The isospin dependence of the nucleon effective mass is investigated in the framework of the Dirac Brueckner-Hartree-Fock (DBHF) approach. The definition of nucleon scalar and vector effective masses in the relativistic approach is clarified. Only the vector effective mass is the quantity related to the empirical value extracted from the analysis in the nonrelatiistic shell and optical potentials. In the relativistic mean field theory, where the nucleon scalar and vector potentials are both energy independent, the neutron vector potential is stronger than that of proton in the neutron rich nuclear matter, which produces a smaller neutron vector effective mass than that of proton. It is pointed out that the energy dependence of nucleon potentials has to be considered in the analysis of the isospin dependence of the nucleon effective mass. In the DBHF the neutron vector effective mass is larger than that of proton once the energy dependence of nucleon potentials is considered. The results are consistent with the analysis of phenomenological isospin dependent optical potentials.
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