Statistical-Theory Calculation of Charge Distribution in Fission

The nuclidic mass formula developed recently by the authors is employed to calculate the most probable charge $Z_p$ of fission products. The predicted values of $Z_p$ for thermal-neutron fission of ${\mathrm{U}}^{235}$ and spontaneous fission of ${\mathrm{Cf}}^{252}$ differ from the experimental values by a root-mean-square deviation of 0.35 and 0.55 charge unit, respectively, the computer calculation being made for charge values varying 0.05 charge unit at a time. These values may be compared with the root-mean-square deviations between two existing sets of experimental results on ${\mathrm{U}}^{235}$ and on ${\mathrm{Cf}}^{252}$, which are 0.34 and 0.50, respectively. The root-mean-square deviations of the predicted $Z_p$ values for many other schemes of charge division are calculated for comparison. The width of the charge-distribution curve of the primary fission fragments (before prompt neutron emission) in the peak-yield regions, calculated by the statistical theory (standard deviation of Gaussian $\sigma =0.51\mathrm{}$), agrees with the empirical value of Ferguson and Read ($\sigma =0.55\mathrm{}$) within 8%. Fine structure of $Z_p$ due to the shell effect is noticed.