Relativistic Brueckner-Hartree-Fock theory in nuclear matter without the average momentum approximation

Brueckner-Hartree-Fock theory allows one to derive the G matrix as an effective interaction between nucleons in the nuclear medium. It depends on the center-of-mass momentum P of the two particles and on the two relative momenta q and q' before and after the scattering process. In the evaluation of the total energy per particle in nuclear matter, usually the angle-averaged center-of-mass momentum approximation has been used. We derive in detail the exact expressions of the angular integrations of the momentum P within relativistic Brueckner-Hartree-Fock (RBHF) theory, especially for the case of asymmetric nuclear matter. In order to assess the reliability of the conventional average momentum approximation for the binding energy, the saturation properties of symmetric and asymmetric nuclear matter are systematically investigated based on the realistic Bonn nucleon-nucleon potential. It is found that the exact treatment of the center-of-mass momentum leads to non-negligible contributions to the higher order physical quantities. The correlations between the symmetry energy E-sym, the slope parameter L, and the curvature K-sym of the symmetry energy are investigated. The results of our RBHF calculations for the bulk parameters characterizing the equation of state are compared with recent constraints extracted from giant monopole resonance and isospin diffusion experiments.