Towards the search of electron electric dipole moment: correlation calculations of the P,T-violation effect in the Eu${}^{++}$ cation

Recently the Eu${}_{0.5}$Ba${}_{0.5}$TiO${}_3$ solid was suggested as a promising candidate for experimental search of the electron electric dipole moment. To interpret the results of this experiment one should calculate the effective electric field acting on an unpaired (spin-polarized) electrons of europium cation in the crystal because the value of this field cannot be measured experimentally. The Eu${}^{++}$ cation is considered in the paper in the uniform external electric field $E_{\mathrm{e}\mathrm{x}\mathrm{t}}$ as our first and simplest model simulating the state of europium in the crystal. We have performed high-level electronic structure correlation calculation using coupled clusters theory (and scalar-relativistic approximation for valence and outer core electrons at the molecular pseudopotential calculation stage that is followed by the four-component spinor restoration of the core electronic structure) to evaluate the enhancement coefficient $K=E_{\mathrm{e}\mathrm{f}\mathrm{f}}\mathrm{/}{E}_{\mathrm{e}\mathrm{x}\mathrm{t}}$ (where $E_{\mathrm{e}\mathrm{x}\mathrm{t}}$ is the applied external electric field and $E_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the induced effective electric field acting on an unpaired electron in Eu${}^{++}$). A detailed computation analysis is presented. The calculated value of $K$ is -4.6.