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Register a new userRelativistic Brueckner-Hartree-Fock in nuclear matter without the average momentum approximation
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Brueckner-Hartree-Fock theory allows to derive the $G$-matrix as an effective interaction between nucleons in the nuclear medium. It depends on the center of mass momentum $bm{P}$ of the two particles and on the two relative momenta $bm{q}$ and $bm{q}$ before and after the scattering process. In the evaluation of the total energy per particle in nuclear matter usually the angle averaged center of mass momentum approximation has been used. We derive in detail the exact expressions of the angular integrations of the momentum $bm{P}$ within relativistic Brueckner-Hartree-Fock (RBHF) theory, especially for the case of asymmetric nuclear matter. In order to assess the reliability of the conventional average momentum approximation for the binding energy, the saturation properties of symmetric and asymmetric nuclear matter are systematically investigated based on the realistic Bonn nucleon-nucleon potential. It is found that the exact treatment of the center of mass momentum leads to non-negligible contributions to the higher order physical quantities. The correlation between the symmetry energy $E_{mathrm{sym}}$, the slope parameter $L$, and the curvature $K_{mathrm{sym}}$ of the symmetry energy are investigated. The results of our RBHF calculations for the bulk parameters characterizing the equation of state are compared with recent constraints extracted from giant monopole resonance and isospin diffusion experiments.
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On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier investigations, the $G$-matrix is calculated only in the space of positive energy solutions. On the other side, for the solution of the relativistic Hartree-Fock (RHF) equations, also the elements of this matrix connecting positive and negative energy solutions are required. So far, in the literature, these matrix elements are derived in various approximations. We discuss solutions of the Thompson equation for the full Dirac space and compare the resulting equation of state with those of earlier attempts in this direction.
Starting from the Bonn potential, relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for nuclear matter in the full Dirac space, which provides a unique way to determine the single-particle potentials and avoids the approximations applied in the RBHF calculations in the Dirac space with positive-energy states (PESs) only. The uncertainties of the RBHF calculations in the Dirac space with PESs only are investigated, and the importance of the RBHF calculations in the full Dirac space is demonstrated. In the RBHF calculations in the full Dirac space, the empirical saturation properties of symmetric nuclear matter are reproduced, and the obtained equation of state agrees with the results based on the relativistic Greens function approach up to the saturation density.
We investigate the appearance of di-neutron bound states in pure neutron matter within the Brueckner-Hartree-Fock approach at zero temperature. We consider Argonne $v_{18}$ and Paris bare interactions as well as chiral two- and three-nucleon forces. Self-consistent single-particle potentials are calculated controlling explicitly singularities in the $g$ matrix associated with bound states. Di-neutrons are loosely bound, with binding energies below $1$ MeV, but are unambiguously present for Fermi momenta below $1$ fm$^{-1}$ for all interactions. Within the same framework we are able to calculate and characterize di-neutron bound states, obtaining mean radii as high as $sim 110$ fm. The resulting equations of state and mass-radius relations for pure neutron stars are analyzed including di-neutron contributions.
With the relativistic representation of the nuclear tensor force that is included automatically by the Fock diagrams, we explored the self-consistent tensor effects on the properties of nuclear matter system. The analysis were performed within the density-dependent relativistic Hartree-Fock (DDRHF) theory. The tensor force is found to notably influence the saturation mechanism, the equation of state and the symmetry energy of nuclear matter, as well as the neutron star properties. Without introducing any additional free parameters, the DDRHF approach paves a natural way to reveal the tensor effects on the nuclear matter system.
The impact of Hartree-Fock correlations on the nuclear momentum distribution is studied in a fully relativistic one boson exchange model. Hartree-Fock equations are exactly solved to first order in the coupling constants. The renormalization of the Dirac spinors in the medium is shown to affect the momentum distribution, as opposed to what happens in the non-relativistic case. The unitarity of the model is shown to be preserved by the present renormalization procedure.
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