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

Using relativistic Hartree-Fock (RHF) approximation, we study the effect of Fock terms on the nuclear properties not only around the saturation density, $rho_{0}$, 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 $rho_{0}$. We find that the Fock contribution suppresses the kinetic term of nuclear symmetry energy at the densities around and beyond $rho_{0}$. It is noticeable that not only the isovector-vector ($rho$) meson but also the isoscalar mesons ($sigma, omega$) 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.