On shielding of nuclear electric dipole moments in atoms

We demonstrate explicitly that some recent calculations of atomic electric dipole moments (EDM) are incomplete. A contribution overlooked therein is pointed out. When included, it cancels exactly the result of those calculations, and thus restores the standard conclusions for nuclear EDM in atoms. The existence of EDMs of elementary particles, nuclei, and atoms is forbidden by CP invariance. The predictions of the standard model of electroweak interactions for these EDMs are at least six orders of magnitude below the present experimental bounds. It makes experimental searches for EDMs, even at present level of accuracy, extremely sensitive to possible new physics beyond the standard model. The best upper limit on EDM of anything was obtained on the Hg atomic dipole moment [1]: d(Hg) < 2.1× 10 e cm. (1) Unfortunately, the implications of this result for the dipole moment of the valence neutron of the Hg nucleus is much less impressive [2]: |dn| < 4.0× 10 −25 e cm (2) (still, it is not so far away from the results of the direct measurements of the neutron EDM [3, 4]: |dn| < (0.6− 1.0)× 10 −25 e cm). The explanation is as follows. For a neutral atom of point particles, in equilibrium under the action of electrostatic forces, there is no effect due to the EDMs of the constituent particles [5, 6]. Indeed, the atom remains at rest when an external electric field Eext is applied. This comes about by an internal rearrangement of the system’s constituents giving rise to an internal field Eint that exactly cancels Eext at each charged particle, as required by the static equilibrium condition. Thus, there is no observable effect due to dipole moments of the system’s constituents; the external field is effectively switched off. A quantum mechanical proof of this statement was given in [7]. It was also pointed out therein that the shielding of atomic nucleus is not complete, observable nuclear EDM effects arise when one takes into account its finite size. Of course, the resulting suppression of these effects is quite