Probabilistic description of particle transport. I. General theory of quasielastic scattering in plane-parallel media

We present a three-dimensional probabilistic model of particle transport in a medium where the particles suffer quasielastic collisions. The model accounts for bulk and surface scattering, as well as partial reflections at the boundaries of the medium. We give analytical and numerical methods for the evaluation of the particle transmission probability in the case of a medium with a plane-parallel geometry. The influence of the various parameters of the model on this probability is also discussed.