Considerations on the Probability of Nuclear Fission

A semiempirical equation for fission thresholds has been extended to include the effects of unpaired nucleons on the rate of spontaneous fission. Excitation functions for the ($\alpha , 4n$) reactions of ${\mathrm{Ra}}^{226}$, ${\mathrm{Th}}^{230}$, and ${\mathrm{U}}^{236}$ have been measured. These results and reported cross sections for other ($\alpha , 4n$) reactions in the heaviest elements have been analyzed in terms of fission and neutron-emission competition to obtain mean values of $\frac{{\Gamma }_n}{{\Gamma }_F}$. These mean values of $\frac{{\Gamma }_n}{{\Gamma }_F}$ have been correlated with neutron binding energies and fission thresholds.