Effect of viscosity on the dynamics of fission

Abstract

We study the effect of ordinary viscosity on nuclear fission by solving clasical equations of motion for the time evolution of fissioning nuclei. The collective potential energy is calculated both by means of the usual liquid-drop model and by means of a modified liquid-drop model that takes into account the lowering in the nuclear macroscopic energy due to the finite range of the nuclear force. The collective kinetic energy is calculated for incompressible, nearly irrotational hydrodynamical flow by use of the Werner-Wheeler method. The Rayleigh dissipation function, which describes the transfer of energy of collective motion into internal excitation energy, is calculated under the assumption that nuclear dissipation arises from individual two-body collisions. Prior to scission the nuclear shape is specified in terms of smoothly joined portions of three quadratic surfaces of revolution. After scission the fission fragments are represented by two spheroids with collinear symmetry axes. In addition to slowing the system down and converting some of the collective energy into internal energy, two-body viscosity hinders the formation of a neck. This leads to a more elongated scission configuration and consequently to a smaller final fission-fragment kinetic energy. From a comparison of calculated and experimental most probable fission-fragment kinetic energies for nuclei throughout the periodic table, we determine that at high excitation energies the average value of the viscosity coefficient $\mu$ is $\mu =0.015\mathrm{}\pm 0.005 \mathrm{TP}=9\mathrm{}\pm 3\times {10}^{-24\mathrm{}}$ MeV s/${\mathrm{fm}}^3$, provided that nuclear dissipation arises from two-body collisions. This is about 30% of the value that is required to critically damp the quadrupole oscillations of idealized heavy actinide nuclei.