Machine learning nuclear orbital-free density functional based on Thomas–Fermi approach

Orbital-free density functional theory (DFT) is much more efficient than the orbital-dependent Kohn–Sham DFT due to the avoidance of the auxiliary one-body orbitals. The machine learning approach has been applied to build nuclear orbital-free DFT recently [Wu et al., Phys. Rev. C105 (2022) L031303] and achieved more precise descriptions for nuclei than existing orbital-free DFTs. Here, improved machine learning nuclear orbital-free density functional is built by including the Thomas–Fermi approach as a basement. Performances of the functional are compared in detail with the ones based on the pure machine learning approach. It is found that with the Thomas–Fermi functional included, the machine-learning-based functional can achieve better performance in directly predicting the kinetic energies and in providing the ground-state properties by the self-consistent procedures.