Unbiased Monte Carlo simulation of the Compton profile

Recent comparisons between analytical (deterministic) computations using the code SHAPE, and Monte Carlo (MC) simulations of Compton scattering using different codes show discrepancies in the shape of the Compton peak (the so-called Compton profile), specially for medium-low energy X-ray excitation. Considering the analytical computations as a reference model, the standard approach adopted for generating the Compton profile in different MC codes (EGSnrc, MCNP, MCSHAPE) has been studied comparatively in order to discover a reason for the difference. Apparently there is a bias in the profile generation which is common to all the codes and is related to the assumption of completely populated atomic orbitals contributing to the scattering. Such an assumption does not agree with the equivalence condition between the integrated Compton profile in the Impulse Approximation (IA) and the Waller-Hartree (WH) scattering function.In this article, we report the comparisons mentioned above for a paradigmatic case and propose an unbiased MC algorithm for the simulation of the Compton scattering.