Using the method of moments to calculate the space-energy distribution of neutron density from flat and point sources in an infinite medium

Abstract

A method is given for calculating the space-energy distribution of neutron densities from flat and point sources in an infinite medium.

The neutron density ψ (x, E) is sought in the form$(\psi , E) = \sum\limits_{i = 1}^N {a_i (E) K [b_i (E)x].}$ · To a large degree the form of the function K(x) is arbitrary; its selection is based on physical principles. From the 2N space moments of the function ψ(x, E), 2N parameters a_i, b_i are found. The neutron density distribution is found in hydrogen and water. The calculations for water are compared with experimental data. A comparison with the accurate solution of Wick [1] in the case of retardation of neutrons by hydrogen shows that from four moments the suggested method can, with sufficient accuracy, find the spatial distribution of neutrons at distances up to 20 free path lengths.