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We study the nuclear symmetry energy S(rho) and related quantities of nuclearphysics and nuclear astrophysics predicted generically by relativisticmean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simpleprescription for preparing equivalent RMF and SHF parametrizations startingfrom a minimal set of empirical constraints on symmetric nuclear matter,nuclear binding energy and charge radii, enforcing equivalence of their Lorenzeffective masses, and then using the pure neutron matter (PNM) equation ofstate (EoS) obtained from ab-initio calculations to optimize the pure isovectorparameters in the RMF and SHF models. We find the resulting RMF and SHFparametrizations give broadly consistent predictions of the symmetry energy Jand its slope parameter L at saturation density within a tight range of <~2 MeVand <~6 MeV respectively, but that clear model dependence shows up in thepredictions of higher-order symmetry energy parameters, leading to importantdifferences in (a) the slope of the correlation between J and L from theconfidence ellipse, (b) the isospin-dependent part of the incompressibility ofnuclear matter K_tau, (c) the symmetry energy at supra-saturation densities,and (d) the predicted neutron star radii. The model dependence can lead toabout 1-2 km difference in predictions of the neutron star radius givenidentical predicted values of J, L and symmetric nuclear matter (SNM)saturation properties. Allowing the full freedom in the effective masses inboth 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<~65MeV, -420<~K_tau<~-325 MeV for the SHF model as a whole. Notably, given PNMconstraints, these results place RMF and SHF models as a whole at odds withsome constraints on K_tau inferred from giant monopole resonance and neutronskin experimental results.

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