Neutron skin thickness of heavy nuclei with $\alpha \mathrm{-particle}$ correlations and the slope of the nuclear symmetry energy

The formation of $\alpha \mathrm{-particle}$ clusters on the surface of heavy nuclei is described in a generalized relativistic mean-field model with explicit cluster degrees of freedom. The effects on the size of the neutron skin of Sn nuclei and ${}^{208}\mathrm{Pb}$ are investigated as a function of the mass number and the isospin-dependent part of the effective interaction, respectively. The correlation of the neutron skin thickness with the difference of the neutron and proton numbers and with the slope of the nuclear symmetry energy is modified as compared to the mean-field calculation without $\alpha$-cluster correlations.

Figure 1

Radial density distribution of $\alpha$ particles (full lines) and neutrons (dashed lines) for a selected set of isotopes of the Sn chain from ${}^{108}\mathrm{Sn}$ (leftmost curve) to ${}^{132}\mathrm{Sn}$ (rightmost curve).

Figure 2

Dependence of the rms radii of neutrons (circles) and protons (squares) on the mass number $A$ of Sn nuclei in the extended RTF calculation with the modified DD2 parametrization. Full red (open blue) symbols denote the results with (without) $\alpha \mathrm{-particle}$ correlations.

Figure 3

Dependence of neutron skin thickness on mass number $A$ of Sn nuclei in the extended RTF calculation with the rescaled DD2 parametrization. Full (open) symbols denote the results with (without) $\alpha \mathrm{-particle}$ correlations.

Figure 4

Dependence of the number of $\alpha$ particles $N_{\alpha }$ on the mass number $A$ of Sn nuclei in the extended RTF calculation with the rescaled DD2 parametrization.

Figure 5

Dependence of the neutron skin thickness of ${}^{208}\mathrm{Pb}$ on the slope parameter $L$. Squares denote the results of the RMF calculation with the original DD2 parametrization in the Hartree approximation and full (open) circles are those of the relativistic TF model with the rescaled DD2 parametrization with (without) $\alpha \mathrm{-particle}$ correlations.