  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.
