Solution of the Neutron Slowing Down Problem via a Multiple Collision Approach

An analytical approach to the solution of the neutron slowing down problem with anisotropic scattering is presented. The basic ideas are the representation of the transport equation by a set of infinitely many first-order linear partial differential equations, the application of the “central limit theorem,” and integral transform techniques. The distribution of the n-times scattered neutrons is given as a superposition of space- and angle-dependent functions with coefficients depending on the energy. In the isotropic case, these coefficients are directly related to the Placzek slowing down distributions.