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

TL;DR

This paper introduces efficient, physically-motivated algorithms based on tree-search methods to smooth discontinuities in one- and two-dimensional potential energy surfaces, improving their accuracy for nuclear fission modeling.

Contribution

It presents novel smoothing algorithms that effectively remove discontinuities in potential energy surfaces, outperforming traditional interpolation methods in terms of resource efficiency and accuracy.

Findings

Successfully smoothed discontinuities in ${}^{252} ext{Cf}$, ${}^{222} ext{Th}$, and ${}^{218} ext{Ra}$.

Compared new methods to adiabatic and linear interpolation, showing improved performance.

Methods are resource-efficient and enhance the fidelity of potential energy surfaces.

Abstract

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 minimising their overall energy. Results: Each of the new methods is applied to smooth candidate discontinuities in ${}^{252}\mathrm{Cf}$, ${}^{222}\mathrm{Th}$ and ${}^{218}\mathrm{Ra}$. The effectiveness of each case is analysed 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 utilise prior knowledge of the potential energy surface to narrow their searches.