Theory of X-Ray Raman Scattering

Inelastic scattering of X-rays by localized electrons, such as K -electrons, in solids is treated theoretically. The wave length of X-rays is chosen to be longer than the orbital radius of localized electrons, but still short enough so that the photon energy is much higher than the ionization energy. On the basis of reasonable approximations, it is found for polycrystals that the differential cross section is proportional to \begin{aligned} {\nu_{0}}^{2}t(\nu_{0}-\nu)(1+\cos^{2}\theta)\sin^{2}(\theta/2). \end{aligned} Here ν 0 and ν are respectively the frequencies of the incident and scattered X-rays, θ being the scattering angle. ν t (ν) is a quantity proportional to the cross section of absorption of the X-rays with frequency ν by the same electrons. The above expression has recently been confirmed experimentally.