An efficient convergence method for calculating the angular distribution of electron multiple elastic scattering

new method based on random walk theory to model multiple elastic scattering of electrons is presented which gives the efficient convergence of scattering series. This method modelled the multiple scattering as a series of random walks on a unit sphere, with each scattering event equivalent to one step in the random walk sequence. The step size of the random walk is characterised by the scattering angle which is determined by the scattering differential cross-section. Dirac partial wave program ELSEPA has been used to calculate the differential cross-sections of electrons and positrons by neutral atoms. The position distribution of a point on this unit sphere after “ n ” steps of random walk yields the angular distribution of multiple scattering. The main advantage of this method is the faster convergence of the scattering series for small step size, which is the most computationally demanding scenario in Monte Carlo multiple scattering simulations in the radiation transport code. Equivalence to Goudsmit–Saunderson’s theory of multiple scattering is also demonstrated and the angular distributions obtained from both the random walk method and Goudsmit–Saunderson’s theory are compared. The convergence of the scattering series is checked by comparing the Legendre polynomial expansion coefficients obtained through the random walk method and Goudsmit–Saunderson’s theory. Comparisons showed that the scattering series converges very fast for smaller path lengths (< 50 × mean free paths).