One of the most challenging problems in nuclear physics is to describe
nuclear fission microscopically starting from nucleonic degrees of freedom.
Such microscopic description is important particularly for low-energy
induced fission, in which the excitation energy of the compound nucleus is
relatively low so that an application of the statistical model may be
questionable. This includes fission in r-process nucleosynthesis as well as in
barrier-top fission. Here we shall discuss our recent attempts with a shell
model, for which many-body configurations are constructed based on a
constrained density functional theory for shapes along a fission path. We
specifically present our calculations with the Skyrme functional for a
neutron induced fission of 235U at barrier-top energies. In this exploratory
study, the configuration space is restricted only to neutron seniority-zero
configurations with a relatively small energy cutoff. We find that the
calculated fission-to-capture branching ratio is quite insensitive to the
fission decay widths of the pre-scission configurations, as is assumed in
transition-state theory. However, the probability flux at the barrier is
spread out over many configurations rather than a few transition-state
channels.
