Space- and Angle-Dependent Steady-State Thermal-Neutron Spectra Inside Small Beryllium Assemblies

Using a multigroup discrete-ordinate form of the transport equation, we have calculated thermal-neutron spectra along four directions at different distances from the source plane within beryllium assemblies of dimensions 35.6 × 35.6 × 50.8 cm³ and 25.4 × 25.4 × 50.8 cm³. In both assemblies our calculated spectra in the forward direction at various distances from the source plane agree well with the corresponding observations of Lake and Kallfelz everywhere, except in a small energy region around 0.007 eV. We show that the increase in the proportion of cold neutrons with distance observed by them arises mainly because of the uncollided neutron flux and that the remaining distribution, i.e., the collided flux, attains pseudo-equilibrium conditions within 20 cm of the source in the larger assembly. Such equilibrium conditions are not established in the smaller assembly. We show that the conclusion drawn by Lake and Kallfelz—that their measured results contradict the earlier diffusion theory results of Ahmed et al.—is not justified. If anything, these measurements lend support to the diffusion theory results.