Kinetic theory of neutron gases. Progress report, October 1, 1974--June 30, 1975

Interim progress reports are presented on four investigations involving the transport of fast neutrons. The common theme tying together the four research projects is the manner in which details of microscopic cross sections affect the macroscopic transport behavior of neutron gases in material media. In the first, the classic problem of transport and slowing down in a non-hydrogenous medium with constant cross section is being reexamined, using Case's method of singular eigenfunctions. Both the asymptotic limit derived by Wick and the age-theory extreme have been recovered, and higher order corrections to these are being derived. Semi-numerical techniques have been developed which should permit calculation of the flux over wide ranges of distance and lethargy. The second investigation is the study of the effects of square-well minima in otherwise constant cross sections. A specialized moments-method code has been developed for the purpose, which gives the flux as far out as 80 to 100 mfp from the source. A simple but highly accurate model has been developed to include the effects of the minima, and it is now feasible to predict under what conditions a given minimum will significantly affect the penetration. In the third study Monte Carlo has been used to obtain the characteristics of neutron histories penetrating to various distances and energies in iron. The role of such cross section phenomena as inelastic scattering and cross section minima is being elucidated. In the last investigation, the discrete energy S/sub N/ method is being applied to various transport problems difficult of access by other methods. For example, an examination is under way of the dependence of fast-neutron albedo on the form of representation of the scattered neutron distribution and on the fine structure of the cross section. (U.S.)