Diffusion cooling of neutrons in a finite solid moderator assembly

Abstract

Following Nelkin, an expression for the decay constant of the fundamental spatial mode of neutron flux as a function of the buckling of moderating assembly is derived, without making any explicit assumption regarding the variation of transport mean free path λ_tr with neutron energy. Numerical results are presented for beryllium, and it is shown that the relation between the diffusion cooling constant and the relaxation time of the last stages of slowing down is a very sensitive function of the variation of λ_tr with energy; as such it is not possible to estimate the relaxation time by a measurement of the diffusion cooling constant.