D. Brusa et al., FAST SAMPLING ALGORITHM FOR THE SIMULATION OF PHOTON COMPTON-SCATTERING, Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment, 379(1), 1996, pp. 167-175
A simple algorithm for the simulation of Compton interactions of unpol
arized 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 accoun
ts for Doppler broadening and electron binding effects. Simplification
s of Ribberfors' 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 p
rofile 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.