Resonance raman scattering near critical points

Resonance Raman scattering is considered for photons near resonance with a critical point in the continuum of electronic intermediate states. The conditions for simultaneous double resonance in scattering at finite wave vector are examined and analytic expressions are derived near $M_0$ and $M_3$ critical points. Double-resonance effects typically occur only for large-wave-vector scattering. They dominate line shapes and intensities in second-order scattering and lead to a cascade picture for scattering of third or higher order. In the case of strong absorption (or inhomogeneity-induced scattering) momentum is not conserved and we find that large-wave-vector forbidden scattering may be important in first order. This is an example of a nonlocal photon-phonon interaction mediated by the electrons and we find that the usual local absorption corrections are not sufficient.