Smoothing of one-and two-dimensional discontinuities in potential energy surfaces

Background: The generation of potential energy surfaces is a critical step in theoretical models aiming to understand and predict nuclear fission. Discontinuities frequently arise in these surfaces in unconstrained collective coordinates, leading to missing or incorrect results. Purpose: This work aims to produce efficient and physically motivated computational algorithms to refine potential energy surfaces by removing discontinuities. Method: Procedures based on tree-search algorithms are developed which are capable of smoothing discontinuities in one-and two-dimensional potential energy surfaces while minimizing their overall energy. Results: Each of the new methods is applied to smooth candidate discontinuities in Cf252, Th222, and Ra218. The effectiveness of each case is analyzed both qualitatively and quantitatively. The one-dimensional method is also compared to the adiabatic and linear interpolation approaches which are commonly used to remove discontinuities. Conclusions: The smoothing methods presented in this work are resource efficient and successful for one-and two-dimensional discontinuities; they will improve the fidelity of potential energy surfaces as well as their subsequent uses in beyond mean-field applications. Complex discontinuities occurring in higher dimensions may require alternative approaches which better utilize prior knowledge of the potential energy surface to narrow their searches.