Multiple-Collision Solutions for Time-Dependent Neutron Transport in Slabs of Finite Thickness

Multiple-collision solutions of the time-, space-, and angle-dependent neutron transport equation in slab geometry are given. Two different monodirectional sources have been used: (a) a δ(t)-shaped pulse of neutrons [δ(t): Dirac delta distribution] impinging on the slab at time t = 0, and (b) a “rectangular” source, emitting neutrons for a time interval Δt, describing a somewhat more realistic situation. Detailed results up to collision order three are discussed and exhibited in several figures. Interestingly, the “scalar” flux of one-time-scattered neutrons for the slab problem turns out to be independent of space in the region influenced by the slab boundaries.