Atomic electric dipole moments: The Schiff theorem and its corrections

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 pointlike, nonrelativistic constituents that interact only electrostatically. Any experimental observation of a nonzero atomic EDM would result from corrections to the pointlike, 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.