  The exact solution for nonresonant A1g and B1g Raman scattering is presented
for the simplest model that has a correlated metal-insulator transition--the
Falicov-Kimball model, by employing dynamical mean field theory. In the general
case, the A1g response includes nonresonant, resonant, and mixed contributions,
the B1g response includes nonresonant and resonant contributions (we prove the
Shastry-Shraiman relation for the nonresonant B1g response) while the B2g
response is purely resonant. Three main features are seen in the nonresonant
B1g channel: (i) the rapid appearance of low-energy spectral weight at the
expense of higher-energy weight; (b) the frequency range for this low-energy
spectral weight is much larger than the onset temperature, where the response
first appears; and (iii) the occurrence of an isosbestic point, which is a
characteristic frequency where the Raman response is independent of temperature
for low temperatures. Vertex corrections renormalize away all of these
anomalous features in the nonresonant A1g channel. The calculated results
compare favorably to the Raman response of a number of correlated systems on
the insulating side of the quantum-critical point (ranging from Kondo
insulators, to mixed-valence materials, to underdoped high-temperature
superconductors). We also show why the nonresonant B1g Raman response is
``universal'' on the insulating side of the metal-insulator transition.
