Constraints on Skyrme equations of state from properties of doubly magic nuclei and ab initio calculations of low-density neutron matter

We use properties of doubly magic nuclei and ab initio calculations of low-density neutron matter to constrain Skyrme equations of state for neutron-rich conditions. All of these properties are consistent with a Skyrme functional form and a neutron-matter equation of state that depends on three parameters. With a reasonable range for the neutron-matter effective mass, the values of the two other Skyrme parameters are well constrained. This leads to predictions for other quantities. The neutron skins for ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$ are predicted to be 0.182(12) and 0.173(5) fm, respectively. Other results including the dipole polarizability are discussed.

Figure 1

The neutron EOS with $m_n^{*}/m=0.90$ and with $R_{np}$ fixed at 0.16, 0.20, and 0.24 fm compared to the ${\mathrm{N}}^3\mathrm{LO}$ neutron-matter band from Ref. [10, 11] (dashed lines). The black lines are those with symmetric-nuclear matter values of $m^{*}/m\approx 1.0$, and the red lines are those with $m^{*}/m=0.70–0.85$. The blue lines are for SLy4 and SkM*.

Figure 2

The neutron EOS from Skyrme fits that include points from ab initio calculations of low-density neutron matter, compared to the ${\mathrm{N}}^3\mathrm{LO}$ neutron-matter band from Ref. [10, 11] (dashed lines). The black lines are those with symmetric-nuclear matter values of $m^{*}/m\approx 1.0$, and the red lines are those with $m^{*}/m=0.70–0.85$. The blue lines are for SLy4 and SkM*.

Figure 3

The neutron EOS at very low density. The total result for the Ska25 fit with a neutron-matter effective mass of 0.9 at a density of $0.10{\mathrm{fm}}^{-3}$ is shown (black solid line) together with the separate contributions from the $a_n$ (red solid line), $b_n$ (blue solid line), $c_n$ (red dashed line), and $d_n$ (black dashed line) terms of Eq. (4). The theoretical data points are shown by the red points with error bars.