Fick's Law and the Neutron Slowing Down Length in Hydrogenous Moderators

It is shown that Fick's law can be used in the calculation of the rigorous neutron slowing down length for hydrogenous moderators (or in fact for any moderator), provided that the corresponding diffusion coefficient is determined within the set of equations of the consistent P₁ approximation. For a given moderator, this coefficient depends solely on lethargy and source spectrum and therefore can be evaluated prior to an actual numerical calculation, which can then be carried out within the simplicity of a diffusion approximation. Furthermore, the flux calculated in this way essentially agrees with the consistent P₁ result in all regions where this approximation is justified. The practical generalization to nonhydrogenous moderators is carried out by means of the Goertzel-Greuling procedure.