On the Multiple Scattering of Neutrons in Hydrogen-like Substances

The spatial moments ,, and are calculated exactly for all energies below the source energy, for a point, isotropic source in an infinite, homogeneous medium in which there is no absorption and in which the scatterers scatter like hydrogen but with a 1/υ cross section. For a monoenergetic source these moments are approximately consistent with a diffusion (Yukawa) radial distribution of the very low energy neutrons. Integration over a fission-like source spectrum, exp (—αE), gives moments consistent with a radial distribution of the very low energy neutrons of the form of a first collision density, r^-2 exp (—r/λ), but with a mean free path λ approximately twice the mean free path at the average source energy. The results are compared with those given by the first collision approximation.