Summary of existing information on the incoherent scattering of photons, particularly on the validity of the use of the incoherent scattering function

X-ray scattering by individual atomic electrons is known as Compton scattering if the simplifying approximation is invoked that the target electrons are initially free and at rest, in which case the differential and integral scattering cross sections can be computed using the compact analytical expressions given by Klein and Nishina in 1929. In real atoms the electrons are neither free nor at rest, resulting in departures from the Klein-Nishina expressions. These departures have been estimated theoretically in varying degrees of sophistication, with correspondingly varying degrees of ease in applying these corrections to the free electron model. This report includes historical survey of and theoretical work on the Compton effect and on the incoherent scattering function. The validity of the use of the incoherent scattering function is examined and discussed. (author)