Effect of Spatial Variations of the Superconducting Gap on Suppression of the Transition Temperature by Impurities

We calculate correction to the critical temperature of a dirty superconductor, which results from the local variations of the gap function near impurity sites. This correction is of the order of $T_c/E_F$ and becomes important for short-coherence length superconductors. It generally reduces a pair-breaking effect. In $s$-wave superconductors small amounts of nonmagnetic impurities can increase the transition temperature.