Generator coordinate method for transition-state dynamics in nuclear fission

Abstract

The existence of transition channels across the fission barrier has been central to the theory of induced fission, but there has been no microscopic theory applicable to energies at the barrier top. We propose a microscopic treatment motivated by the Generator Coordinate Method (GCM) and Gaussian Overlap Approximation (GOA) to parameterize both the dynamics within the channels and their incoherent couplings to states outside the barrier. The physical characteristics of the channels (often called "transition states") examined here are their effective bandwidths for crossing the barrier and the quality of the coupling to compound-nucleus states as measured by the transmission factor T . We also investigate the spacing of GCM states with respect to their degree of overlap. We find that a rather coarse mesh provides an acceptable accuracy for estimating the bandwidths and transmission factors. The common numerical stability problem in using the GCM is avoided due to the choice of meshes and the finite bandwidths of the channels.