Effect of Bragg Cutoff on the Diffusion of Thermal Neutrons in a Finite Solid Medium

To study the diffusion of thermal neutrons in a solid medium, we divide the neutron energy range into two groups, one above and another below the Bragg cutoff energy for the medium. We then apply the method of groups to study the problem. As examples we have considered infinite slabs of beryllium at temperatures of 100°K and 300°K, with an infinite plane source of neutrons at one end of the slab. The flux distributions and the mean neutron energy are calculated for the different cases. It is found that, while for beryllium at 300°K the mean energy is not very much different from the Maxwellian value, for beryllium at T = 100°K results are markedly different from those for a Maxwellian distribution at that temperature. In order to emphasize the effect of the interaction between the two groups in determining the equilibrium flux distributions, we have also made calculation neglecting the interaction and compared these with the earlier results which take account of the interaction.