Impact of Fock terms on the isospin properties of nuclear matter

Abstract

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.The isospin properties of nuclear matter, such as the nuclear symmetry energy, the nucleon isovector (symmetry) potential, and the neutron-proton effective mass splitting, play essential roles in studying several topics of nuclear structure, nuclear reactions and nuclear astrophysics [1][2][3][4][5][6][7]. Among them of great contemporary interest is the nuclear symmetry energy E S [8], which has been investigated extensively within both phenomenological approaches and microscopic many-body theories using almost all available effective and/or realistic nuclear interactions, see, e.g., Refs. [9][10][11][12][13][14]. Due F -to our limited knowledge about the in-medium effects of nucleon-nucleon (NN) interactions and correlations along with technical difficulties to treat quantum many-body systems accurately, distinct deviations of predicted E S values appear beyond the nuclear saturation density ρ 0 .For the description of the structural properties of nuclear systems, the covariant density functional (CDF) theory has achieved great success during recent decades [15][16][17][18][19][20][21][22][23]. One of the most popular representatives is the relativistic Hartree approach with the no-sea approximation, namely, the relativistic mean field (RMF) theory [15,[24][25][26]. However, due to the limit of the approach itself, significant system degrees of freedom are missing in RMF, such as the one-pion exchange. The non-local effects of nuclear forces and the momentum dependence of self-energies are also hardly to be treated. With the growth of computational facilities and the development of new methods, such defects can be eliminated with the inclusion of exchange (Fock) terms, which generates a new CDF model -the relativistic Hartree-Fock (RHF) theory with density-dependent meson-nucleon couplings (i.e., the DDRHF theory) [27]. Substantial improvements are gained by DDRHF in the selfconsistent description of the ground state properties [27][28][29][30][31][32][33][34][35][36][37][38], the excitation modes [39][40][41][42] of finite nuclei and nuclear astrophysics as well [43][44][45][46].It has been shown from several studies that the inclusion of the Fock terms in the CDF theory could ...

Towards understanding astrophysical effects of nuclear symmetry energy

“…Indeed, much efforts and progresses have been made in recent years. In particular, effects of the Fock terms on the symmetry energy have been studied in the Relativistic Hartree-Fock (RHF) model or covariant density functional theory [174,175,176,177,178,179]. In the following, a few main results of the very recent work by Tsuyoshi Miyatsu et al [179] within their extended RHF (ERHF) approach are used to illustrate the main roles of the Fock exchange terms on the E sym (ρ) and some remaining issues.…”

Fock contributions to nuclear symmetry energy and its slope parameter based on Lorentz-covariant decomposition of nucleon self-energies

“…( 34) and ( 35) are different from those given in Refs. [65][66][67]. Since the nucleon self-energies, Σ s,0,v N , can be separated into the direct and exchange contributions, the direct one in E pot sym is exactly the same as in RH approximation [6,79]:…”

“…On the other hand, some theoretical calculations on E sym have been carried out in the RHF model [64][65][66][67], and E sym is again often divided into E kin sym and E pot sym , which are expressed in terms of the derivatives of the expectation valuables, T and V , where the nuclear matter Hamiltonian is given as H = T +V [68]. Since this decomposition does not correspond to that in the experimental analyses, it may be misleading to compare the components, E kin sym and E pot sym , in the experimental results with the theoretical results calculated in Refs.…”

“…Since this decomposition does not correspond to that in the experimental analyses, it may be misleading to compare the components, E kin sym and E pot sym , in the experimental results with the theoretical results calculated in Refs. [64][65][66][67]. In contrast, an alternative decomposition based on the Lorentz-covariant forms of nucleon self-energies has been proposed in Refs.…”

Interplay of short-range correlations and nuclear symmetry energy in hard-photon production from heavy-ion reactions at Fermi energies

“…[26,27]. For example, properties of the short-range tensor force and ramifications of the HMT on the Equation of State (EOS) of neutron-rich matter [28][29][30][31][32], especially the density dependence of nuclear symmetry energy E sym (ρ) are still poorly known. The E sym (ρ) encodes information about the isospin dependence of nuclear EOS, it is measured in the so-called parabolic approximation of the EOS by the change in single nucleonic energy when all protons are replaced by neutrons [33].…”