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Constraints of the multiple‐scattering theory of Molière in Monte Carlo simulations of the transport of charged particles
Author(s) -
Andreo Pedro,
Medin Joakim,
Bielajew Alex F.
Publication year - 1993
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.596982
Subject(s) - monte carlo method , scattering , statistical physics , radiation transport , physics , computational physics , nuclear physics , computer science , optics , mathematics , statistics
The breakdown of Molière's multiple‐scattering theory for short pathlengths occurring during Monte Carlo simulations with charged particles is demonstrated. It has been found that in certain conditions where the theory is assumed to be valid, significant distortions of the angular distribution occur that make the sampling of the polar angle questionable in numerous steps of Monte Carlo simulations. The limits of the theory have been investigated, both using a large number of terms in the Molière's series and using steps of Molière's theory where 1/ B expansions are not involved. At B =4.5 the commonly accepted 3‐term series expansion yields differences up to ±6% compared with the evaluation of the complete Molière angular distribution, and up to 7 terms in the series are needed in order to achieve agreement within ±2%. One percent agreement requires B =10. Numerical values of the full distribution are given in terms of Molière's parameters B and reduced angle ϑ. By using the general dependence of the distribution results are valid for both electron and proton Monte Carlo simulations in any material.