CONSTRAINTS OF THE MULTIPLE-SCATTERING THEORY OF MOLIERE IN MONTE-CARLO SIMULATIONS OF THE TRANSPORT OF CHARGED-PARTICLES

The breakdown of Moliere'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 Moliere's series and using steps of Moliere'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 Moliere 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 Moliere's parameters B and reduced angle theta. By using the general dependence. of the distribution results are valid for both electron and proton Monte Carlo simulations in any material.