Effect of dissipation on ternary fission in very heavy nuclear systems

On the basis of a macroscopic dynamical model, we explore the effect of two prototype dissipation mechanisms that represent opposite extremes of small and large dissipation on the formation of a third fragment during the fission of very heavy nuclear systems. With five collective coordinates to describe axially symmetric and reflection-symmetric nuclear shapes, we solve the generalized Hamilton equations of motion numerically to determine the time evolution of the system. The nuclear potential energy of deformation is calculated as the sum of a repulsive Coulomb energy and an attractive Yukawa-plus-exponential potential, the inertia tensor is calculated for incompressible, nearly irrotational flow by use of the Werner-Wheeler method and the dissipation tensor is calculated for both two-body viscosity and one-body dissipation. For light nuclei the dynamical evolution leads to compact binary scission shapes, but for sufficiently heavy nuclei it leads to shapes with long necks that subsequently contract at the extremities to form three fragments. This ternary division, whose onset begins at Z 2 A∼35 for two-body viscosity and much later at Z 2 A∼57 for one-body dissipation, is examined in terms of a neck instability that is analogous to the Plateau-Rayleigh hydrodynamic instability of an uncharged, infinite, initially stationary cylinder. For nuclear systems with mass numbers ranging from 200 to 500, we calculate the mass of the third fragment that forms under certain circumstances, the translational kinetic energy of the two end fragments at infinity, and the time required for the system to descend from its saddle point to scission.