An improved description of nuclear fission with the Time Dependent Generator Coordinate Method

Abstract

The discovery of nuclear fission in the 1930s dramatically influenced the history of the 20th century, and the process still has many crucial applications in the world today. While theoretical and experimental investigations of nuclear fission have often been intertwined, the presently expanding frontiers of its research are largely driven by experimental work, accompanied by an increasing demand for accurate and predictive simulations of fission. The purpose of this thesis is to present several new improvements to nuclear fission models based on the time-dependent generator coordinate method (TDGCM), with the overarching aim of producing a theoretical description of nuclear fission that can both verify and predict experimental outcomes.

Before simulating fission dynamics, the energetics of the deforming compound nucleus must first be mapped by calculating a potential energy surface (PES). While the procedure of obtaining a PES is well established, it often leads to the presence of artefacts on the surface known as discontinuities. New search-based methods to characterise and remove discontinuities are proposed and tested in order to produce a smooth PES that accurately represents the configurations of the fissioning nucleus. These algorithms are simple, deterministic, and efficient, but it is expected that new approaches will be better suited for the treatment of more complex discontinuities in future, and some recent literature presenting such techniques is reviewed.

Given a discontinuity-free PES, fission dynamics can then be simulated with the TDGCM; however, the majority of previous attempts to do so have utilised the Gaussian overlap approximation (GOA) to simplify calculations. Their results are mostly suitable for qualitative interpretations, and furthermore the validity of the GOA is not always well established. In the current work it is argued that the removal of the GOA will lead to more predictive outcomes, as well as better theoretical grounding for models. A new GOA-free formulation of TDGCM is explained in detail, and both one- and two-dimensional implementations of this model are tested. While the initial results obtained are not representative of the fission process, careful analysis leads not only to improvements of the underlying theory and how it is applied, but also to unexpected insights that may influence future descriptions of nuclear fission with TDGCM. The upcoming prospects for the new TDGCM model are discussed, and potential research directions to advance the field of nuclear fission models in general are presented.