Extension of the Schiff theorem to ions and molecules

Abstract

According to the Schiff theorem the nuclear electric dipole moment (EDM) is screened in neutral atoms. In ions this screening is incomplete. We extend a derivation of the Schiff theorem to ions and molecules. The finite nuclear size effects are considered including Z^2 alpha^2 corrections to the nuclear Schiff moment which are significant in all atoms and molecules of experimental interest. We show that in majority of ionized atoms the nuclear EDM contribution to the atomic EDM dominates while in molecules the contribution of the Schiff moment dominates. We also consider the screening of electron EDM in ions

Lorentz-violating contributions to the nuclear Schiff moment and nuclear EDM

“…In accordance with the literature [10,15,22], the term inside brackets in Eq. (8) corresponds to an octupole moment operator that can be neglected.…”

“…Numerical evaluations of the Schiff moment [17] and their relation to the atomic EDM magnitude (for a few heavy atoms) are also known [18]. Further developments include, for example, a more general form of the Schiff moment obtained via calculations at the operator level [19], the evaluation of internal nucleon contribution to the Schiff moment [20], the enhancement of Schiff and octupole moments (by more than 2 orders of magnitude) in atoms with asymmetrically deformed nuclei with collective P and T-odd electromagnetic interactions [21], analysis of the Schiff theorem in ions and molecules [22], and other important results [23].…”

Measurement of the permanent electric dipole moment of the Xe129 atom

“…Here, the colocated nuclear polarized 3 He atoms solely serve as a co-magnetometer. EDM contributions in helium are strongly suppressed by Schiff screening (d ∝ Z 2 ) [15,16]. Note that for ideal co-magnetometry, the weighted frequency difference directly projects out the EDM effect one is looking for, without the need to switch the electric field.…”

Screening of nucleon electric dipole moments in nuclei

“…For completeness we present a short proof of the Schiff theorem that applies to neutral systems, and can be adapted to charged systems (see [11] for an example of the Schiff theorem applied to ions). The total Hamiltonian of non-relativistic particles in a constant electric E field, interacting through electrostatic forces can be written as:…”

“…The Schiff theorem (see [6] and its extensions [7][8][9][10][11]) states that in a neutral system of non-relativistic point-like particles with Coulomb interactions, the particles' intrinsic electric dipole moments are completely screened. As a consequence, in a neutral atomic system the nuclear EDM is screened and only the residual EDM of the nucleus after screening, known as the nuclear Schiff moment, can be observed.…”