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

Abstract

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 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. At present the most widely used treatment of these departures is via the incoherent scattering function S( x, Z) in which x is a momentum transfer variable dependent on the incident photon energy and the scattered-photon deflection angle, and Z is the atomic number of the atom associated with the target electron. The incoherent scattering function S( x, Z) also enters into calculations of the cross section for electron-positron pair production in the fields of the atomic electrons, known also as triplet production. This report includes a historical survey of experimental 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.