Strong-coupling properties of unbalanced Eliashberg superconductors

In this paper we investigate the thermodynamical properties of "unbalanced" superconductors, namely, systems where the electron-boson coupling lambda is different in the self-energy and in the Cooper channels. This situation is encountered in a variety of situations, for instance, in d-wave superconductors. Quite interesting is the case where the pairing in the self-energy is smaller than the one in the gap equation. In this case we predict a finite critical value lambda(c) where the superconducting critical temperature T-c diverges but the zero temperature gap is still finite. The specific heat, magnetic critical field, and the penetration depth are also evaluated.