  In a recent article, Kim and Overhauser [Phys. Rev. B 47, 8025 (1993)] have
found fault with the theory of impure superconductors by Abrikosov and Gor'kov
and have proposed an alternative formalism based on Green's functions which are
not derivable from a Dyson equation. Although the corrections to the
Abrikosov-Gor'kov theory found by Kim and Overhauser are correct for
non-retarded interactions, I argue that these corrections do not appear when
one treats realistic retarded interactions within the field-theoretic approach
of Abrikosov and Gor'kov. Direct numerical computation of the impurity-induced
suppression of the superconducting transition temperature Tc for both retarded
and non-retarded interactions illustrates these points. I conclude that
Abrikosov-Gor'kov theory applied to physical electron-electron interactions
yields a tractable formalism which accurately predicts the effects of magnetic
and non-magnetic impurities on Tc.
