A Monte Carlo study of neutron thermalization

Abstract

The slowing down of neutrons from fission to absorption energies in a homogeneous medium has been treated by a Monte Carlo method. Thermalization by elastic collisions in both light and heavy water was computed on an IBM 650. One-sixth the mean-square distance travelled by the neutrons was interpreted as the migration area. This quantity was analysed to give the age, τ, both above and below the indium resonance, and the thermal diffusion constant, D, as functions of the moderator temperature, the effective moderator mass, the moderator composition, the scattering and absorption laws, and the energy distribution of the neutron source.

The migration area from the fission energy source to below the indium resonance energy (1·46 eV) was found to be 26·3 cm² for H₂O and 115 cm² for D₂O. By varying the absorption cross-section, the migration area from the indium resonance energy to absorption of the neutrons could be decomposed into components D/gS_a and τ_s. D and τ_s were found to be 0·19 cm and 0·77 cm² respectively for H₂O, and 0·87 cm and 20 cm² for D₂O. D was found to increase with the thermal agitation of the moderator at the rate of 0·13 per cent/°C for H₂O and 0·14 per cent/°C for D₂O. Neutron energy distributions found from the scattering frequency agree with those derived by analytical methods.