Dynamical interpretation of average fission-fragment kinetic energy systematics and nuclear scission

Abstract

A dynamical interpretation of the well-known systematics for average total kinetic energy of fission fragments $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ over a wide range of the Coulomb parameter ($600<{Z}^{2}/{A}^{1/3}<2200$) is given. Different scission criteria traditionally employed in fission theory---at zero neck radius and at finite neck radius---have been applied in dynamical calculations. Both have resulted in a fairly good description of the dependence of $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ on the Coulomb parameter. The results of dynamical calculations of $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ within three-dimensional Langevin dynamics show that the mean distance between the centers of mass of nascent fragments at the scission configuration increases linearly with the parameter ${Z}^{2}/{A}^{1/3}$. This distance changes approximately from $2.35{R}_{0}$ for $^{119}\mathrm{Xe}$ to $2.6{R}_{0}$ for $^{256}\mathrm{Fm}$. In spite of this increase in mean distance between future fragments at scission, the linear dependence of $\ensuremath{\langle}{E}_{K}\ensuremath{\rangle}$ on the parameter ${Z}^{2}/{A}^{1/3}$ remains approximately valid over a wide range of the Coulomb parameter ${Z}^{2}/{A}^{1/3}$.