The Decay of Equilibrium Neutron Flux Inside Beryllium Blocks at Different Temperatures

Equilibrium neutron energy spectra inside finite blocks of beryllium at different temperatures have been calculated by solving the energy-dependent Boltzmann equation in the diffusion approximation by numerical iteration. Different sizes of the assembly have been considered. The values of the transport mean free path, λ_tr (E), (for various temperatures) have been taken from earlier work. Because of the peaks in the transport mean free path, the calculated equilibrium flux differs markedly from the Maxwellian, particularly for small sizes and low temperatures. Calculations also give the values of the decay constant, λ for equilibrium neutrons. Values of λ based on Placzek kernel agree very well with the experimental values. The reasons why the present calculated values, as also the experimental values of λ, exceed Corngold's theoretical upper bound have been discussed. The effect on λ of ‘trapped neutrons’ and that of cold neutrons has also been studied by taking different forms for σ_tr (E).