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

Impurities with the pronounced forward scattering (FS impurities) change analytical properties of the quasiparticle Green's function substantially compared to the isotropic 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 \alpha is small. The FS impurities make \alpha =1/2 in the dirty limit and affect in the same way the s- and d-wave FEP pairing. The FS impurities are pair-weakening in both pairing channels. The usual isotropic impurity scattering is pair-weakening for the s-wave and pair-breaking for the d-wave FEP pairing.