Relativistic Brueckner-Hartree-Fock Theory: an ab initio Approach for Nuclear Matter and for Finite Nuclei

Recent years have seen considerable progress with ab-initio calculations of the nuclear structure by non-relativistic many-body methods. Dirac-Brueckner-Hartree-Fock Theory provides a relativistic ab-intio approach, which is able to reproduce saturation properties of symmetric nuclear matter without three-body forces. However, so far, the corresponding equations have been solved only for positive energy states. Negative energy states have been included for forty years in various approximations, leading to differences in the isospin dependence. This problem has been solved only recently by a complete solution of the self-consistent relativistic Brueckner-Hartree-Fock equations in asymmetric nuclear matter. Due to its numerical complexity, however, it is very difficult to extend the Relativistic Brueckner-Hartree-Fock theory to the study of finite nuclear systems. Recent efforts will be discussed to overcome this problem.