Model of a Heavy Moderator and an Analytical Solution of the Neutron Thermalization Problem

Abstract

In recent years, solutions of the neutron-transfer equation have been obtained with computers in comprehensive form, so that it has become possible to solve almost any concrete problem in the theory of neutron thermalization, provided that the differential characteristics of the interaction between the neutrons and matter are known with sufficient accuracy, i.e., when the scattering probability and the absorption cross section are known. However, even in the case of moderators which were most extensively researched, the neutron-scattering probabilities are still incompletely and inexactly known. Therefore, calculations are of any value only when the possible influence of errors and of the incompleteness of the data can be assessed. Apart from this, it is frequently necessary to study neutron distributions for various geometries and parameters of the moderator, for example, when the optimum parameters of a moderator are to be determined. Numerical solutions to problems of this type require very laborious calculations and the numerical results are sometimes rather sketchy.