The Energy Distribution of Neutrons Slowed by Elastic Impacts

Abstract

The problem of finding the distribution in energy of particles of mass $m$, initially of the same energy, which have made $n$ impacts with particles of mass $M$ all initially at rest, is solved. It is supposed the impacts are elastic and the distribution in angle isotropic in a coordinate system in which the center of mass is at rest. If $x$ is the ratio of the energy after $n$ impacts to the initial energy then the chance that $x$ lie in $\mathrm{dx}$ at $x$ is $\frac{{\left(\frac{log1}{x}\right)}^{n-1\mathrm{}}}{\mathrm{}(n-1\mathrm{})!}$ for $m=M$. For unequal masses the expression is more complicated but easy to calculate. The results have some interest in connection with the slowing of neutrons by elastic impacts with other nuclei, especially with hydrogen nuclei.