Anisotropy effects in superconductors with magnetic impurities. I

The influence of Fermi surface anisotropy on the superconducting transition temperature of strong coupling superconductors containing magnetic and nonmagnetic impurities is investigated. It is found that the concentration dependent transition temperature shows typical departures from the corresponding curve of a single-band isotropic superconductor. These departures occur either for very small (_ij) or for very large (_ij0) interband scattering of conduction electrons on nonmagnetic impurities (i, j label the states in different bands or in different zones of the Fermi surface). In the case of unequal cut-off frequencies for different zones on the Fermi surface it is shown that all effects of unequal cut-offs can be eliminated by introducing effective electron-phonon pairing interactions. In the presence of impurities these effective pairing interactions become weakly impurity dependent giving rise to a new pair-weakening mechanism. Quantitative results on the basis of a simple two-band or two-zone model are presented.