Effect on the superconducting temperature of the momentum dependence of the electron-electron interaction

Abstract

The pairing interaction V(k-k 1) is often replaced by a constant V (usually taken to be the average of V(k-k 1) over the Fermi surface) in the calculation of the superconducting transition temperature T c in the standard BCS theory. We examine here the effect of an anisotropic momentum dependence in V(k-k 1) on T c. We present here results for a model separable interaction containing a parameter that controls the anisotropy. We show that for this model T c is always larger than the corresponding BCS averaged value.