In analogy with the idea of the effective interaction commonly used in the nonielativistic approach, the relativistic effective interactions are adopted to incorporate the relativistic Brueckner-Hartree-Fock (RBHF) results in the relativistic mean field approach (RMF) or relativistic Hartree-Fock approach (RHF). It is desired to remedy the deficiencies of RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The relativistic effective interactions are used to describe the ground state properties of nuclei and medium-energy nucleon-nucleus scattering in this paper.

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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. PACS numbers: 21.65.+f, 24.10.Jv, 24.19.Cn, 21.10.Gv The nucleon effective mass characterizes the propagation of a nucleon in the nuclear medium, which is adopted to describe an independent quasi-particle model in the nuclear many-body system [1,2]. Recently, the radioactive beam physics has become one of the frontiers in nuclear physics. It offers the possibility to broaden our understanding of nuclear properties. In the neutron rich side, one of the most interesting questions is the isospin dependence of the nucleon effective interaction as well as the nucleon effective mass. The knowledge about the isospin dependence of the nucleon effective mass is critically important for understanding properties of neutron stars and the dynamics of nuclear collisions induced by radioactive beams [3,4,5]. Unfortunately, up to now the knowledge about the isospin dependence of those quantities from experiments is very little. Recently Li[6] studied the constraint of the neutron-proton effective mass splitting in the neutron-rich nuclear matter. He found that an effective mass splitting of m * n < m * p leads to a symmetric potential that is inconsistent with the energy dependence of the Lane potential constrained by the nucleon-nucleus scattering experimental data. The purpose of this work is to study the isospin dependence of the nucleon effective mass microscopically in a relativistic approach. It is known that there also exist some confusions on the nucleon effective mass in the relativistic approach [7]. We shall first clarify the definition of the nucleon effective mass in the relativistic approach and, then investigate the isospin dependence of the nucleon effective mass in the Dirac Brueckner-Hartree-Fock (DBHF) approach.In the non-relativistic approach the nuclear microscopic potential V (k, ε) is nonlocal and of frequency * Correspondence author: Zhong-yu Ma email: mazy12@iris.ciae.ac.cn dependence. The effective mass represents the nonlocalit...

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