On the Stiffness of Fission Fragments

Abstract

The steep rises of the stiffness of fission fragments near N=50 and Z=50 (or N=82) closed shells are assumed to be ascribed to variation of the surface tension from nucleus to nucleus. The deformation energy of the fragments at scission and the average total kinetic energy of the fragment pair are calculated by using the tangent spheroid approximation of two deformed liquid drops. General tendencies of the low energy fission, such as Terrel's universal curve of the prompt neutron numbers and the salient dip of the total kinetic energy of frag­ ment pair in the symmetric region of mass splits, are qualitatively reproduced. 1. In recent few years, refined experiments on the low energy fission phenomena have established unexpected facts such as a drastic dip of the total kinetic energy of a fragment pair in the symmetric region of mass splie) and the so-called saw-tooth structure in the average number of prompt neutrons emitted per fragment as a function of the individual fragment mass.2) ]_ Terrel suggested that these phenomena are due to the special property of N=50 and Z=50 (or N=82) magic nuclides that in their neighbourhood nuclei are considered to have unusual stiffness against defor­ mation and prefer spherical shape.3) Although fission fragments have excess neutrons comparing with the stable nuclei, the steep rises of their stiffness in the neighbourhood of N=50 and Z=50 (or N=82) magic numbers are seen from the fission data and the extrapolation of the Coulomb excitation data. 4) Taking into account of this by making use of the very simple model,) our previous calculations were carried out successfully to some extent. It is very complicated to derive the variation of the stiffness as a function of mass number (or proton and neutron number) even from the phenome­ nological theory. In what follows we will treat this effect by assuming tentative dependence on the mass of fragments. 2. We will assume that the fragment configuration at scission can be approximated by two spheroidally deformed fragments co-axially in contact each other, and we describe the shape of the fragments simply by axial symmetric (r=O) {3 deformation: