Distributions of Fission Neutron Numbers

It is shown, on reasonable assumptions as to the distribution of excitation energy among fission fragments, that the probabilities P_ν of observing ν neutrons from fission are given approximately, in cumulative form, by the "Gaussian" distribution, ${Σ}{{ν}}{n=0}{P}ₙ={(2{π})}^{{-}1/2}{∫}{{-}{∞}}^{{({ν}{-}{{ν}}+1/2+b)}{{σ}}}exp({-}{{t}²}{2})dt.$ In this equation ${{ν}}$ is the average number of neutrons, related to the average total excitation, $b$ is a small adjustment ($b<{10}^{{-}2}$), and ${σ}$ is the root-mean-square width of the distribution of total excitation in units of the average excitation energy change ${E}₀$ per emitted neutron. It is shown that all experimental data on neutron emission probabilities are reasonably well represented by this distribution with ${σ}{}1.08$, with the exception of ${Cf}²⁵²$, which requires ${σ}=1.21±{}0.01$. An estimate that ${E}₀=6.7±{}0.7$ Mev gives an excitation energy distribution and a rate of change of ${{ν}}$ with incident neutron energy (${d{{ν}}}{d{E}ₙ}{}{1}{{E}₀}$) in reasonable accord with experiment. These conclusions should also hold approximately for fission induced by higher energy neutrons, in which case a few neutrons may be emitted before fission.