Transient neutron spectra and the slowing down relaxation time in beryllium

The Boltzmann equation in the diffusion approximation has been numerically solved by the time-step method to determine transient neutron spectra, following a burst of fast neutrons inside beryllium assemblies of various sizes. Such a study also gives information about the decay constant of the fundamental mode and the slowing down relaxation time. We find that for B2 < 4 × 10⁻² cm^2̄, the decay constant as well as the neutron energy distribution at long,times agrees well with the corresponding quantities calculated by an iteration procedure. However, for larger B₂ up to the time investigated (600 μsec after the initial burst) equilibrium is not established. Timedependent neutron spectra have been compared with the measurements of GAERTTNER et al.

The slowing down relaxation time for an infinite assembly comes out to be 114 μsec. This result is compared with the measurements of ZHEZHERUN et al. who report a considerably higher value: 185 ± 20 μsec. The possible causes of this difference are discussed.