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modified Maxwell-Boltzmann distributions having a characteristic energy kT. Because of the distribution of energies of the scattering nuclei, a scattering collision does not always result in a decrease in neutron energy. Collisions in which the neutron gains energy become possible and the probability for collisions with an energy loss become smaller. Thermal neutron scattering is further complicated by chemical binding effects associated with the lattice structure of solids and the molecular structure of liquids. The effects of nuclear motion and chemical binding on scattering collisions are included in the theory of neutron thermalization (19), and will not be treated here. A concise description of neutron thermalization problems is given by Beckurts and Wirtz (20).

        Microscopic thermal neutron absorption cross

sections are functions of the relative neutron speed. In general, this speed dependent cross section is not the same as the experimentally measured average cross section. In order to use measured absorption cross sections in reactor calculations, the experimentally determined values must be properly weighted to include the effects of relative speed (21).

        The preceding discussion of the Boltzmann transport equation has considered only neutrons in a solid core reactor. To summarize this discussion, the application