Coherent potential approximation for strong-coupling superconducting transition-metal alloys

Within the coherent potential approximation (CPA) a theory for strong-coupling superconducting transition-metal alloys is developed. The configurational dependence of the selfenergy-part is discussed and, in analogy to McMillan, an expression forT _c is derived for a singles band as well as for anΓ′₂₅-band. The electron-phonon coupling constantλ occuring in this expression depends explicitly on: the average component density of states,N _A (0) andN _B (0), the electron-phonon matrix elements of the components, the difference of the atomic energy levels,δ, and the phonon Green's function at zero frequency. In the limit of the pure metal this expression reduces to that developed by Appel and Kohn. It is shown that the change of the phonon density of states in an alloy due to the atomic mass differences — which is very complicated — does not influence the value ofλ.