Systematic study of one-point kinetic energy density functionals for atomic nuclei

TL;DR

This study systematically benchmarks 36 one-point kinetic energy density functionals, originally designed for electron systems, to assess their suitability and optimize their parameters for nuclear physics applications using OF-DFT.

Contribution

It demonstrates that re-optimizing parameters of GGA functionals for nuclear densities yields consistent accuracy and captures key nuclear features.

Findings

Optimized functionals achieve ~13 MeV RMS error.

Original electron-based parameters perform inconsistently.

Optimized functionals reflect nuclear liquid-drop behavior and shell effects.

Abstract

To explore the applicability of orbital-free density functional theory (OF-DFT) in nuclear physics, we perform a systematic benchmark of 36 one-point kinetic energy density functionals, which are originally developed for electron systems in condensed matter physics. It is found that the direct use of the original parameters for electron systems leads to inconsistent performance, with certain functionals exhibiting physically unacceptable asymptotic behaviors. However, through parameter re-optimization targeting nuclear densities, different mathematical forms of generalized gradient approximation (GGA) functionals converge to a consistent root-mean-square error of approximately 13 MeV. From a physical perspective, this consistent behavior signifies that the optimized semi-local GGAs have successfully captured the macroscopic, liquid-drop-like background of the nucleus, while the residual deviations appear as periodic oscillations at the magic numbers that could reflect the quantum shell effects.