The mean-field description of nuclear fission

Potential energy surfaces for fission studies of a model rare-earth nucleus are calculated in a constrained static Hartree-Fock approximation using both single-centre and two-centre trial functions. Difficulties in interpreting the results in terms of a fission barrier are discussed. The time evolution of the static configurations boosted by a quadrupole velocity field is studied within the framework of the time-dependent Hartree-Fock theory. Single-centre configurations exhibit a rapidly damped oscillatory behaviour while two-centre configurations can be induced to fission. It is clear that the extreme mean-field picture is inadequate to describe the fission process. The failure lies principally with the single-determinant approximation. Any process, such as pairing, which causes a mixing of determinants will ameliorate the problem. (author)