Impact of anomalous effects on the angular distribution of coherently scattered photons using Monte Carlo simulation

Comprehensive theoretical and experimental studies on the importance and application of anomalous scattering factors can be found in the literature. The aim of this study was to determine the role and impact of anomalous scattering factors on the Rayleigh scattering of photons, particularly within the regions around the elemental absorption edges, using Monte Carlo sampling techniques. In doing so, an improved version of the already established Monte Carlo techniques for Rayleigh scattering is proposed. The improved version is capable of using the available state-of-the-art anomalous scattering factors, and illustrates and highlights their role in calculating accurate coherent scattering amplitudes. A substantial increase in the forward scattering by the neutral atoms of germanium, caesium and lead, which is a maximum around the K edges due to the inclusion of anomalous scattering factors, was observed at all the energies that were examined. The results show that the angular distribution of coherent scattering of the photons depended upon the anomalous scattering factors. Serious errors could be produced when measuring the exact scattering amplitudes, particularly within the regions around the elemental absorption edges, by ignoring the effects of coherently scattered photons in the Monte Carlo sampling. Furthermore, the improved model provides some extra information on elemental K-edge energies by producing dips in the plots of the calculated normalized cumulative probability distribution function against the energy of the incident photons for all three elements. In conclusion, the use of complex atomic form factors has produced an improved and fairly good approximation which is in very good agreement with the corresponding experimental and scattering-matrix results.