New Calculation of Fission Barriers for Heavy and Superheavy Nuclei

Abstract

On the basis of the macroscopic-microscopic method we have performed a new calculation of the nuclear potential energy of deformation for heavy and superheavy nuclei. Our primary emphasis has been to develop techniques that permit more accurate extrapolations both to the large deformations encountered in fission and heavy-ion reactions and to new regions of nuclei. With this purpose in mind, we specify the nuclear shape with five degrees of freedom, in terms of smoothly joined portions of three quadratic surfaces of revolution (e.g., two spheroids connected by a hyperboloidal neck). The single-particle potential is obtained by folding a Yukawa function with a uniform sharp-surface generating potential of appropriate shape. The parameters describing the potential are obtained from statistical (Thomas-Fermi) calculations that reproduce correctly the average trends throughout the Periodic Table of a variety of nuclear properties. To solve the Schrödinger equation for the single-particle energies and wave functions, we have used mainly an expansion of the wave function in a set of deformed harmonic-oscillator basis functions, but have also investigated a finite-difference method. Shell and pairing corrections are calculated from the single-particle energies by means of the methods developed by Strutinsky and added to the surface and Coulomb energies of the liquid-drop model to obtain the total potential energy of deformation.