The asymmetric nuclear matter is investigated in the DBHF approach with a new decomposition of the Dirac structure of nucleon self-energy. The coupling constants of σ, ω, δ and ρ mesons are deduced by reproducing the self-energy of DBHF calculation at every density and every asymmetry parameter in the RMF approximation. With these couplings the properties of finite nuclei are investigated. It is found that both scalar and vector potentials of neutron in the neutron rich nuclear matter become stronger although the isospin dependence of them is weaker. A significant difference in comparison with those, that the nucleon self-energy is deduced from the single particle energy, is observed. The nuclear binding energy as a function of the asymmetry parameter fulfills the empirical
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