Probing the single-particle behavior above $^{132}$Sn via electromagnetic moments of $^{133,134}$Sb and $N=82$ isotones

Magnetic and quadrupole moments of the $7/2^+$ ground state in $^{133}$Sb and the ($7^-$) isomer in $^{134}$Sb have been measured by collinear laser spectroscopy to investigate the single-particle behavior above the doubly magic nucleus $^{132}$Sn. The comparison of experimental data of the $7/2^+$ states in $^{133}$Sb and neighboring $N = 82$ isotones to shell-model calculations reveals the sensitivity of magnetic moments to the splitting of the spin-orbit partners $\pi 0g_{9/2}$ and $\pi 0g_{7/2}$ across the proton shell closure at $Z = 50$. In contrast, quadrupole moments of the N = 82 isotones are insensitive to cross-shell excitations, but require the full proton model space from $Z = 50$ to 82 for their accurate description. In fact, the linear trend of the quadrupole moment follows approximately the expectation of the seniority scheme when filling the $\pi 0g_{7/2}$ orbital. As far as the isomer in $^{134}$Sb is concerned, its electromagnetic moments can be perfectly described by the additivity rule employing the moments of $^{133}$Sb and $^{133}$Sn, respectively. These findings agree with shell-model calculations and thus confirm the weak coupling between the valence proton and neutron in $^{134}$Sb.