AtomicCP-violating polarizability

Abstract

Searches for $CP$-violating effects in atoms and molecules provide important constrains on competing extensions to the standard model of elementary particles. In particular, $CP$ violation in an atom leads to the $CP$-odd (T,P-odd) polarizability ${\ensuremath{\beta}}^{\mathrm{CP}}$: a magnetic moment ${\ensuremath{\mu}}^{\mathrm{CP}}$ is induced by an electric field ${\mathcal{E}}_{0}$ applied to an atom, ${\ensuremath{\mu}}^{\mathrm{CP}}={\ensuremath{\beta}}^{\mathrm{CP}}{\mathcal{E}}_{0}$. We estimate the $CP$-violating polarizability for rare-gas (diamagnetic) atoms He through Rn. We relate ${\ensuremath{\beta}}^{\mathrm{CP}}$ to the permanent electric dipole moment (EDM) of the electron and to the scalar constant of the $CP$-odd electron-nucleus interaction. The analysis is carried out using the third-order perturbation theory and the Dirac-Hartree-Fock formalism. We find that, as a function of nuclear charge $Z,\phantom{\rule{0.2em}{0ex}}{\ensuremath{\beta}}^{\mathrm{CP}}$ scales steeply as ${Z}^{5}R(Z)$, where slowly varying $R(Z)$ is a relativistic enhancement factor. Finally, we evaluate the feasibility of setting a limit on electron EDM by measuring $CP$-violating magnetization of liquid Xe. We find that such an experiment could provide competitive bounds on electron EDM only if the present level of experimental sensitivity to ultraweak magnetic fields [Kominis et al., Nature 422, 596 (2003)] is improved by several orders of magnitude.