By assuming that the superconducting pairing is due to the forward E-P scattering (F EP pairing) it is shown that the critical temperature of clean systems Tc0 depends linearly on the E-P coupling constant λ and the isotope effect α is very small. Impurities with the pronounced forward scattering (F S impurities) change analytical properties of the quasiparticle Green's function substantially compared to the case of the isotropic scattering. The F S impurities are pair-breaking and affect in the same way sand d-wave F EP pairing making α = 1/2 in the dirty limit.The usual isotropic impurity scattering is pair-weakening for s-wave and pair-breaking for the d-wave F EP pairing.PACS. 74.20.-z Theories and models of superconducting state -74.25.-q General properties; correlations between physical properties in normal and superconducting states

We investigate effects of a nonadiabatic electron-phonon(boson) interaction on the quasiparticle self-energy in the lowest order in the coupling constant.Existing approaches either overestimate, or underestimate these effects because of different approximations for momentum and frequency dependences of the vertex corrections. The connection between the nonadiabaticity and a possible instability of the interacting Fermi system is discussed as well.

In some newly discovered materials the ratio of phonon to electron energies is no longer small. We have investigated the basement of the recently proposed gauge-invariant self-consistent method and found conditions of its applicability.

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The sharp forward electron-phonon (F EP ) and impurity (F IS) scattering change the normal and superconducting properties significantly. The pseudo-gap like features are present in the density of states for ω < Ω, where Ω is the phonon frequency. The superconducting critical temperature Tc, due to the F EP pairing, is linear with respect to the electron-phonon coupling constant. The F IS impurities are pair weakening for s− and d − wave pairing.