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Register a new userNuclear matter in relativistic Brueckner-Hartree-Fock theory with Bonn potential in the full Dirac space
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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.
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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.
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.
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.
The isospin dependence of the nucleon effective mass is investigated in the framework of the Dirac Brueckner-Hartree-Fock (DBHF) approach. The definition of nucleon scalar and vector effective masses in the relativistic approach is clarified. Only the vector effective mass is the quantity related to the empirical value extracted from the analysis in the nonrelatiistic shell and optical potentials. In the relativistic mean field theory, where the nucleon scalar and vector potentials are both energy independent, the neutron vector potential is stronger than that of proton in the neutron rich nuclear matter, which produces a smaller neutron vector effective mass than that of proton. It is pointed out that the energy dependence of nucleon potentials has to be considered in the analysis of the isospin dependence of the nucleon effective mass. In the DBHF the neutron vector effective mass is larger than that of proton once the energy dependence of nucleon potentials is considered. The results are consistent with the analysis of phenomenological isospin dependent optical potentials.
Tensor force is identified in each meson-nucleon coupling in the relativistic Hartree-Fock theory. It is found that all the meson-nucleon couplings, except the $sigma$-scalar one, give rise to the tensor force. The effects of tensor force on various nuclear properties can now be investigated quantitatively, which allows fair and direct comparisons with the corresponding results in the non-relativistic framework. The tensor effects on nuclear binding energies and the evolutions of the $Z,,N = 8,,20$, and $28$ magic gaps are studied. The tensor contributions to the binding energies are shown to be tiny in general. The $Z,,N = 8$ and $20$ gaps are sensitive to the tensor force, but the $Z,,N = 28$ gaps are not.
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