A THEOREM ON NEUTRON MULTIPLICATION

Abstract

The asymptotic behaviour of the neutron distribution due to a point source in an infinite homogeneous medium in which a convergent chain reaction (multiplication constant k<1) takes place is investigated without special assumptions about the properties of the medium and the mechanism of neutron diffusion. It is shown under very general assumptions that at large distances r from the point source the neutron distribution always has the form[Formula: see text]General expressions for the constants μ and A of this asymptotic form of the distribution are given for any k<1 in terms of the Fourier transform of the spatial distribution of primary fission neutrons. These expressions reduce to particularly simple form for (1 − k) << 1. The exact expression for the neutron distribution throughout the medium is given in integral form. Four special frequently occurring cases are discussed as illustrations of the general result.