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The isospin splitting of the Dirac mass obtained with the relativisticBrueckner-Hartree-Fock (RBHF) theory is thoroughly investigated. From theperspective in the full Dirac space, the long-standing controversy between themomentum-independence approximation (MIA) method and the projection method onthe isospin splitting of the Dirac mass in asymmetric nuclear matter (ANM) isanalyzed in detail. We find that, the \textit{assumption procedure} of the MIAmethod, which assumes that the single-particle potentials are momentumindependent, is not a sufficient condition that directly leads to the wrongsign of the isospin splitting of the Dirac mass, while the \textit{extractionprocedure} of the MIA method, which extracts the single-particle potentialsfrom the single-particle potential energy, leads to the wrong sign. Byapproximately solving the set of equations involved in the \textit{extractionprocedure}, a formal expression of the Dirac mass is obtained. The wrongisospin splitting of the Dirac mass is mainly caused by that the\textit{extraction procedure} forcely assumes the momentum dependence of thesingle-particle potential energy to be a quadratic form where the strength issolely determined by the constant scalar potential.

Isospin splitting of the Dirac mass probed by the relativistic Brueckner-Hartree-Fock theory in the full Dirac space