Constructing Inverse Scattering Potentials for α-α System using Physics Informed Machine Learning

Abstract

An accurate way to incorporate long-range Coulomb interaction alongside short-range nuclear interaction remains challenging for theoretical physicists till date. Machine learning algorithms for global optimization, with physics equations guiding the process, are able to obtain robust models from available experimental data. In this article, we utilize the phase equation, which requires only potential and scattering energies as inputs, to obtain scattering phase shifts for the alpha-alpha system to construct the inverse potentials for its S, D, and G states. By incorporating the phase equation within an iterative loop of optimization code, mean absolute percentage error(MAPE) is minimized to obtain the best model parameters for a chosen reference potential. The key to successfully incorporating Coulomb interaction is in designing a reference potential. Here, a combination of two smoothly joined Morse functions, one regular followed by an inverted one, is considered. While the former takes care of short-range nuclear and Coulomb interactions, the latter accounts for expected barrier height due to the long-range Coulomb part that dominates once nuclear interaction subsides. The constructed inverse potentials for S, D, and G states have resulted in MAPE of 0.9, 0.5, and 0.4 and resonances(experimental) at 0.1240(0.0918), 2.95(3.03), and 11.89(11.35) respectively.