Theory of inelastic x-ray scattering from condensed matter

We review the basic formation for the inelastic scattering of x-rays by matter. The differential cross sections are related to the scattering function S(q, omega), which in turn can be expressed in terms of various correlation functions and response functions of the electron system. We show how the scattering by electronic excitations may be related to the dielectric function of the electron gas at high energy transfers, while at low energy transfers we derive the cross section for scattering by phonon excitations.