Single-Particle Resonant States in Relativistic Hartree-Fock Theory: A Green's Function Approach
Relativistic Hartree-Fock theory is combined with the Green's function method in coordinate space to study both single-particle bound and resonant states within a unified framework. Within this approach, single-particle resonance energies and widths are unambiguously extracted from the density of states, and the influence of the Coulomb exchange effects on proton resonances in $N=82$ isotones are systematically examined. It is found that the exact treatment of Coulomb exchange terms reduces proton resonance energies of approximate $0.09\sim0.21$ MeV, a significantly smaller effect than that obtained from the phenomenological treatment. Moreover, except for rather narrow resonances, the proton resonance widths are visibly reduced by the Coulomb exchange terms, also being much less pronounced than the phenomenological approach. Notably, clear shell effects are observed in the isotonic evolutions of the resonance energy reductions for specific resonances. All these highlight the necessity of a microscopical and exact treatment of the Coulomb exchange terms.