Distributions of Fission Neutron Numbers

It is shown, on reasonable assumptions as to the distribution of excitation energy among fission fragments, that the probabilities $P_{\nu }$ of observing $\nu$ neutrons from fission are given approximately, in cumulative form, by the "Gaussian" distribution, $\Sigma \stackrel{\nu }{n=0\mathrm{}}{P}_n={\left(2\mathrm{}\pi \right)}^{-\frac{1}{2}}\int {-\infty }^{\frac{(\nu -\overline{\nu }+\frac{1}{2}+b)}{\sigma }}\exp (-\frac{t^2}{2})dt.$ In this equation $\overline{\nu }$ is the average number of neutrons, related to the average total excitation, $b$ is a small adjustment ($b<\mathrm{}{10}^{-2\mathrm{}}$), and $\sigma$ 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 $\sigma \cong 1.08$, with the exception of ${\mathrm{Cf}}^{252}$, which requires $\sigma =1.21\mathrm{}\pm 0.01$. An estimate that $E_0=6.7\mathrm{}\pm 0.7$ Mev gives an excitation energy distribution and a rate of change of $\overline{\nu }$ with incident neutron energy ($\frac{d\overline{\nu }}{d{E}_n}\cong \frac{1}{E_0}$) 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.