A new approach to barrier-top fission dynamics

We proposed a calculational framework for describing induced fission that avoids the Bohr-Wheeler assumption of well-defined fission channels. The building blocks of our approach are configurations that form a discrete, orthogonal basis and can be characterized by both energy and shape. The dynamics is to be determined by interaction matrix elements between the states rather than by a Hill-Wheeler construction of a collective coordinate. Within our approach, several simple limits can be seen: diffusion; quantized conductance; and ordinary decay through channels. The specific proposal for the discrete basis is to use the $K^\pi$ quantum numbers of the axially symmetric Hartree-Fock approximation to generate the configurations. Fission paths would be determined by hopping from configuration to configuration via the residual interaction. We show as an example the configurations needed to describe a fictitious fission decay $^{32}{\rm S} \rightarrow ^{16}{\rm O} + ^{16}{\rm O}$. We also examine the geometry of the path for fission of $^{236}$U, measuring distances by the number of jumps needed to go to a new $K^\pi$ partition.