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 subsaturation densities is constrained from 54 Skyrme parameter sets. The extracted nuclear symmetry energy at subsaturation 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 ${}^{208}$Pb, ten Skyrme forces with slope parameter of $28\le L\le 65$ are selected for the description of the symmetry energy around saturation densities.

Figure 1

Single-particle potentials and the single-particle energies (SPEs) of bound states for ${}^{132}$Sn with the Skyrme Hartree-Fock calculation by using SLy7 force. The dashed lines denote the highest SPE of the occupied states for nucleons in ${}^{132}$Sn at its ground state.

Figure 2

Fermi-energy difference as a function of separation-energy difference. The red squares denote the experimental data for six doubly magic nuclei [34, 35]. Others are the calculated results with difference Skyrme forces.

Figure 3

Average deviation as a function of nuclear symmetry energy $E_{\mathrm{sym}}$ at the density of (a) $\rho =0.09$ fm${}^{-3}$ and (b) 0.11 fm${}^{-3}$, with 54 different Skyrme forces. The solid curves denote the parabolic fit to the squares. The dashed line show the position of 1.19 MeV.

Figure 4

Average deviation as a function of (a) saturation density ${\rho }_0$ and (b) incompressibility coefficient $K_{\infty }$ of symmetric nuclear matter, based on the calculations of the 54 Skyrme forces.

Figure 5

The same as Fig. 3, but at the density of (a) $\rho =0.13$ and (b) 0.16 fm${}^{-3}$.

Figure 6

Slope parameter of nuclear symmetry energy as a function of neutron-skin thickness of ${}^{208}$Pb. The region between the two dashed vertical lines denotes the measured neutron-skin thickness of ${}^{208}$Pb, $0.131\le \Delta R_{\mathrm{np}}{(}^{208}\mathrm{Pb})\le 0.218$ fm [23, 24, 25, 26].

Figure 7

Nuclear symmetry energy as a function of density. The squares denotes the results from the 17 selected Skyrme forces based on the Fermi-energy difference. Other symbols and curves denote the results of ten selected Skyrme forces with which both the Fermi-energy difference and the neutron-skin thickness of ${}^{208}$Pb can be reasonably well described.