The hybrid model for sampling multiple elastic scattering angular deflections based on Goudsmit-Saunderson theory

Abstract

An algorithm for the Monte Carlo simulation of electron multiple elastic scattering based on the framework of SuperMC (Super Monte Carlo simulation program for nuclear and radiation process) is presented. This paper describes efficient and accurate methods by which the multiple scattering angular deflections are sampled. The Goudsmit-Saunderson theory of multiple scattering has been used for sampling angular deflections. Differential cross-sections of electrons and positrons by neutral atoms have been calculated by using Dirac partial wave program ELSEPA. The Legendre coefficients are accurately computed by using the Gauss-Legendre integration method. Finally, a novel hybrid method for sampling angular distribution has been developed. The model uses efficient rejection sampling method for low energy electrons (500 mean free paths). For small path lengths, a simple, efficient and accurate analytical distribution function has been proposed. The later uses adjustable parameters determined from the fitting of Goudsmith-Saunderson angular distribution. A discussion of the sampling efficiency and accuracy of this newly developed algorithm is given. The efficiency of rejection sampling algorithm is at least 50 % for electron kinetic energies less than 500 keV and longer path lengths (>500 mean free paths). Monte Carlo Simulation results are then compared with measured angular distributions of Ross et al. The comparison shows that our results are in good agreement with experimental measurements.

Keywords

• Monte Carlo
• multiple scattering
• Goudsmit-Saunderson
• SuperMC
• differential cross-section
• angular distribution
• ELSEPA