Fast sampling algorithm for the simulation of photon Compton scattering

A simple algorithm for the simulation of Compton interactions of unpolarized photons is described. The energy and direction of the scattered photon, as well as the active atomic electron shell, are sampled from the double-differential cross section obtained by Ribberfors from the relativistic impulse approximation. The algorithm consistently accounts for Doppler broadening and electron binding effects. Simplifications of Ribberforsʹ formula, required for efficient random sampling, are discussed. The algorithm involves a combination of inverse transform, composition and rejection methods. A parameterization of the Compton profile is proposed from which the simulation of Compton events can be performed analytically in terms of a few parameters that characterize the target atom, namely shell ionization energies, occupation numbers and maximum values of the one-electron Compton profiles.