The mean field description of nuclear fission

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Abstract
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. It is not clear which degrees of freedom should be invoked in order to obtain an optimal description of the fission phenomena.