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 parameterizations 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 parameterizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of \lesssim 2 MeV and \lesssim 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 \lesssim J \lesssim 31.5 MeV , 35 \lesssim L \lesssim 60 MeV , -330 \lesssim K _ { \tau } \lesssim - 216 MeV for the RMF model as a whole and 30 \lesssim J \lesssim 33 MeV , 28 \lesssim L \lesssim 65 MeV , -420 \lesssim K _ { \tau } \lesssim - 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 .