Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei

Expressing explicitly the parameters of the standard Skyrme interaction in terms of the macroscopic properties of asymmetric nuclear matter, we show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. We find that existing data on neutron skin thickness $\Delta r_{\mathit{np}}$ of Sn isotopes give an important constraint on the symmetry energy $E_{\mathrm{sym}}({\rho }_0)$ and its density slope $L$ at saturation density ${\rho }_0$. Combining these constraints with those from recent analyses of isospin diffusion and the double neutron/proton ratio in heavy-ion collisions at intermediate energies leads to a more stringent limit on $L$ approximately independent of $E_{\mathrm{sym}}({\rho }_0)$. The implication of these new constraints on the $\Delta r_{\mathit{np}}$ of ${}^{208}\mathrm{Pb}$ as well as the core-crust transition density and pressure in neutron stars is discussed.

Figure 1

The coefficient $G_V$ dependence of $G_S$ and $W_0$ (a), Landau parameters $G_0({\rho }_0)$, $G_0^{\text{'}}({\rho }_0)$, $G_1({\rho }_0)$, $G_0^{\text{'}}({\rho }_0)$ (b), and the reduced critical density ${\rho }_{\mathrm{cr}}/{\rho }_0$ for symmetric nuclear matter and pure neutron matter (c).

Figure 2

Relative deviation of the binding energies and charge rms radii of ${}^{16}\mathrm{O}$,${}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}$, ${}^{56}\mathrm{Ni}$,${}^{78}\mathrm{Ni}$, ${}^{90}\mathrm{Zr}$, ${}^{100}\mathrm{Sn}$,${}^{132}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ obtained using SHF with MSL0 from the measured values.

Figure 3

The neutron skin thickness $\Delta r_{\mathit{np}}$ of ${}^{208}\mathrm{Pb}$, ${}^{120}\mathrm{Sn}$, and ${}^{48}\mathrm{Ca}$ from SHF with MSL0 by varying individually$L$ (a), $G_V$ (b), $G_S$ (c), $E_0({\rho }_0)$ (d), $E_{\mathrm{sym}}({\rho }_0)$ (e), $K_0$ (f), $m_{s,0}^{*}$ (g), $m_{v,0}^{*}$ (h), ${\rho }_0$ (i), and $W_0$ (j).

Figure 4

Relative deviation of the binding energies of ${}^{208}\mathrm{Pb}$, ${}^{120}\mathrm{Sn}$, and ${}^{48}\mathrm{Ca}$ obtained using SHF with MSL0 from the measured values by varying individually $L$ (a), $G_V$ (b), $G_S$ (c), $E_0({\rho }_0)$ (d), $E_{\mathrm{sym}}({\rho }_0)$ (e), $K_0$ (f), $m_{s,0}^{*}$ (g), $m_{v,0}^{*}$ (h), ${\rho }_0$ (i), and $W_0$ (j).

Figure 5

Same as Fig. 4 but for the charge rms radii.

Figure 6

(a) The $\Delta r_{\mathit{np}}$ data for Sn isotopes from different experimental methods and results from SHF calculation using MSL0 with $L=20$, $60$, and $100$ MeV. (b) ${\chi }^2$ as a function of $L$. (c) Constraints on $L$ and $E_{\mathrm{sym}}({\rho }_0)$ from the ${\chi }^2$ analysis of the $\Delta r_{\mathit{np}}$ data on Sn isotopes (gray band as well as dashed and dotted lines).

Figure 7

Contour curves in the $E_{\mathrm{sym}}({\rho }_0)$-$L$ plane for the $\Delta r_{\mathit{np}}$ of ${}^{208}\mathrm{Pb}$ (a) and the core-crust transition density ${\rho }_t$ (b) from SHF calculation with MSL0. The shaded region represents the overlap of constraints obtained in the present work (dashed lines) and that from Ref. [11] (dash-dotted lines).

Figure 8

Same as Fig. 3 but for the core-crust transition density ${\rho }_t$ in neutron stars.

Figure 9

Same as Fig. 3 but for the core-crust transition pressure $P_t$ in neutron stars.