Isospin splitting of the Dirac mass probed using the relativistic Brueckner-Hartree-Fock theory

he isospin splitting of the Dirac mass obtained using the relativistic Brueckner-Hartree-Fock (RBHF) theory was thoroughly investigated. From the perspective in the full Dirac space, the long-standing controversy between the momentum-independence approximation (MIA) method and the projection method on the isospin splitting of the Dirac mass in asymmetric nuclear matter was analyzed in detail. We found that the \textit{assumption procedure} of the MIA method, which assumes that the single-particle potentials are momentum independent, is not a sufficient condition that directly leads to the opposite sign of the isospin splitting of the Dirac mass, whereas the \textit{extraction procedure} of the MIA method, which extracts the single-particle potentials from single-particle potential energy, changes the sign. A formal expression of the Dirac mass was obtained by approximately solving a set of equations involved in the \textit{extraction procedure}. The opposite isospin splitting of the Dirac mass was mainly caused by that the \textit{extraction procedure}, which forcibly assumed that the momentum dependence of the single-particle potential energy was in a quadratic form, in which the strength was solely determined by a constant scalar potential. Improved understanding of the isospin splitting of the Dirac mass from ab initio calculations could enhance our knowledge of neutron-rich systems, such as exotic nuclei and neutron stars.