Equilibrium Spectra and Diffusion Lengths of Neutrons in Semi-Infinite Moderator Block—Part I

Asymptotic neutron-energy spectra inside a semi-infinite beryllium block have been calculated by an iteration procedure using for the scattering kernel both the one-phonon scattering cross section and the first term of the Placzek expansion. Different absorptions have been considered. The values of the transport mean free path, λ_tr(E), have been taken from Bhandari's work. Because of the sudden large variation of λ_tr(E) near the Bragg cutoff, the calculated equilibrium flux differs markedly from the Maxwellian, particularly for high moderator absorptions. For a pure beryllium block at room temperature (σ_a = 0.01 barn), the deviation from Maxwellian is small. Calculations also give the values of the diffusion length at different absorptions, from which data the diffusion constant D₀ and the diffusion cooling constant C have been evaluated.