Finite-angle Multiple Scattering

A multiple-scattering distribution is calculated for angles larger than the maximum single-scattering angle. The small-angle Bothe formulation with appropriate modifications is used in the power-cross-section approximation. Although the distribution is asymptotically a Gaussian function multiplied by a series of Laguerre polynomials, a series expansion similar to those for the usual Bothe theory converges well out to large angles. The cutoff of the single-scattering kernel is ambiguous, so there is a free parameter. The alternative Goudsmit-Saunderson formalism is difficult to evaluate and is not easily summed to give asymptotic expansions, but with the aid of some tricks yields numerical results in good agreement with experiment.