Effects of inelastic electron-electron scattering on branch imbalance relaxation

The rate for branch-imbalance relaxation in a superconductor associated with inelastic electron-electron (Coulomb) scattering is derived, valid at arbitrary temperatures. The calculation is performed for clean superconductors, and shown to extend to cases where impurity scattering is important, using a technique of Schmid. As expected, for temperatures in the vicinity of Tc the form for the relaxation rate is identical with that arising from inelastic electron-phonon processes, if one replaces the inelastic electron-phonon scattering time with the inelastic electron-electron scattering time.