Nuclear electric dipole moment with relativistic effects in Xe and Hg atoms

Abstract

The atomic electric dipole moment (EDM) is evaluated by considering the relativistic effects as well as nuclear finite size effects in Xe and Hg atomic systems. Due to Schiff's theorem, the first order perturbation energy of EDM is canceled out by the second order perturbation energy for the point nucleus. The nuclear finite size effects arising from the intermediate atomic excitations may be finite for deformed nucleus but it is extremely small. The finite size contribution of the intermediate nuclear excitations in the second order perturbation energy is completely canceled by the third order perturbation energy. As the results, the finite contribution to the atomic EDM comes from the first order perturbation energy of relativistic effects, and it amounts to around 0.3 and 0.4 percents of the neutron EDM ${d}_{n}$ for Xe and Hg, respectively, though the calculations are carried out with a simplified single-particle nuclear model. From this relation in Hg atomic system, we can extract the neutron EDM which is found to be just comparable with the direct neutron EDM measurement.