Model-space nuclear matter calculations with the Paris nucleon-nucleon potential

Using a model-space Brueckner-Hartree-Fock approach, we have carried out nuclear matter calculations using the Paris nucleon-nucleon potential. The self-consistent single particle spectrum from this approach is continuous for momentum up to $k_M$, where $k_M$≊2$k_F$ is the momentum space boundary of our chosen model space. The nuclear matter average binding energy and saturation Fermi momentum given by our calculations are ∼15.6 MeV and ∼1.56 ${\mathrm{fm}}^{\mathrm{-}1}$, respectively. When using the conventional Brueckner-Hartree-Fock approach with a spectrum which has a gap at $k_F$, the corresponding results are ∼11.5 MeV and ∼1.50 ${\mathrm{fm}}^{\mathrm{-}1}$. The gain of approximately 4 MeV in binding energy between the two calculations comes mainly from the ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$ partial wave channels. We have investigated the effect of adding an empirical density dependent central potential to the Paris potential. It is found that the addition of such a potential whose strength is ∼10% of the central component of the Paris potential is adequate in making the nuclear matter binding energy and saturation density in simultaneous agreement with the empirical values.