Theory of Raman scattering in superconductors

The electronic Raman scattering by pairs of quasiparticles is calculated at zero temp., generalizing previous calculations that were based on the Bardeen--Cooper--Schrieffer model of a superconductor. Analytical and numerical results are presented for the spectrum as a function of wave vector q, and an integration is performed over q sub z to include the effect of a finite optical penetration depth. Allowing for gap anisotropy, the results are corrected for vertex and Coulomb polarization effects. The theoretical results for finite q are used to calculate spectra for Nb sub 3 Sn, V sub 3 Si, and Nb, neglecting gap anisotropy. Experimental data are presented for V sub 3 Si and Nb. The data for V sub 3 Si are fit to a zero-q theory that includes gap anisotropy, with results similar to those presented earlier for Nb sub 3 Sn. The role of possible excitons on the Raman spectra is examined. These theoretical results are then used to discuss the self-energy of a Raman-active optical phonon in a superconductor. 34 ref.--AA