On the Theory of the Slowing Down of Neutrons in Heavy Substances

Abstract

The rigorous solution of the integral equation for the stationary energy distribution in the case of slowing down without capture is given. Its relation to the average energy loss is discussed (Sections 1, 2). In Section 3, the problem of mixtures is treated. It is shown, in particular, that for mixtures of a light and a heavy substance concentrations exist for which the energy distribution is at the beginning entirely determined by the energy loss in the heavy substance and at the end by the energy loss in the light substance. The effects of capture are discussed in Sections 4-6. It is shown that the solution assumes a simpler form if the ratio of the mean free paths for scattering and capture varies slowly over energy regions of the order of the average energy loss. The case of $\frac{1}{v}$—capture is treated in detail (Section 5); rapidly varying capture is discussed in Section 6. In Section 7, a simplified treatment, based on the concept of neutron age, is given, and its limitations are discussed. Section 8 contains the discussion of the effects of the chemical binding on the energy distribution. An expression for the mean square distance of diffusion and its mass dependence is derived (Section 9).