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 this significantly impacts the accuracy and physical relevance of the results.

 I will briefly present the background theory of PES generation, followed by new methods I developed to smooth unphysical artefacts on the PES known as discontinuities. I will then introduce the theory of TDGCM, and highlight some of the problems I have faced in its application without the GOA to the context of nuclear fission. Next, I will explain the initial results that I obtained, and how they motivate the addition of a finite element basis to support calculations on an irregular mesh of constraints. Finally, I will present and analyse my most recent results to draw conclusions from my research and consider its impact on the future of nuclear fission models.

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