Fully self-consistent relativistic Brueckner-Hartree-Fock theory for finite nuclei

Starting from the relativistic form of the Bonn potential as a bare nucleon-nucleon interaction, the full Relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for finite nuclei in a fully self-consistent basis. This provides a relativistic ab initio calculation of the ground state properties of finite nuclei without any free parameters and without three-body forces. The convergence properties for the solutions of these coupled equations are discussed in detail at the example of the nucleus $^{16}$O. The binding energies, radii, and spin-orbit splittings of the doubly magic nuclei $^{4}$He, $^{16}$O, and $^{40}$Ca are calculated and compared with the earlier RBHF calculated results in a fixed Dirac Woods-Saxon basis and other non-relativistic ab initio calculated results based on pure two-body forces.