Normal and superconducting state in the presence of forward electron-phonon and impurity scattering

By assuming that the superconducting pairing is due to the forward E-P scattering (FEP pairing) it is shown that the critical temperature of clean systems T-c0 depends linearly on the E-P coupling constant lambda and the isotope effect ct is very small. Impurities with the pronounced forward scattering (FS impurities) change analytical properties of the quasiparticle Green's function substantially compared to the case of the isotropic scattering. The FS impurities are pair-breaking and affect in the same way sand d-wave FEP pairing making alpha = 1/2 in the dirty limit. The usual isotropic impurity scattering is pair-weakening for s-wave and pair-breaking for the d-wave FEP pairing.