Influence of Anisotropic Scattering on Stopping by Elastic Collisions

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Abstract
Calculations of spatial moments 〈zn〉 for particles from a plane source in an infinite medium of randomly located target atoms are extended to a scattering cross section which is a product of factors depending on energy and angle separately. It is shown that expressions for Laplace transforms of moments of the flux fnl(s) which were used before for isotropic scattering continue to be valid, provided the definition of the functions Gl(s) is broadened in a natural way. For classical scattering by several inverse power repulsive potentials, and for various ratios of target mass to fast particle mass, spatial moments at zero energy have been calculated through n=4. Deviations of distributions from the Gaussian form prove to be moderate, and Edgeworth expansions may be used to give approximate curves. With certain additional approximations the results can be applied for scattering by a Thomas‐Fermi potential. A few comparisons are made with published Monte Carlo results and with measurements on range distributions of kilovolt ions in gases.