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Generic Constraints on the Relativistic Mean-Field and Skyrme-Hartree-Fock Models from the Pure Neutron Matter Equation of State

We study the nuclear symmetry energy S(rho) and related quantities of nuclear physics and nuclear astrophysics predicted generically by relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simple prescription for preparing equivalent RMF and SHF parametrizations starting from a minimal set of empirical constraints on symmetric nuclear matter, nuclear binding energy and charge radii, enforcing equivalence of their Lorenz effective masses, and then using the pure neutron matter (PNM) equation of state (EoS) obtained from ab-initio calculations to optimize the pure isovector parameters in the RMF and SHF models. We find the resulting RMF and SHF parametrizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of <~2 MeV and <~6 MeV respectively, but that clear model dependence shows up in the predictions of higher-order symmetry energy parameters, leading to important differences in (a) the slope of the correlation between J and L from the confidence ellipse, (b) the isospin-dependent part of the incompressibility of nuclear matter K_tau, (c) the symmetry energy at supra-saturation densities, and (d) the predicted neutron star radii. The model dependence can lead to about 1-2 km difference in predictions of the neutron star radius given identical predicted values of J, L and symmetric nuclear matter (SNM) saturation properties. Allowing the full freedom in the effective masses in both models leads to constraints of 30<~J<~31.5 MeV, 35<~L<~60 MeV, -330<~K_tau<~-216 MeV for the RMF model as a whole and 30<~J<~33 MeV, 28<~L<~65 MeV, -420<~K_tau<~-325 MeV for the SHF model as a whole. Notably, given PNM constraints, these results place RMF and SHF models as a whole at odds with some constraints on K_tau inferred from giant monopole resonance and neutron skin experimental results.