Abstract
A complete analytic solution in Fourier space is presented of the four dimensional small angle, multiple scattering distribution MSD in angle and space, produced by an energy dependent single scattering cross section from an initial pencil beam of heavy particles. Independently, simple integrals are derived for the central moments of the energy dependent MSD in the continuous-slowing-down approximation. The distributions of the projections t and x of the scattering angle and displacement into a plane through the axis of propagation are evaluated numerically for a truncated Rutherford scattering cross section using a fast Fourier transform. The resulting MSDs for a wide range of particles, initial and final momenta, and scattering materials are found to be approximately represented by one-dimensional set of standard distributions symmetrized by a linear transformation in t− x-space.
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