Constraining the nuclear symmetry energy from electric dipole polarizability and neutron skin in ${}^{208}\mathrm{P}\mathrm{b}$ within antisymmetrized molecular dynamics

The electric dipole polarizability ${\alpha }_D$ and the neutron skin thickness $\mathrm{\Delta }{R}_{np}$ of ${}^{208}\mathrm{P}\mathrm{b}$ are two powerful and clean probes to constrain the symmetry energy at subsaturation density. Within the framework of the antisymmetrized molecular dynamics (AMD) model, we found that the sensitive densities of ${\alpha }_D$ and $\mathrm{\Delta }{R}_{np}$ ranges from the 0.2${\rho }_0$ to 0.57${\rho }_0$. To well describe the data of ${\alpha }_D$ and $\mathrm{\Delta }{R}_{np}$, the effective interaction parameters with $S_0\sim 34$ MeV and $L=66-75$ MeV are favored. The constraints of symmetry energy over the density ranging from 0.2${\rho }_0$ to 0.57${\rho }_0$ are obtained, and the values of symmetry energy at the starting and ending density region are $S(\rho =0.2{\rho }_0)=10.5\pm 0.63$ MeV and $S(\rho =0.57{\rho }_0)=23.1\pm 0.4$ MeV.