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A self-consistent chiral Dirac-Hartree-Fock (CDHF) approximation generated by an effective model of the (σ, ω, π) quantum hadrodynamics is discussed and applied to nuclear matter and neutron stars. The CDHF approximation maintains conditions of thermodynamic consistency connected to the fundamental requirement of density functional theory (DFT). The self-consistent conditions to nuclear matter approximations generate functional equations for self-energies; accurate and rigorous solutions to self-energies are obtained and examined. The difference of solutions constructed by thermodynamic consistency (or DFT) and Feynman diagram approach is compared and discussed explicitly, which should be declared as an open question for many-body theory.
Exchange interactions are more important than direct interactions at nuclear matter saturation density, which suggests that an appropriate nuclear ground state approximation be the HF approximation rather than the mean-field (Hartree) approximation. The current CDHF approximation produces incompressibility and symmetry energy, K = 218 MeV and a4 = 21.3 MeV. The application to neutron stars yields Mmax star /M⊙ = 2.21 in the unit of solar mass and radius R = 11.6 km, which improves mean-field results.
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