Atomic Electric Dipole Moments: The Schiff Theorem and Its Corrections

TL;DR

This paper reformulates Schiff's theorem at the operator level, clarifies the origin of corrections to atomic EDMs, and identifies the limitations of previous models, enhancing the theoretical framework for interpreting EDM experiments.

Contribution

The paper introduces a new operator-level reformulation of Schiff's theorem, deriving a corrected Schiff moment operator and highlighting previously overlooked corrections.

Findings

Derived a new form of the Schiff moment operator accounting for finite nuclear size.

Showed that previous operators are special cases under certain approximations.

Identified additional corrections to Schiff screening not included in earlier models.

Abstract

Searches for the permanent electric dipole moments (EDMs) of diamagnetic atoms provide powerful probes of CP-violating hadronic and semileptonic interactions. The theoretical interpretation of such experiments, however, requires careful implementation of a well-known theorem by Schiff that implies a vanishing net EDM for an atom built entirely from point-like, nonrelativistic constituents that interact only electrostatically. Any experimental observation of a nonzero atomic EDM would result from corrections to the point-like, nonrelativistic, electrostatic assumption. We reformulate Schiff's theorem at the operator level and delineate the electronic and nuclear operators whose atomic matrix elements generate corrections to "Schiff screening". We obtain a form for the operator responsible for the leading correction associated with finite nuclear size -- the so-called "Schiff moment" operator -- and observe that it differs from the corresponding operator used in previous Schiff moment computations. We show that the more general Schiff moment operator reduces to the previously employed operator only under certain approximations that are not generally justified. We also identify other corrections to Schiff screening that may not be included properly in previous theoretical treatments. We discuss practical considerations for obtaining a complete computation of corrections to Schiff screening in atomic EDM calculations.