Theoretical studies of the effect of pair scattering process on two-gap superconductivity in Eliashberg theory

Two‐gap superconductivity is investigated from the viewpoint of strong electron–phonon coupling including effective electron–electron interaction within an extension of the Eliashberg theory. The two‐band Eliashberg theory is extended to a more general formalism, including the pair scattering process between two bands. We present a coupled extended Eliashberg equation. We discuss the contribution of effective electron–electron interaction and the electron–phonon coupling to two‐gap superconductivity in relation to frequency dependence, using the extended Eliashberg equation and a model for phonon spectral density. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006