Abstract
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.
Highlights
In this talk we will advocate a radically different approach to the theory of induced fission
Shown in green, the dynamics is driven by the pairing interaction
The concept of a channel demands that the wave function can be written as a product of an internal part and a one-dimensional function of some collective coordinates. This is leads to the Born-Oppenheimer approximation in molecular dynamics, which is well justified by the large separation of electron and nucleus mass scales
Summary
In this talk we will advocate a radically different approach to the theory of induced fission. The concept of a channel demands that the wave function can be written as a product of an internal part and a one-dimensional function of some collective coordinates This is leads to the Born-Oppenheimer approximation in molecular dynamics, which is well justified by the large separation of electron and nucleus mass scales. That is O.K. for the Born-Oppenheimer framework for molecular physics, but the separation of collective and intrinsic energy scales is not present in nuclear physics. Another problem is the non-orthogonality of the channel wave functions in the GCM. We heard in the Workshop a report on a microscopic dynamical model that produced a fission time so large that inertial motion would be highly over-damped [8]
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