Further studies in the liquid-drop theory on nuclear fission

Abstract

We study the properties of the division of an idealized nucleus using a simplified version of the liquid-drop model. The shape of the nuclear surface is specified by means of a parameterization that has six degrees of freedom, defined in terms of three smoothly joined portions of quadratic surfaces of revolution (e.g. two spheroids connected by a hyperboloidal neck). The system's Hamiltonian is treated in an approximation in which the potential energy is considered to be a sum of surface and Coulomb energies. The kinetic energy is calculated according to the method of Werner and Wheeler, which approximates the internal hydrodynamical flow by the flow of circular layers of fluid; this type of flow corresponds approximately to the irrotational flow of a non-viscous incompressible fluid. On the basis of this model, we calculate probability distributions for the masses and kinetic energies of the fragments at infinity. For nuclei throughout the periodic table, the calculated distributions are compared with experimental distributions as functions of the internal excitation energy of the compound nuclei undergoing fission. The comparisons indicate that this simplified version of the non-viscous irrotational liquid-drop model is not capable of accounting for the properties of the division of heavy nuclei at low excitation energies (e.g. for the observed mass asymmetry). However, it does reproduce approximately experimental fission-fragment mass and energy distributions for the fission of heavy nuclei at high excitation energies (energies above about 40 MeV) and medium-weight nuclei at all excitation energies. In all cases, the experimental kinetic energies and widths are larger than the calculated ones (for non-viscous irrotational flow), and this and other evidence suggest that in the fission process the flow of nuclear matter is either rotational or viscous.