Degrees of deformation at scission and correlated fission properties of atomic nuclei

Abstract

The degrees of the deformation of atomic nuclei at scission configurations of the mass-symmetric and mass-asymmetric fission modes are studied. The \ensuremath{\beta} shape elongation of the fissioning nucleus, associated with the asymmetric fission is found to be constant for ${A}_{f}=213\char21{}260,$ while that associated with the symmetric fission is larger but also constant for a wide range of fissioning nuclei ${(A}_{f}=205\char21{}260)$ except for the low-energy induced and spontaneous fission of heavy nuclei with ${A}_{f}=245\char21{}262$ where a change of the nucleon number by one unit is found to cause a very rapid change in \ensuremath{\beta}. A systematic correlation between the scission deformation and the fission properties such as the mass-yield distribution and the TKE are found. The constancy of the \ensuremath{\beta} gives rise to new formulas of ${\mathrm{TKE}}_{\mathrm{sym}}=0.1173\ifmmode\times\else\texttimes\fi{}{(Z}_{f}^{2}{/A}_{f}^{1/3})+7.5\mathrm{MeV}$ for symmetric fission, and of ${\mathrm{TKE}}_{\mathrm{asym}}=0.1217\ifmmode\times\else\texttimes\fi{}{(Z}_{f}^{2}{/A}_{f}^{1/3})+3.5\mathrm{MeV}$ for asymmetric fission. The physical origin of the well-known simple linear function for the TKE released in the fission process is found to be the invariance of the degrees of the elongation of scissioning nuclei. The mass dispersion of fission products was found to have a direct correlation with the \ensuremath{\beta} value; as \ensuremath{\beta} becomes larger, the width of the mass yield distribution becomes wider. Our understanding of the spontaneous fission properties of heavy nuclides in the ${}^{258}\mathrm{Fm}$ region is presented. In this region, two different scission configurations, one giving $\ensuremath{\beta}\ensuremath{\sim}1.53$ which is the characteristic value for the asymmetric deformation and the other giving $\ensuremath{\beta}\ensuremath{\sim}1.33$ which is for the symmetric deformation, are found.