Large-scale shell-model calculations of nuclear Schiff moments of ${}^{129}$Xe and ${}^{199}$Hg

Abstract

The theoretical uncertainty in the nuclear Schiff moment is an obstacle to set constraints on $CP$ violation beyond the standard model from experimental upper bounds on atomic electric dipole moments. We perform large-scale shell-model calculations of the ${}^{129}$Xe and ${}^{199}$Hg nuclei with realistic effective interactions. To estimate the Schiff moments caused by the $P$, $T$-odd $\pi NN$ interaction perturbatively, we employ the one-particle one-hole approximation to the intermediate states. The Schiff moments of ${}^{129}$Xe and ${}^{199}$Hg are reduced due to the configuration mixing by $\sim 10\%$ from the evaluation of the independent particle model. On the other hand, the reduction is more significant in mean-field based calculations and shell-model calculations with a drastic truncation. In order to resolve the discrepancy in the Schiff moment of ${}^{199}$Hg among several nuclear models, we survey low-energy nuclear structure. The large-scale shell-model calculations reveal that the Schiff moment of ${}^{199}$Hg is considerably quenched in the second ${\frac{1}{2}}^{-}$ state.