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

The pairing interaction V(k-k¹) is often replaced by a constant V (usually taken to be the average of V(k-k¹) 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-k¹) 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.