Abstract
The authors study the multiple scattering process of light particles in random media in the small-angle approximation. Particular consideration is given to the reflection of particles impinging under a glancing angle on a surface. The particle flux is described by a linear integro-differential equation. Results for the space, angle and path-length-dependent particle flux are derived using the method of eigenfunctions. The properties of the solution are discussed for various power-law scattering potentials, and the differences from the well known diffusion case, corresponding to Coulomb scattering, are emphasized. For the special case of an inverse-square interaction potential, a rigorous solution of the transport equation is derived, and compared to two approximations which have been employed in the literature: deviations occur in particular for small path lengths travelled (small energy loss). The influence of the boundary condition at the surface on the solution is investigated. Applications of the theory to energy loss spectra of reflected particles are discussed.
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