Theory of s-wave superconductor containing impurities with retarded interaction with quasiparticles

We propose a perturbation theory and diagram technique for a disordered metal when scattering of quasiparticles by nonmagnetic impurities is caused with a retarded interaction. The perturbation theory generalizes a case of elastic scattering in a disordered metal. Eliashberg equations for s-wave superconductivity are generalized for such a disordered superconductor. Anderson's theorem is found to be violated in the sense that embedding of the impurities into an s-wave superconductor increases its critical temperature. We show that the amplification of superconducting properties is a result of nonelastic effects in a scattering by the impurities.