On the Space Distribution of Slow Neutrons

Abstract

The behavior of the neutron density about a plane- or point-source of fast neutrons within a homogeneous slowing-down medium has been re-investigated. For the case of constant mean free path a known analytical expression for the neutron density has been reduced to a form, which is valid for slow neutrons and for any distance from the source. The feasibility of a numerical evaluation of the formula is demonstrated for $M=1\mathrm{}$ (hydrogen). In particular, the asymptotic behavior at very large distances has been studied. For the more realistic example of a medium in which the mean free path decreases with decreasing energy of the neutrons, formulae are presented describing the asymptotic density and the asymptotic energy spectrum at large distances from the source.