Theory of Raman scattering in superconductors

The electronic Raman scattering by pairs of quasiparticles is calculated at zero temperature, generalizing previous calculations that were based on the Bardeen-Cooper-Schrieffer model of a super-conductor. Analytical and numerical results are presented for the spectrum as a function of wave vector →q, and an integration is performed over qz to include the effect of a finite optical penetration depth. Allowing for gap anisotropy, we correct the results for vertex and Coulomb polarization effects. The theoretical results for finite q are used to calculate spectra for Nb₃Sn, V₃Si, and Nb, neglecting gap anisotropy. Experimental data are presented for V₃Si and Nb. The data for V₃Si are fit to a zero-q theory that includes gap anisotropy, with results similar to those presented earlier for Nb₃Sn. 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.