Transport mean free path related to trajectory patterns: Comparison of nonrelativistic and highly relativistic electron penetration through matter

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Abstract
This analysis is based on the similarity between multiple scattering and slowing down (random walk) processes described by the same transport mean‐free‐path function λtr(s) (s=path length). We discuss the connection between λtr(s) and the characteristic appearance and scale of the trajectory pattern. Straggling is considered by means by stochastically discontinuous λtr(s) functions. In the application to electron penetration, we show that while nonrelativistic electron penetration is modeled by λtr=(r−s)/α, where r is the range and α is a material‐dependent dimensionless constant, highly relativistic electron penetration is modeled by λtr∝exp(−s/Λ), where Λ is a length characteristic for the penetrated material. The respective trajectory patterns are distinctly different. The effect of straggling on the trajectory pattern in the highly relativistic case is demonstrated by means of a simple model of the stochastic λtr(s) behavior.