The binding energy of nuclear matter with pionic degree of freedom

The renormalization of pion exchange nucleon self-energy in nuclear matter is made by dispersion relation. The exchange and correlation energies (in the ring approximation) of pion, σ and ω mesons, are derived and used to calculate the binding energy of nuclear matter at zero temperature. We find that σ, ω and π mesons cannot saturate the binding energy of nuclear matter in the relativistic RPA approximation, but the saturation can be achieved by making a density-dependent correction to the σNN, ωNN coupling constants. We also verify that the binding energy can saturate in the relativistic Hartree approximation plus the exchange and correlation energies of π meson.