Asymptotic Solutions to the Transport Equation for a Plane Lattice

A transport calculation of the lattice diffusion length, yielding the “gross” decay of the asymptotic flux in a lattice, is made using the method of K. M. Case. Refinements over the diffusion calculation are shown to be 1) slight adjustments in the slab widths due to boundary effects, and 2) the appearance of exact homogeneous diffusion lengths as calculated by transport theory. The extension to “asymptotic” time-dependent problems is also given. For the neutron-wave problem, the complex-valued diffusion length is derived as a function of frequency, and the relation between the time decay constant and the buckling is given for the pulsed-neutron problem. Limiting cases involving very wide slabs are discussed. Finally, some experiments are briefly described for which the analysis of this paper might be applicable.