Nuclear Schiff moment and time-invariance violation in atoms

Parity- and time-invariance-violating $(P,T$-odd) nuclear forces produce $P,T$-odd nuclear moments. In turn, these moments can induce electric dipole moments (EDMs) in atoms through the mixing of electron wave functions of opposite parity. The nuclear EDM is screened by atomic electrons. The EDM of an atom with closed electron subshells is induced by the nuclear Schiff moment. Previously the interaction with the Schiff moment has been defined for a pointlike nucleus. No problems arise with the calculation of the electron matrix element of this interaction as long as the electrons are considered to be nonrelativistic. However, a more realistic model obviously involves a nucleus of finite size and relativistic electrons. In this work we have calculated the finite nuclear size and relativistic corrections to the Schiff moment. The relativistic corrections originate from the electron wave functions and are incorporated into a “nuclear” moment, which we term the local dipole moment. For ${}^{199}\mathrm{Hg}$ these corrections amount to $\sim 25\%.$ We have found that the natural generalization of the electrostatic potential of the Schiff moment for a finite-size nucleus corresponds to an electric-field distribution which, inside the nucleus, is well approximated as constant and directed along the nuclear spin, and outside the nucleus is zero. Also in this work the ${}^{239}\mathrm{Pu}$ atomic EDM is calculated.