DOUBLE-CENTRE OSCILLATOR AND ITS APPLICATION TO FISSION

A single-particle potential appropriate for the description of the nuclear fission process has been investigated. This potential is based on a two-centre harmonic oscillator and includes the proper boundary condition for the ground state of the fissioning nucleus as well as for the two separated fragments. Therefore, this potential may be directly used in a Hamiltonian for a schematic fission model. The single-particle solutions of the Schrödinger equation of this potential have been found by a matching procedure. They are given analytically. Therefore these wave functions are very suitable as a basis for the treatment of potentials with similar shapes. The collective potential energy surface calculated within the two-centre shell model has the proper asymptotic behaviour, e.g. the potential energy decreases for large deformations (separations). © 1969.