Thermal-Neutron Transport Processes in Heavy Water in the Temperature Range of 253 to 4 K

Calculations are reported for time-dependent, space-dependent, and steady-state neutron spectra in D₂O ice assemblies of different dimensions and in the temperature range of 253 to 4 K. The scattering kernel used for these studies incorporates one- and two-phonon processes and is based on the Debye distribution function for the lattice vibrations of the D₂O crystal. The multigroup Boltzmann diffusion equation was diagonalized to obtain transient and asymptotic spectra in assemblies at different temperatures with bucklings ranging from 0 to 0.15 cm-². The calculated values of the effective decay constant are found to agree reasonably well with the experimental values reported by Salaita and Robeson at 253 K for waiting times of 160 to 320 μsec. The decay constants reported by Salaita and Robeson do not correspond to the asymptotic values, as claimed by the authors. The appropriate Boltzmann operator for the space-dependent problem was diagonalized to obtain its eigenvalues and eigenfunctions. By using these eigenfunctions, neutron spectra at different distances from the source plane were calculated in D₂O ice at 253 K, and the diffusion lengths of neutrons were determined. Steady-state spectra in heavy ice assemblies at 77, 21, and 4 K were also investigated. The results for the effective neutron temperatures and the cold-neutron fractions agree well with the experimental results of Rush et al.