Exact-exchange relativistic density functional theory in three-dimensional coordinate space

TL;DR

This paper introduces a novel three-dimensional relativistic density functional theory for atomic nuclei, solving the exact-exchange problem without symmetry restrictions, and demonstrates its effectiveness through benchmarking and analysis of neutron-rich isotopes.

Contribution

It presents the first 3D solution of exact-exchange relativistic DFT for nuclei, incorporating exchange correlations beyond traditional methods.

Findings

Accurate binding energies, charge radii, and density distributions.

Revealed gamma-softness in neutron-rich Ru isotopes.

Established a foundation for symmetry-unrestricted nuclear studies.

Abstract

The exact-exchange relativistic density functional theory (Ex-RDFT) of atomic nuclei has been solved in three-dimensional lattice space for the first time. The exchange energy is treated within the framework of the orbital-dependent relativistic Kohn-Sham density functional theory, wherein the local Lorentz scalar and vector potentials are derived using the relativistic optimized effective potential method. The solutions of binding energies, charge radii, and density distributions are benchmarked against the traditional relativistic Hartree-Fock approach for spherical and axially deformed nuclei. Furthermore, the triaxial neutron-rich $^{104-120}\text{Ru}$ isotopes are investigated with the exchange correlations, which is beyond the current capacity of the traditional relativistic Hartree-Fock approach. The results notably indicate the $\gamma$-softness of these neutron-rich nuclei, which is consistent with experimental observations. This novel approach establishes a foundation for the study of nuclei without imposing any symmetry restrictions employing relativistic density functional with exchange correlations.