Density-dependent Relativistic Hartree-Fock Theory Research Articles

Publisher's Note: Δ(1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars [Phys. Rev. C 94, 045803 (2016)

Received 16 July 2020DOI:https://doi.org/10.1103/PhysRevC.102.019905©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEquations of state of nuclear matterNuclear density functional theoryNuclear forcesNuclear many-body theoryNuclear matter in neutron starsPhysical SystemsHyperonsNuclear Physics

Impact of Fock terms on the isospin properties of nuclear matter

Several topics on the isospin properties of nuclear matter studied within the density-dependent relativistic Hartree-Fock theory are summarized. In detail, the effects of the Fock terms on the nuclear symmetry energy are listed, including the extra enhancement from the Fock terms of the isoscalar meson-nucleon coupling channels, the extra hyperon-induced suppression effect originating from the Fock channel, self-consistent tensor effects embedded automatically in the Fock diagrams, the enhanced density-dependent isospin-triplet potential part of the symmetry energy at high densities, a reduced kinetic symmetry energy at supranuclear density and so on. The results demonstrate the importance of the Fork diagram, especially from the isoscalar mesonnucleon coupling channels, on the isospin properties of the in-medium nuclear force.

Symmetry energy of nuclear matter in relativistic Hartree-Fock theory

Several topics on the symmetry energy of nuclear matter in relativistic Hartree-Fock theory are reviewed. General formulism of the newly developed density-dependent relativistic Hartree-Fock theory for hadronic matter is presented briefly. The effects of Fock terms on the nuclear symmetry energy are reviewed in detail from three aspects: the extra enhancement from the Fock terms of the isoscalar meson-nucleon coupling channels, the extra hyperon-induced suppression effect originating from the Fock channel, self-consistent tensor effects embedded automatically in the Fock diagrams. The naturally involved tensor force components in the Fock diagrams soften the density-dependent behavior of the symmetry energy and consequently lead neutron stars to be more compact. Finally, the error estimates of theoretical models are performed by doing a variation procedure, and possible ways to improve the relativistic Hartree-Fock models are discussed.

Spin symmetry in Dirac negative-energy spectrum in density-dependent relativistic Hartree-Fock theory

The spin symmetry in the Dirac negative energy spectrum and its origin are investigated for the first time within the density-dependent relativistic Hartree-Fock (DDRHF) theory. Taking the nucleus $^{16}$O as an example, the spin symmetry in the negative energy spectrum is found to be a good approximation and the dominant components of the Dirac wave functions for the spin doublets are nearly identical. In comparison with the relativistic Hartree approximation where the origin of spin symmetry lies in the equality of the scalar and vector potentials, in DDRHF the cancellation between the Hartree and Fock terms is responsible for the better spin symmetry properties and determines the subtle spin-orbit splitting. These conclusions hold even in the case when significant deviations from the G-parity values of the meson-antinucleon couplings occur.

Neutron star equation of state in density dependent relativistic Hartree–Fock theory

The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree–Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M⊙, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.

Shell structure and ρ-tensor correlations in density dependent relativistic Hartree-Fock theory

A new effective interaction PKA1 with \ensuremath{\rho}-tensor couplings for the density dependent relativistic Hartree-Fock (DDRHF) theory is presented. It is obtained by fitting selected empirical ground state and shell structure properties. It provides satisfactory descriptions of nuclear matter and the ground state properties of finite nuclei at the same quantitative level as recent DDRHF and relativistic mean field (RMF) models. Significant improvement in the single-particle spectra is also found due to the inclusion of \ensuremath{\rho}-tensor couplings. As a result, PKA1 cures a common disease of the existing DDRHF and RMF Lagrangians, namely, the artificial shells at 58 and 92, and recovers the realistic subshell closure at 64. Moreover, the proper spin-orbit splittings and well-conserved pseudospin symmetry are obtained with the new effective interaction PKA1. Due to the extra binding introduced by the \ensuremath{\rho}-tensor correlations, the balance between the nuclear attractions and the repulsions is changed, and this constitutes the physical reason for the improvement of the nuclear shell structure.

Pseudo-spin symmetry in density-dependent relativistic Hartree–Fock theory

The pseudo-spin symmetry (PSS) is investigated in the density-dependent relativistic Hartree-Fock theory by taking {the} doubly magic nucleus $^{132}$Sn as a representative. It is found that the Fock terms bring significant contributions to the pseudo-spin orbital potentials (PSOP) and make it comparable to the pseudo-centrifugal barrier (PCB). However, these Fock terms in the PSOP are counteracted by other exchange terms due to the non-locality of the exchange potentials. The pseudo-spin orbital splitting indicates that the PSS is preserved well for the partner states $\lrb{\nu 3s_{1/2}, \nu2d_{3/2}}$ of $^{132}$Sn in the relativistic Hartree-Fock theory.

Neutron rich nuclei in density dependent relativistic Hartree-Fock theory with isovector mesons

Density dependent relativistic Hartree-Fock theory has been extended to describe properties of exotic nuclei. The effects of Fock exchange terms and of π- and ρ- meson contributions are discussed. These effects are found to be more important for neutron rich nuclei than for nuclei near the valley of stability.

Contribution of Fock Term to Properties of Exotic Nuclei

Density dependent relativistic Hartree-Fock theory has been extended to describe properties of exotic nuclei. The contribution of Fock exchange terms is emphasized in this letter. It turns out that the influence of Fock terms on properties of neutron rich nuclei is very different from those for nuclei near stability line.