On the representation of electron multiple elastic-scattering distributions for Monte Carlo calculations

Abstract A new representation of elastic electron–nucleus (Coulomb) multiple-scattering distributions is developed. Using the screened Rutherford cross section with the Moliere screening parameter as an example, a simple analytic angular transformation of the Goudsmit–Saunderson multiple-scattering distribution accounts for most of the structure of the angular distribution leaving a residual 3-parameter (path-length, transformed angle and screening parameter) function that is reasonably slowly varying and suitable for rapid, accurate interpolation in a computer-intensive algorithm. The residual function is calculated numerically for a wide range of Moliere screening parameters and path-lengths suitable for use in a general-purpose condensed-history Monte Carlo code. Additionally, techniques are developed that allow the distributions to be scaled to account for energy loss. This new representation allows “on-the-fly” sampling of Goudsmit–Saunderson angular distributions in a screened Rutherford approximation suitable for Class II condensed-history Monte Carlo codes.

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