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An Accurate Approximation for the Highly Efficient Sampling of Polar Scattering Angle of Electron Elastic Single-Scattering Events

Alexander S. Pasciak and John R. Ford

Texas A&M University, Department of Nuclear Engineering, College Station, Texas, USA

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Summary: In single-event Monte Carlo electron transport simulations, elastic scattering events dominate the changes in electron trajectories due to collisions. Classically, the polar scattering angle due to an elastic collision can be sampled efficiently from the screened Rutherford cross section. However, the screened Rutherford cross section fails for both high Z materials and when the incident electron energy becomes too low. Alternatively, improved simulation accuracy for electrons in all energy ranges and through all materials may be obtained by sampling directly from differential data derived from partial-wave-expansion method (PWEM) calculations based on theoretical atomic potential models. While sampling directly from wave calculations will yield simulation results to the best known physical accuracy, it comes at the cost of simulation time. This is due to a sampling process that is typically more involved when compared with using the screened Rutherford cross section. In this work we present a relationship capable of reproducing the moments of the differential cross section derived from PWEM calculations, resulting in good preservation of forward and backscattering peaks. The relationship is directly invertible and is as easily sampled as the Rutherford cross section. Most important, the data presented in this paper in combination with this relationship produce Monte Carlo simulation results which are comparable with those using the exact differential cross section from PWEM calculations for elements Z = 1 to 96 and for incident electron energies from 300,000 down to 50 eV.