Effects of pairing correlations on the neutron skin thickness and the symmetry energy

We investigated effects of pairing correlations on the neutron skin thickness and the symmetry energy of finite nuclei. In this calculation we used Hartree-Fock-Bogoliubov method with Skyrme forces and effective pairing interactions. The results have been compared with available experimental data, Hartree-Fock results as well as the predictions by droplet model. Finally, our discussion was extended to study of the pairing interaction in nuclear matter. Roles of isospin $T=0$ pairing in the nuclear matter were also discussed.

Figure 1

Neutron skin thickness (S) calculated by the Skyrme Hartree-Fock-Bogoliubov (HFB) model with SkI3, SLy4, SVI interactions and density-dependent $\delta$ interaction (DDDI) for the pairing force, comparing with the antiprotonic measurement data [20].

Figure 2

Symmetry energy $E_{\mathrm{sym}}$ (upper panel) and coefficient $a_{\mathrm{sym}}$ (lower panel) as a function of NST for Pb isotopes ($A=180,184,...,212$). The filled symbols denote the results given by the Skyrme functional SLy4 of HFB calculation with (square) and HF calculation without (circle) pairing interaction. The open symbols denote the results in the droplet model (DM) without surface width corrections (circle), with the surface width correction of $c=-0.05$ fm (square) and $c=+0.07$ fm (triangle).

Figure 3

Similar as Fig. 2, but for Sn isotopes with $A=120,124,...,152$.

Figure 4

Symmetry energy density distribution $g\left(r\right)=4\pi r^2{\mathcal{H}}_{\mathrm{sym}}$ in ${}^{196}\mathrm{Pb}$ (upper panel) and ${}^{144}\mathrm{Sn}$ (lower panel) obtained by the HF (dashed line) and HFB (solid line) calculation with SLy4 functional.

Figure 5

Similar with Fig. 2, but calculated by the Skyrme functional SVI.

Figure 6

Similar with Fig. 3, but calculated by the Skyrme functional SVI.

Figure 7

Pairing gaps obtained with the density-dependent $\delta$ interaction of which parameters are determined in regard to SLy4 (upper panel) and SLy5 Skyrme (lower panel) functionals.

Figure 8

Energy per nucleon versus density in symmetric nuclear and pure neutron matter for the SLy4 (upper panel) and SLy5 Skyrme (lower two panels) functionals.