Compton effect in dielectric medium
  We determine the Compton effect from the Volkov solution of the Dirac equation for a process in a medium with the index of refraction n. Volkov solution involves the mass shift, or, the mass renormalization of an electron mass. We determine the modified Compton formula for the considered physical situation. The index of refraction causes that the wave lenghths of the scattered photons are shorter for some angles than the wave lengths of the original photons. This is anomalous Compton effect. Since the wave length shift for the visible light is only 0,01 percent, it means that the Compton effect for the visible light in the dielectric medium needs experimental virtuosity. 
Miroslav Pardy