Incoherent-x-ray-scattering functions and cross sections ( d σ d Ω ′ ) incoh by means of a pocket calculator

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.