for odd and odd-odd nuclei, respectively. Life times range between $\sim$10ns and $\sim$$\mu$s. High-spin isomers have stretch coupled configurations resulting from the breaking of a neutron magic 82 core, such as [$\nu$(f$_{7/2}$h$_{9/2}$i$_{13/2}$) $\pi$h$_{11/2}$$^2$]$_{49/2}$$^+$ for odd nuclei and [$\nu$(f$_{7/2}$h$_{9/2}$i$_{13/2}$) $\pi$(d$_{5/2}^{-1}$h$_{11/2}$$^2$)]$_{27}$$^+$ for odd-odd nuclei. These high-spin isomers have oblate shapes and are called to be high-spin shape isomers. The proton pairing correlations of high-spin isomers are empirically extracted for the first time by using the excitation energies of these isomers as well as binding energies, based on the odd-even mass difference. The experimental pairing correlations of high-spin isomers are found to be almost the same as those of the ground states in $N$=83 isotones. Theoretical studies of the excitation energies and the pairing correlations of high-spin isomers are also performed and compared with the experimental data.