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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 Ru104−120 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 γ-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.

We present a systematic ab initio study of clustering in hot dilute nuclear matter using nuclear lattice effective field theory with an SU(4)-symmetric interaction. We introduce a method called light-cluster distillation to determine the abundances of dimers, trimers, and alpha clusters as a function of density and temperature. Our lattice results are compared with an ideal gas model composed of free nucleons and clusters. Excellent agreement is found at very low density, while deviations from ideal gas abundances appear at increasing density due to cluster-nucleon and cluster-cluster interactions. In addition to determining the composition of hot dilute nuclear matter as a function of density and temperature, the lattice calculations also serve as benchmarks for virial expansion calculations, statistical models, and transport models of fragmentation and clustering in nucleus-nucleus collisions.

The inclusion of nucleonic exchange energy has been a long-standing challenge for the relativistic density functional theory (RDFT) in nuclear physics. We propose an orbital-dependent relativistic Kohn-Sham density functional theory to incorporate the exchange energy with local Lorentz scalar and vector potentials. The relativistic optimized effective potential equations for the local exchange potentials are derived and solved efficiently. The obtained binding energies and charge radii for nuclei are benchmarked with the results given by the traditional relativistic Hartree-Fock approach, which involves complicated nonlocal potentials. It demonstrates that the present framework is not only accurate but also efficient.