PLURAL AND MULTIPLE SMALL-ANGLE SCATTERING FROM A SCREENED RUTHERFORD CROSS-SECTION

The object of this paper is to employ the screened Rutherford cross section to construct a charged-particle multiple-scattering theory that does not suffer from either the small step-size artefact associated with the conventional Moliere multiple-scattering distribution or the large step-size instability of the theory of Keil et al. [Z. Naturforsch. 15a (1960) 1031]. An exact numerical solution to the Wentzel elastic-scattering integral is found for charged particle step-sizes less than about 3000 mean-free-paths. The new distribution contains explicitly the expected single and no-scattering distributions in the limit of small step-size, matches the standard Moliere distribution for large step-sizes and is expressed in terms of simple functional forms and numerical tables that may be sampled quickly for use in Monte Carlo methods. The new distribution may be expressed entirely in terms of only two parameters - a 'reduced'' angle and the mean free path. The large-angle limit of the distribution is expressed analytically and compared to the results of Keil et al. and Moliere. Despite the fact that the conventional Moliere distribution is based upon the assumption that many interactions participate in the development of the multiple-scattering angle, it is found that Moliere's large-angle limit is mostly correct although the large-angle behaviour is dominated by one or two interactions! The design of a Monte Carlo electron transport algorithm that incorporates the unique features of the new distribution is discussed.