  Brueckner-Hartree-Fock theory allows to derive the $G$-matrix as an effective
interaction between nucleons in the nuclear medium. It depends on the center of
mass momentum $\bm{P}$ of the two particles and on the two relative momenta
$\bm{q}$ and $\bm{q'}$ 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
$\bm{P}$ 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 correlation between the symmetry energy $E_{\mathrm{sym}}$, the slope
parameter $L$, and the curvature $K_{\mathrm{sym}}$ 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.
