Nuclear symmetry energy from the Fermi-energy difference in nuclei

The neutron-proton Fermi-energy difference and the correlation to nucleon separation energies for some magic nuclei are investigated with the Skyrme energy density functionals and nuclear masses, with which the nuclear symmetry energy at sub-saturation densities is constrained from 54 Skyrme parameter sets. The extracted nuclear symmetry energy at sub-saturation density of 0.11 fm$^{-3}$ is 26.2 $\pm$ 1.0 MeV with 1.5 $\sigma$ uncertainty. By further combining the neutron-skin thickness of 208Pb, ten Skyrme forces with slope parameter of 28<L<65 are selected for the description of the symmetry energy around saturation densities.