Ab initio determination of the $P$- and $T$-violating coupling constants in atomic Xe by the relativistic-coupled-cluster method

The parity (P) and time-reversal (T) odd coupling constant associated with the tensor-pseudotensor (T-PT) electron-nucleus interaction and the nuclear Schiff moment (NSM) have been determined by combining the result of the measurement of the electric dipole moment (EDM) of a ${}^{129}\mathrm{Xe}$ atom and our calculations based on the relativistic-coupled-cluster (RCC) theory. Calculations using various relativistic many-body methods have been performed at different levels of approximation. The accuracies of our results are estimated by comparing our dipole polarizability calculations of the ground state of Xe with its most precise available experimental data, and taking into consideration the difference of the results of our RCC single- and double-excitation calculations with and without the important triple excitations as well as the size of our basis set. The nonlinear terms that arise in the RCC theory were found to be crucial for achieving high accuracy in the calculations. We obtain the upper limits for the T-PT electron-nucleus coupling coefficient and NSM as $1.6\times {10}^{-6}$ and $1.2\times {10}^{-9}e{\text{fm}}^3$, respectively, by combining our calculations with the available measurement. Our results, in combination with future EDM measurements in atomic Xe, could improve these limits further.

Figure 1

Example of a few dominant non-CPHF diagrams from the MBPT(3) method involving $D$ and the corresponding perturbed interaction operator $H_{\text{add}}$.

Figure 2

Diagram involving effective one-body dipole operator $\overline{D}$ and the perturbed wave operator ${\Omega }^{\left(1\right)}$ that accounts for the contributions from the singly excited configurations.