Neutron skin thickness and equation of state in asymmetric nuclear matter

The neutron skin thickness of stable and unstable nuclei is studied in Skyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models to investigate the relation between the pressure and the equation of state in neutron matter. We found a clear linear correlation between the neutron skin thickness in heavy nuclei ${}^{132}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$ and the pressure of neutron matter in both SHF and RMF models, while the correlation is weak in the unstable nuclei ${}^{32}\mathrm{Mg}$ and ${}^{44}\mathrm{Ar}$. Relations between the neutron skin thickness and other nuclear matter properties such as the symmetry energy coefficients and the nuclear incompressibility are discussed.

Figure 1

The neutron skin thickness of ${}^{132}\mathrm{Sn}$ and the binding energy difference between ${}^{132}\mathrm{Sn}$ and ${}^{100}\mathrm{Sn}$ are plotted for 18 parameter sets of the SHF model (open circles and open diamonds) and 5 parameter sets of the RMF model (filled circles and filled diamonds). The experimental binding energy difference is shown as a dotted line. The numbers are a shorthand notation for the different interactions: 1 for SI, 2 for SIII, 3 for SIV, 4 for SVI, 5 for Skya, 6 for SkM, 7 for ${\text{SkM}}^{*}$, 8 for SLy4, 9 for MSkA, 10 for SkI3, 11 for SkI4, 12 for SkX, 13 for NLSH, 14 for NL3, 15 for NLC, 16 for SII, 17 for SV, 18 for Skyb, 19 for SGI, 20 for SGII, 21 for SLy10, 22 for NL1, and 23 for NL2.

Figure 2

The neutron skin thickness of ${}^{208}\mathrm{Pb}$ and the difference between the binding energies of ${}^{208}\mathrm{Pb}$ and ${}^{182}\mathrm{Pb}$ are plotted for 18 parameter sets of the SHF model (open circles and open diamonds) and 5 parameter sets of the RMF model (filled circles and filled diamonds). The experimental binding energy difference is shown as a dotted line. See the caption of Fig. 1 for details.

Figure 3

The neutron equations of state are shown for the 12 parameter sets of the SHF model (solid lines) and 3 parameter sets of the RMF model (dashed lines) which in Figs. 1, 2 were shown to reproduce the differences of experimental binding energies reasonably well. Filled circles correspond to the variational calculations using the $v_{14}$ nucleon-nucleon potential and a phenomenological three-nucleon interaction, while the long-dashed curve corresponds to the SGII interaction. See the caption of Fig. 1 for details.

Figure 4

The pressure of neutron matter as a function of neutron densities. The same parameter sets as those of Fig. 3 are used. The variational calculations with the $v_{14}$ potential are shown by filled circles. The results of the SHF model are given by the solid lines, while those of the RMF model are given by the dashed lines. The long-dashed curve shows the results of the SGII interaction. See the caption of Fig. 1 for details.

Figure 5

The correlations between the pressures of neutron matter and the neutron skin thickness of ${}^{208}\mathrm{Pb}$ obtained with the same SHF (open circles) and RMF (filled circles) parameter sets as were used in Fig. 3. (a) The result for pressure at ${\rho }_{\mathrm{n}}=0.1{\text{fm}}^{-3}$, (b) that at ${\rho }_{\mathrm{n}}=0.2{\text{fm}}^{-\mathrm{3}}$. See the caption of Fig. 1 for details.

Figure 6

The correlations between the pressures of neutron matter and the neutron skin thickness of ${}^{132}\mathrm{Sn}$ obtained by use of the same SHF (open circles) and RMF (filled circles) parameter sets as were used in Fig. 3. (a) The result for pressure at ${\rho }_{\mathrm{n}}=0.1{\text{fm}}^{-3}$, (b) that at ${\rho }_{\mathrm{n}}=0.2{\text{fm}}^{-\mathrm{3}}$. See the caption of Fig. 1 for details.

Figure 7

The correlations between the pressures of neutron matter and the neutron skin thickness of ${}^{32}\mathrm{Mg}$ (reversed open triangles), ${}^{38}\mathrm{Ar}$ (filled triangles), ${}^{44}\mathrm{Ar}$ (open triangles), ${}^{100}\mathrm{Sn}$ (filled diamonds), ${}^{132}\mathrm{Sn}$ (open diamonds), ${}^{138}\mathrm{Ba}$ (crosses), ${}^{182}\mathrm{Pb}$ (open circles), ${}^{208}\mathrm{Pb}$ (filled circles), ${}^{214}\mathrm{Pb}$ (open squares) for the pressure at ${\rho }_{\mathrm{n}}=0.1{\text{fm}}^{-3}$. The parameter sets of SHF model are the same as those of Fig. 3. See the caption of Fig. 1 for details.

Figure 8

The neutron skin thickness of ${}^{208}\mathrm{Pb}$ vs the volume symmetry energy coefficient obtained with the same SHF (open circles) and RMF (filled circles) parameter sets as were used in Fig. 3. See the caption of Fig. 1 for details.

Figure 9

The neutron skin thickness of ${}^{208}\mathrm{Pb}$ vs the incompressibility of asymmetric nuclear matter. The SHF (open circles) and RMF (filled circles) parameter sets are the same as in Fig. 3. See the caption of Fig. 1 for details.

Figure 10

The neutron skin thickness of ${}^{208}\mathrm{Pb}$ vs the surface symmetry energy coefficient of semi-infinite asymmetric nuclear matter. The SHF (open circles) and RMF (filled circles) parameter sets are the same as in Fig. 3. See the caption of Fig. 1 for details.