Revisiting neutron-skin thickness and dipole polarizability constraints on the symmetry energy in Antisymmetrized Molecular Dynamics

Abstract

The neutron-skin thickness and electric dipole polarizability are among the most sensitive probes of the symmetry energy at subsaturation densities. Motivated by the tension raised by recent analyses of PREX-II and CREX data within density-functional-based approaches, we perform a unified study of static and dynamical isovector observables within the antisymmetrized molecular dynamics (AMD) framework. Using thirty interaction parameter sets that span different values of the symmetry-energy coefficient $S_0$, slope parameter $L$, and neutron-proton effective-mass splitting $\Delta m_{np}^{\ast }$, we systematically analyze the neutron-skin thicknesses of nuclei from ${}^{40}$Ca to ${}^{238}$U together with the electric dipole polarizability ${\alpha }_D$ of ${}^{208}$Pb. A combined ${\chi }^2$ analysis of neutron-skin thicknesses and the electric dipole polarizability yields preferred values of $L$ that increase with $S_0$, reflecting the joint constraint from the static and dynamical observables. Furthermore, we identify the density region mainly probed by these observables as 0.019 $\le \rho /{\rho }_0\le$0.60, where the relative narrowing strength function varies by less than 10% compared to its maximum narrowing strength. The maximum reduction of the uncertainty of $S(\rho )$ occurs at 0.28 ${\rho }_0$, where the symmetry energy within 1${\sigma }_{post}$ uncertainty is constrained to be $S(0.28{\rho }_0)=13.84\pm 1.31$ MeV. These results demonstrate that a unified AMD analysis of neutron-skin systematics and dipole polarizability provides a complementary constraint on the symmetry energy below saturation density.

Comments: 9 pages, 5 figures