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 Zₚ of fission products. The predicted values of Zₚ for thermal-neutron fission of U²³⁵ and spontaneous fission of Cf²⁵² 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 U²³⁵ and on Cf²⁵², which are 0.34 and 0.50, respectively. The root-mean-square deviations of the predicted Zₚ 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 σ=0.51), agrees with the empirical value of Ferguson and Read (σ=0.55) within 8%. Fine structure of Zₚ due to the shell effect is noticed.