Electronic Raman response in anisotropic metals

Using a generalized response theory we derive the electronic Raman response function for metals with anisotropic relaxation rates. The calculations account for the long--range Coulomb interaction and treat the collision operator within a charge conserving relaxation time approximation. We extend earlier treatments to finite wavenumbers ($|{bf q}|ll k_{rm F}$) and incorporate inelastic electron--electron scattering besides elastic impurity scattering. Moreover we generalize the Lindhard density response function to the Raman case. Numerical results for the quasiparticle scattering rate and the Raman response function for cuprate superconductors are presented.