Neutron-skin thickness determines the surface tension of a compressible nuclear droplet

We systematically investigate the neutron-skin thickness of neutron-rich nuclei within a compressible droplet model, which includes several parameters characterizing the surface tension and the equation of state (EOS) of asymmetric nuclear matter as well as corrections due to the surface diffuseness. Such a systematic analysis helps towards constraining the EOS parameters of asymmetric nuclear matter and the poorly known density dependence of the surface tension; the latter is estimated with help of available experimental data for the neutron and proton density distributions and the nuclear masses. Validity of the present approach is confirmed by calculating realistic density distributions of Ca, Ni, Zr, Sn, Yb, and Pb isotopes within a microscopic Skyrme-Hartree-Fock+BCS method for various sets of the effective nuclear force. Our macroscopic model accompanied by the diffuseness corrections works well in the sense that it well reproduces the evolution of the microscopically deduced neutron-skin thickness with respect to the neutron number for selected sets of the effective nuclear force. We find that the surface tension of the compressible nuclear droplet is a key to bridging a gap between microscopic and macroscopic approaches.

Figure 1

Charge radii of (a) Sn and (b) Pb isotopes. The point-proton radii obtained by the HF+BCS proton density distributions are converted to the charge radius by taking into account finite size corrections of the proton and neutron charge radii and the Darwin-Foldy term [47]. The experimental charge radii are taken from Ref. [46].

Figure 2

Surface widths of Ca, Ni, Zr, Sn, Yb, and Pb isotopes extracted from the (left) neutron and (right) proton density distributions, respectively. For calculations of these distributions, the (a) SkM*, (b) SLy4, and (c) SkI3 interactions are employed from top to bottom, respectively.

Figure 3

Neutron-skin thickness (circles) calculated for Sn and Pb isotopes within the compressible droplet model using the empirical density distributions [12, 13]. Decomposition into the volume (triangles) and surface (squares) terms and the empirical skin-thickness values (inverted triangles for Pb; diamonds for Sn) are also given. Error bars of the total neutron-skin thickness and its volume contribution indicate a range of the calculated values with $S_0=28$–36 MeV.

Figure 4

Neutron-skin thickness of Ca, Ni, Zr, Sn, Yb, and Pb isotopes (from left to right, respectively) as a function of the asymmetry parameter $\delta =(N-Z)/A$. The SkM*, SLy4, and SkI3 interactions (from top to bottom, respectively) are employed for the HF+BCS calculations (circles) and for the droplet formula (solid lines) with the volume term (dashed lines) and the surface term (dotted lines).

Figure 5

Same as Fig. 4 but for (left) Sn and (right) Pb isotopes with the (a) KDE0v1, (b) LNS, (c) SkT1, (d) SkT2, (e) SkT3, and (f) SV-sym32 interactions.

Figure 6

Surface widths of Sn and Pb isotopes that are extracted from the neutron and proton density distributions calculated in the presence (HF+BCS) and absence (HF) of the pairing interaction. The SkM* interaction is employed for calculations of the density distributions.

Figure 7

Same as Fig. 6 but for the surface contribution to the neutron-skin thickness of (a) Sn and (b) Pb isotopes. To guide the eyes, arrows indicating the regions of ${}^{116–124}\mathrm{Sn}$ and ${}^{206–208}\mathrm{Pb}$ in which experimental data are available are drawn in panels (a) and (b), respectively.