A new two-center shell model for nuclear fission

Abstract

A two-center single-particle potential is proposed which has the Lawrence family of liquid-drop shapes as its equipotentials. An improved parameterization of these shapes is given that facilitates their use. Only two deformation parameters are required to describe all relevant nuclear shapes for symmetric fission. These encompass Nilsson ground state shapes with ϵ and (approximately) ϵ 4 deformations, dumbbells and spheroidal fragments at large separation. The corresponding potential evolves from a deformed harmonic oscillator for the ground state of the fissioning nucleus to two deformed harmonic oscillators for well-separated fragments. In the single-particle calculation, a Thomas-type spin-orbit potential is used together with an l 2 correction term. The nuclear deformation energy is calculated by Strutinsky's prescription, including pairing energy. Results are given as deformation energy maps for the symmetric fission mode of various actinide nuclei. The asymmetric generalization of the model is outlined.