Abstract
A three-dimensional scattering process is studied using the theory of discontinuous Markov processes, extending results previously obtained in one dimension by Brockwell and Moyal. The scattered particles are assumed to move in one of a set of thirty directions in space. Constant mean free path is assumed, scattering is axially symmetric and velocity transition probabilities ψθ(dv|u) are defined for each collision depending on the angular deflection, θ. It is shown how the results obtained for the discrete set of directions can be used to approximate the physically more realistic continuous case; a numerical comparison with exact results is given for the well-known Milne problem with isotropic scattering. For a steady stream of particles incident on one face of a slab {x: a ≤x ≤b} it is shown how to determine the time-independent solution for the mean number of particles per second crossing a plane x = ξ in any given direction. The distribution of velocity and direction with which particles emerge from a slab is also determined assuming the probabilities ψgq(dv | u) satisfy a certain commutativity condition. If there is a constant (nonzero) probability of absorption at a collision no essential modification of the analysis is required.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
