Generator coordinate method for transition-state dynamics in nuclear fission

TL;DR

This paper introduces a microscopic reaction-theoretic approach using the Generator Coordinate Method to model transition-state dynamics in nuclear fission, addressing a longstanding gap in the theory.

Contribution

It develops a GCM-based methodology with the Gaussian Overlap Approximation to analyze transition states in nuclear fission microscopically.

Findings

Coarse meshes yield acceptable accuracy for bandwidth and transmission estimates.

The approach avoids numerical stability issues common in GCM calculations.

Channel bandwidths are mainly influenced by zero-point energy in GCM configurations.

Abstract

Since its beginnings, fission theory has asumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Neverthess, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the Generator Coordinate Method (GCM). Simple reaction-theoretic models are constructed with the 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 examined here are their effective bandwidths 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. The bandwidths of the channels are largely controlled by the zero-point energy with respect to the collective coordinate in the GCM configurations.