Distribution of Nuclear Charge in Low-Energy Fission of Transthorium Elements

The variation of the nuclear charge dispersion $\sigma$ in the thermal neutron fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ was examined in three limited product mass ranges. By using measured or estimated $\sigma$ values and fractional chain yields, the "experimental" most probable charge values $Z_p\mathrm{}\left(A\right)\mathrm{}$ were derived. For chains outside the mass regions mentioned, the average dispersion $\sigma =0.57\mathrm{}\pm 0.07$ was used. From the derived experimental $Z_p\mathrm{}\left(A\right)\mathrm{}$ values, a new empirical $Z_p\mathrm{}\left(A\right)\mathrm{}$ function covering the whole fission-product mass region was drawn. This empirical function agrees with all published experimental data. The way of estimating product yields from this function is described. The effects of closed shells on the shape of the curve are discussed. The empirical function is preserved in shape for other types of low-energy fission, but is shifted by a constant $\Delta \delta$. A simple empirical relation for calculating $\Delta \delta$ is given.