Impurities with retarded interaction with quasiparticles in a s-wave superconductor

A perturbation theory and a diagram technique for a disordered metal are proposed when scattering of quasiparticles by nonmagnetic impurities is caused with a retarded interaction. The perturbation theory generalizes a case of the 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 a s-wave superconductor increases its critical temperature. We showed the amplification of superconducting properties is a result of nonelastic effects in a scattering by the impurities.