Constraints on the Skyrme Equations of State from Properties of Doubly Magic Nuclei

I use properties of doubly magic nuclei to constrain symmetric nuclear matter and neutron matter equations of state. I conclude that these data determine the value of the neutron equation of state at a density of ${\rho }_{on}=0.10\mathrm{nucleons}/{\mathrm{fm}}^3$ to be 11.4(10) MeV. The slope at that point is constrained by the value of the neutron skin. Analytical equations are given that show the dependence of the Skyrme equations of state on the neutron skin.

Figure 1

(a) EOS obtained from the Skyrme interactions. (b) EOS obtained from the Skyrme interactions fitted to properties of doubly magic nuclei and with a constraint of $R_{np}=0.20\mathrm{fm}$ for the neutron skin of ${}^{208}\mathrm{Pb}$. The black lines are those from the CSkP set with $m^{*}/m\approx 1.0$, the red lines are those from the CSkP set with $m^{*}/m=0.70–0.85$. The blue lines are those for SLy4 and SkM*. The vertical line is placed at $\rho =0.16{\mathrm{fm}}^{-3}$.

Figure 2

(a) EOS obtained from the Skyrme interactions fitted to properties of doubly magic nuclei with 0.20 fm for the neutron skin of ${}^{208}\mathrm{Pb}$ and $m_n^{*}/m=0.90$ at ${\rho }_{on}=0.10{\mathrm{fm}}^{-3}$. (b) EOS obtained from the Skyrme interactions fitted to properties of doubly magic nuclei with values of 0.16 and 0.24 fm for the neutron skin of ${}^{208}\mathrm{Pb}$ together with $m_n^{*}/m=0.90$. See caption to Fig. 1. The vertical lines are placed at $\rho =0.10$ and $0.16{\mathrm{fm}}^{-3}$. The horizontal lines are placed at 25 MeV for $S$ and 11 MeV for $E/N$.

Figure 3

The neutron EOS at low density for $R_{np}=0.16$, 0.20, and 0.24 fm. They are compared to the theoretical results from 14 (dashed lines). See caption to Fig. 1. The vertical lines are placed at $\rho =0.10$ and $0.16{\mathrm{fm}}^{-3}$. The horizontal line is placed at 11 MeV.