Calculation of a $P$- and $T$-Nonconserving Weak Interaction in Xe and Hg with Many-Body Perturbation Theory

The electronic part of a possible $P$- and $T$-nonconserving neutral-weak-current-induced electric dipole moment in atomic Xe and Hg was calculated with many-body perturbation theory. After the effects of this $P$- and $T$-nonconserving interaction on all core orbitals were treated self-consistently, thereby including all single-particle effects to all orders but no correlation effects, the results ${\mu }_e=(5.2\mathrm{}\times {10}^{-23\mathrm{}}e \mathrm{m})C_T{\sigma }_N$ and ${\mu }_e=-(6.0\mathrm{}\times {10}^{-22\mathrm{}}e \mathrm{m})C_T{\sigma }_N$, respectively, were obtained for Xe and Hg. The value for Xe can be combined with the recent experimental result, $\left|{\mu }_e\right({}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}\left)\right|<\mathrm{}{10}^{-28\mathrm{}}e \mathrm{m}$, to give the upper limit $\left|C_T\right|<\mathrm{}2\mathrm{}\times {10}^{-6\mathrm{}}$.