Machine learning orbital-free density functional theory: taming quantum shell effects in deformed nuclei

TL;DR

This paper introduces a machine learning-enhanced orbital-free density functional theory that accurately captures quantum shell effects in deformed nuclei, overcoming longstanding challenges in nuclear modeling.

Contribution

It presents the first successful application of a machine learning-based orbital-free density functional to describe shell effects in deformed nuclei.

Findings

Achieved high accuracy in ground-state properties of spherical and deformed nuclei.

Demonstrated the practical viability of orbital-free density functional theory for nuclear systems.

Successfully tamed complex shell effects in deformed nuclei using machine learning.

Abstract

Accurate description of deformed atomic nuclei by the orbital-free density functional theory has been a longstanding textbook challenge, due to the difficulty in accounting for the intricate quantum shell effects that are present in such systems. Orbital-free density functional theory is, in principle, capable of describing all effects of nuclear systems, as guaranteed by the Hohenberg-Kohn theorem. However, from a microscopic perspective, shell and deformation effects are believed to be intrinsically connected to single-orbital structures, posing a significant challenge for orbital-free approaches. Here, we develop a machine learning approach to the orbital-free density functional theory, which is capable of achieving a high level of accuracy in describing the ground-state properties and potential energy curves for both spherical $^{16}$O and deformed $^{20}$Ne nuclei. This is the inaugural instance where a fully orbital-free energy density functional has succeeded in taming the complex shell effects in deformed nuclei. It demonstrates that the orbital-free energy density functional, which is directly based on the Hohenberg-Kohn theorem, is not only a theoretical concept but also a practical one for nuclear systems.