Nuclear Charge Distribution in Fission Fragments

A model has been proposed for the fissioning nucleus which in the early stages of the fission process undergoes charge polarization into two parts, each with a number of neutrons corresponding to the ground-state $\ensuremath{\beta}$-stable nuclides for the two charges. The rest of the neutrons are then randomly distributed between the two impending fragments, as in an order-disorder process. The model is checked in detail for the thermal-neutron fission of $^{235}\mathrm{U}$. The yield distributions of fission fragments having the same charge $Z$ along isotopic lines (isotopic distributions) are found to be single peaked but not exactly Gaussian. The $\overline{\ensuremath{\nu}}(Z)$ distribution is found to closely resemble the experimental $\overline{\ensuremath{\nu}}(A)$ distribution. The distribution of total isotopic yield versus $Z$, calculated from the isotopic distributions given by the model and experimental fragment-mass yield distribution, shows odd-even $Z$ effects in the form of well-defined fine structure except in the high-slope region. The isotopic distributions, taken in conjunction with total isotopic yield versus $Z$ distribution, give the usual approximately Gaussian distribution along isobaric lines (charge distribution) and provides a rationale for the variation in spread of the distributions. The variation of the mean charge ${Z}_{p}$ of the isobaric distributions is studied by plotting the parameter ${Z}_{p}\ensuremath{-}{Z}_{\mathrm{UCD}}$ (${Z}_{\mathrm{UCD}}$ being the charge for a mass given by unchanged charge density), as a function of the mass $A$. This function obtained in the present work shows very good agreement with that calculated from published ${Z}_{p}$ values for products. The fine structure observed in this function is found to correspond to the fine structure in the fragment-mass yield distribution.Distributions of total isotopic yield versus $Z$ for the thermal-neutron fission of $^{233}\mathrm{U}$ and $^{239}\mathrm{Pu}$ and the spontaneous fission of $^{252}\mathrm{Cf}$ are also presented. In these distributions, the higher-$Z$ peak is found to be clustered around 54 (\ifmmode\pm\else\textpm\fi{}2). The mass of 141 (\ifmmode\pm\else\textpm\fi{}5), where the peaks in the fragment-mass yield curves are obtained, also has these $Z$'s as the most probable charges. In all these distributions, odd-even $Z$ effects are pronounced. The function ${Z}_{p}\ensuremath{-}{Z}_{\mathrm{UCD}}$ for the four cases studied shows vertical shift as well as horizontal shift of the peaks in the distributions with increasing charge and mass of the fissioning nucleus.