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

Abstract

Using relativistic Hartree-Fock (RHF) approximation, we study the effect of Fock terms on the nuclear properties not only around the saturation density, ρ 0 , but also at higher densities. In particular, we investigate how the momentum dependence due to the exchange contribution affects the nuclear symmetry energy and its slope parameter, using the Lorentz-covariant decomposition of nucleon self-energies in an extended version of the RHF model, in which the exchange terms are adjusted so as to reproduce the single-nucleon potential at ρ 0 . We find that the Fock contribution suppresses the kinetic term of nuclear symmetry energy at the densities around and beyond ρ 0 .It is noticeable that not only the isovector-vector (ρ) meson but also the isoscalar mesons (σ, ω)and pion make significant influence on the potential term of nuclear symmetry energy through the exchange diagrams. Furthermore, the exchange contribution prevents the slope parameter from increasing monotonically at high densities.

Towards understanding astrophysical effects of nuclear symmetry energy

“…Shown in Fig. 21 are the kinetic and potential parts of E sym (ρ) and L in the four cases obtained by Miyatsu et al [179]. While quantitatively effects of the exchange terms depend on how the model parameters are fixed, several interesting qualitative observations were made [179].…”

“…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.…”

“…Similar to their non-relativistic counterparts discussed in Sect. 2.2, the relativistic expressions for E sym (ρ) and L from the HVH decomposition were found useful [26,178,179]. The self-energy Σ N (k) of a nucleon with (three) momentum k can be written as…”

“…the L kin and L pot will be reduced to their counterparts in the RH approximation [179,182] L kin,dir = 1 3…”

“…However, there are still serious difficulties to describe properly the experimentally constrained nucleon SEP over large energy ranges. For example, Miyatsu et al [179] used two parameter sets by adjusting the exchange terms within their extended RHF (ERHF) model. As shown in Fig.…”