As practical uses and experimental observations of nuclear fission continue to develop in the modern world, there is an increasing demand for theoretical models to accurately describe and predict the outcomes of this complex process. My research explores a pathway to such models using the Time-Dependent Generator Coordinate Method (TDGCM), with the goal of extracting mass and charge numbers of fission fragments for comparison with experiment. The TDGCM simulates time evolution of a nucleus across a potential energy surface (PES) describing how the total energy of the nucleus varies with its collective shape. Successful applications of this formalism have so far relied on the Gaussian Overlap Approximation (GOA) to simplify computations, but at a significant cost in accuracy and physical relevance.

I will briefly explain the problem of discontinuities, unphysical artefacts arising during PES generation which prohibit time evolution, and present methods I have developed to effectively remove them. I will then give an overview of the theory of TDGCM in the context of nuclear fission, as well as the problems that have so far hindered its exact implementation without the GOA. Two particular challenges are the construction of an above-barrier initial state for time evolution and the extraction of probabilities for different fission fragments; I will explain in more detail the new and redeveloped techniques I have used to overcome them, and finally summarise how my current and upcoming work will fit together into a predictive model of nuclear fission.