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

TL;DR

This paper performs large-scale shell-model calculations to estimate the nuclear Schiff moments of $^{129}$Xe and $^{199}$Hg, reducing theoretical uncertainties and exploring nuclear structure effects to better constrain CP violation beyond the standard model.

Contribution

The study introduces large-scale shell-model calculations with realistic interactions to evaluate Schiff moments, addressing discrepancies among nuclear models and highlighting the impact of configuration mixing.

Findings

Schiff moments are reduced by ~10% due to configuration mixing.

Significant quenching of the Schiff moment occurs in the second 1/2- state of $^{199}$Hg.

Shell-model results differ from mean-field and truncated models, emphasizing the importance of detailed nuclear structure.

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.