Neutron-Transfer Theory for Inhomogeneous Media

Abstract

The transition of neutrons through a homogeneous moderator has been rather thoroughly studied in both theory and experiment. In several cases of practical interest, we have to consider the neutron transfer in media with extended inhomogeneities in space. Problems of this type are encountered when the methods of neutron physics are used in nuclear geophysics or when the neutron diffusion in boiling liquids is examined. The parameters of the medium change irregularly from point to point and this leads to fluctuations of the neutron density. Both the average neutron density and the mean square density are of particular interest in practice. An averaging over the fluctuations in the medium is performed. The experimental results concerning the neutron density are usually compared with the calculated results obtained from a solution of the kinetic equation with averaged parameters. Under certain conditions, the calculated values may differ considerably from the average neutron density and errors in the interpretation of the experimental values are the consequence. A moderator with a periodic structure, for example, a lattice of a heterogeneous reactor, is an important particular case of an inhomogeneous medium. A large number of publications deals with the transition of neutrons through media of this type.* However, an analytic solution to this problem could be given only when very restrictive conditions for the moderator properties were assumed: either one ignores the neutron absorption, or one limits the discussion to a medium with a simple geometry and uses the diffusion approximation.