Space-age distribution of neutrons arising from the spontaneous fission of uranium nuclei in a two-layer medium with a cylindrical interface

Abstract

Let us consider two media separated by an infinite circular cylinder of radius r 0. The inner medium (r r 0) the ore seam. The symmetry axis of the inhomogeneous system under consideration coincides with the z axis of the cylindrical coordinate system employed (r, z, q~). Let the mineralization be one-dimensional, i.e., the number of sources in unit volume of the medium A(z) be a function of one coordinate z. We shall assume that the mineralization does not affect the properties of the ore seam under consideration as regards the transport of neutrons; the slowing-down properties of the ore and surrounding rocks will then be identical. We require to find the slowing-down density of the spontaneous-fiss ion neutrons in the two media. We shall use the age approximation of transport theory, representing the retardation as a process of three-dimensiona l neutron diffusion, accompanied by a continuous loss of energy. Analysis of theoretical and experimental data indicates that the age approximation defines the behavior of the neutrons at shortdistances from the source fairly accurately in media of arbitrary isotopic composition. Even in describing the spatial distribution of neutrons retarded in water, the age approximation is accurate up to a distance of the order of 10 cm from the source [1]. The geometrical conditions normally employed in measuring the density of neutrons arising from the spontaneous fission of uranium nuclei in ore borings (the mean radius of the boreholes usually lies between 5 and 6 cm) indicate that the age approximation may validly be used for solving this problem, since the average distances traveled by the neutrons in the borehole lie within the range of practical applicability of the age approximation. Mathematically, the problem of the slowing down of spontaneous-fiss ion neutrons may be solved by using the system of age equations