Statistics and Nuclear Reactions

TLDR

Statistical methods can be applied to nuclear processes when the incident energies are much larger than the lowest nuclear excitation energies, yielding expressions analogous to the evaporation probability of a particle from a low‑temperature body. The resulting formulas give the emission probability of neutrons or charged particles from highly excited heavy nuclei, predict a mean energy loss per impact of \(E[1-2(a/E)^{1/2}]\) with \(a\approx0.05-0.2\) MV, and show that the scattered neutrons follow an approximate Maxwellian distribution with mean energy \(2(\mathrm{aE})^{1/2}\).

Abstract

It is possible to apply statistical methods to the calculation of nuclear processes provided that the energies involved are large in comparison with the lowest excitation energies of nuclei. Expressions are obtained for the emission probability of neutrons or charged particles by highly excited heavy nuclei. These expressions are built up in a similar way to the formula for the probability of evaporation of a particle from a body at low temperatures. In applying it to the impact of high energy neutrons on heavy nuclei, the mean energy loss per impact turns out to be $E[1\ensuremath{-}2{(\frac{a}{E})}^{\frac{1}{2}}]$ where $E$ is the energy of the incident neutrons and $a$ is dependent on the nuclear structure; we can put approximately $a\ensuremath{\sim}0.05\ensuremath{-}0.2$ MV. The energy distribution of the scattered neutrons is approximately a Maxwellian one with a mean energy of $2{(\mathrm{aE})}^{\frac{1}{2}}$.