Expressions for the incoherent-scattering function and the inelastic-scattering cross-section differential with respect to the solid angle for detection of scattered x rays from atomic, molecular, and condensed-matter targets are derived in the relativistic impulse approximation for Compton scattering. It is shown that the incoherent-scattering functions, defined as an integral over Compton profiles, can be computed easily by means of a "linear" approximation. Numerical results for Al, Fe, and Pb are compared with available experimental values and with the Waller-Hartree theory.

• Received 28 December 1981

DOI:https://doi.org/10.1103/PhysRevA.26.3325