Neutron Diffusion Across an Absorption Discontinuity in Water Assemblies

Some theoretical calculations concerning the diffusion of thermal neutrons (2.5 × 10⁻⁴ to 0.7 eV) across an absorption discontinuity in water assemblies consisting of pure water on one side and the water solutions of boron (a 1/v absorber) having different concentrations on the other side have been performed by solving the Boltzmann transport equation in the diffusion approximation using the multigroup formalism. The Nelkin scattering kernel of water at 293 K has been tried in the present case. At the boundary, the equilibrium neutron distribution is disturbed and is reestablished to the equilibrium distribution of the second medium within a few centimetres from the boundary. The diffusion lengths so obtained show a good agreement with the experimental results of Martinho and Costa Paiva.