Multiconfiguration Dirac-Hartree-Fock calculations of atomic electric dipole moments of ${}^{225}\mathrm{Ra}$, ${}^{199}\mathrm{Hg}$, and ${}^{171}\mathrm{Yb}$

The multiconfiguration Dirac-Hartree-Fock method is employed to calculate atomic electric dipole moments in the ground states of ${}^{225}\mathrm{Ra}$, ${}^{199}\mathrm{Hg}$, and ${}^{171}\mathrm{Yb}$. For the calculations of the matrix elements we extend the relativistic atomic structure package grasp2k. The extension includes programs to evaluate matrix elements of $\mathcal{P}\mathcal{T}$-odd electron-nucleus tensor-pseudotensor and pseudoscalar-scalar interactions, the atomic electric dipole operator, the nuclear Schiff moment, and the interaction of the electron electric dipole moment with nuclear magnetic moments. The interelectronic interactions are accounted for through valence and core-valence electron correlation effects. The electron shell relaxation is included with separately optimized wave functions of opposite parities.

Figure 1

Large components $P\left(r\right)$ of the one-electron $np$ radial orbitals of the triplet states $6snp{}^3{P}_1$ ($n=6,7,8,9$) of ${}^{199}\mathrm{Hg}$. The solid line (colored) sections represent the radial shapes of the orbitals inside the ${}^{199}\mathrm{Hg}$ nucleus. The $P\left(r\right)$ are in arbitrary units and the radial grid is in atomic units. See the text for further details.

Figure 2

Tensor-pseudotensor interaction contributions to the atomic EDM in ${}^{199}\mathrm{Hg}$, multiplied by the energy denominators, as a function of the effective quantum number $n^{*}$ of the $np$ orbitals ($n=6,7,8,9,10$) from the triplet $6snp{}^3{P}_1$ (blue solid line with circles) and the singlet $6snp{}^1{P}_1$ (red dashed line with squares) individual states of ${}^{199}\mathrm{Hg}$. See the text for further details.