Steady-State Diffusion Under Conditions of Generalized Source and Incident Current Distributions

The method of Laplace transformations is extended to the more general case of neutron diffusion in half-infinite media containing source distributions, and an exact expression for the emergent current distribution is obtained. This expression depends on the total m.f.p., on the ratio $N$ of the capture to scattering m.f.p., and on the type of source distribution. For a uniform source distribution and with $N$ sufficiently large, the values of the normalized current as a function of angle agree closely with those given by the Fermi law. More significant discrepancies between the results of elementary theories and the exact theory are to be found in the ratio $R$ of detector activities corresponding to positions deep within the medium and at the surface. The exact theory gives $R={\mathrm{}(N+1\mathrm{})\mathrm{}}^{\frac{1}{2}}+1\mathrm{}$ for uniform source distributions. A recent quotation of $R=14\mathrm{}$ for the case of thermal neutron diffusion in paraffin then implies $N=168\mathrm{}$ instead of 196 as given by the elementary theory.