The isovector density-dependence of the M3Y nucleon-nucleon interactions and related soft and hard equations of state

Towards a precise equation of state (EOS) of nuclear matter (NM) based on a realistic interaction, we use non-relativistic Brueckner-Hartree-Fock (BHF) scheme to deduce the isovector (IV) density dependence (DD) of M3Y-Paris and Reid nucleon-nucleon interactions, via comparison with previous BHF calculations of nucleon optical potential. The single particle rearrangement correction is taken into account. With analytical parameterization of the isoscalar DD, the IV DD is parameterized (IVF1) for a broad range of EOSs, from soft EOS of saturation incompressibility K0 = 150 MeV to stiff one with K0 = 300 MeV. These Paris (Reid) EOSs indicate symmetry energy coefficient of 30.06 & PLUSMN; 0.02 MeV (31.76 & PLUSMN; 0.06 MeV), with corresponding density-slope sticks around L = 49.7 MeV (51.9 MeV). We found that the IVF1 DD indicates larger (smaller) saturation binding-energy (density) of asymmetric NM, and more high-density repulsion increasing with density and isospin asymmetry, as well as higher pressure, than those based on the IVF0 DD that scaled in terms of the isoscalar DD. Also, the IVF1 confirms the mostly indicated hard symmetry energy at supra-saturation density, on the contrary of the IVF0 that indicates soft one. Increasing the stiffness of the EOS increases the NM energy, though it decreases the symmetry energy. The more neutron-rich NM gets less bound, over less bound-density range. Only the fine ranges of Paris (K0 = 240 -250 MeV) and Reid (K0 = 230 -240 MeV) EOSs maintain simultaneous consistency with earlier experimental constraints and accurate calculations on NM energy, symmetry energy, and pressure.& COPY; 2023 Elsevier B.V. All rights reserved.