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Register a new userSelf-consistent tensor effects on nuclear matter system under relativistic Hartree-Fock approach
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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.
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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.
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.
A new relativistic Hartree-Fock approach with density-dependent $sigma$, $omega$, $rho$ and $pi$ meson-nucleon couplings for finite nuclei and nuclear matter is presented. Good description for finite nuclei and nuclear matter is achieved with a number of adjustable parameters comparable to that of the relativistic mean field approach. With the Fock terms, the contribution of the $pi$-meson is included and the description for the nucleon effective mass and its isospin and energy dependence is improved.
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 study relativistic nuclear matter in the $sigma - omega$ model including the ring-sum correlation energy. The model parameters are adjusted self-consistently to give the canonical saturation density and binding energy per nucleon with the ring energy included. Two models are considered, mean-field-theory where we neglect vacuum effects, and the relativistic Hartree approximation where such effects are included but in an approximate way. In both cases we find self-consistent solutions and present equations of state. In the mean-field case the ring energy completely dominates the attractive part of the energy density and the elegant saturation mechanism of the standard approach is lost, namely relativistic quenching of the scalar attraction. In the relativistic Hartree approach the vacuum effects are included in an approximate manner using vertex form factors with a cutoff of 1 - 2 GeV, the range expected from QCD. Due to the cutoff, the ring energy for this case is significantlysmaller, and we obtain self-consistent solutions which preserve the basic saturation mechanism of the standard relativistic approach.
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