A study of the pulsed neutron problem in ice in the temperature range 273 to 210K

Calculations on the decay of a neutron pulse in H2O ice assemblies of various bucklings and at various temperatures in the range 273 to 21°K are reported. The scattering kernel is based on the Debye frequency distribution function of lattice vibrations, with a suitably chosen Debye temperature. Contributions from one- and two-phonon processes have been considered. The Boltzmann equation in the diffusion approximation has been solved both by an iterative procedure to obtain the fundamental mode of decay, and by a matrix diagonalization method. This latter method enables us to calculate neutron spectra at various times after the introduction of the neutron pulse. These time-dependent spectra have been compared with available experimental results with considerable success. By studying the time variation of the mean energy of the neutron distribution, we have calculated the slowing down relaxation times τth in ice at various temperatures and compared these with the measured values. We have also studied the heating up of a low-energy neutron pulse in ice assemblies at a few temperatures and find that, unlike the case of beryllium (Grover and Kothari) the heating up relaxation time τH comes out to be nearly the same as τth.The calculated values of diffusion coefficient D0, and diffusion cooling coefficient C at various temperatures have been compared with the experimental results. The agreement between the two sets of values is very good for D0, but not so good for C.