Theory for the effects of impurities on the Raman spectra of superconductors. II. Temperature dependence and influence of final-state interactions

The influence of final-state interactions on the electronic Raman scattering by pairs of quasiparticles in disordered superconductors is presented using the formalism developed in a previous paper [Phys. Rev. B 45, 12 965 (1992)]. Below the gap, the effect of impurities on both the position and strength of the bound state is calculated, while additional modifications of the Raman spectrum above the gap due to final-state interactions are presented. Previous results for the position of the bound state by Maki and Tsuneto are obtained, while it is additionally shown that the strength of the collective mode diminishes rapidly with increasing disorder. While the Raman spectrum above the gap sharpens with the inclusion of final-state interactions for small disorder, for larger disorder the effects of final-state interactions become completely negligible. The temperature dependence of the theory is investigated and it is shown that a non-BCS temperature dependence of the peak in the Raman spectrum can be obtained for strong impurity scattering.