  An outstanding problem in the theory of nuclear fission is to understand the
Hamiltonian dynamics at the scission point. In this work the fissioning nucleus
is modeled in self-consistent mean-field theory as a set of Generator
Coordinate (GCM) configurations passing through the scission point. In contrast
to previous methods, the configurations are constructed in the Hartree-Fock
approximation with axially symmetric mean fields and using the K-partition
numbers as additional constraints. The goal of this work is to find paths
through the scission point where the overlaps between neighboring
configurations are large. A measure of distance along the path is proposed that
is insensitive to the division of the path into short segments. For most of the
tested K-partitions two shape degrees of freedom are adequate to define smooth
paths. However, some of the configurations and candidate paths have sticking
points where there are substantial changes in the many-body wave function,
especially if quasiparticle excitations are present. The excitation energy
deposited in fission fragments arising from thermal excitations in the
pre-scission configurations is determined by tracking orbital occupation
numbers along the scission paths. This allows us to assess the validity of the
well-known scission-point statistical model, in which the scission process is
assumed to be fully equilibrated up to the separated fission fragments. The
nucleus 236U is taken as a representative example in the calculations.
