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Electric Dipole Polarizability in $^{208}$Pb as a Probe of the Symmetry Energy and Neutron Matter around $ρ_0/3$

It is currently a big challenge to accurately determine the symmetry energy $E_{\text{sym}}(ρ)$ and the pure neutron matter equation of state $E_{\text{PNM}}(ρ)$, even their values around saturation density $ρ_0 $. We find that the electric dipole polarizability $α_ {\text{D}}$ in $^{208}$Pb can be determined uniquely by the magnitude of the $E_{\text{sym}}(ρ)$ or almost equivalently the $E_{\text{PNM}}(ρ)$ at subsaturation densities around $ρ_0/3 $, shedding a light upon the genuine correlation between the $α_ {\text{D}}$ and the $E_{\text{sym}}(ρ)$. By analyzing the experimental data of the $α_ {\text{D}}$ in $^{208}$Pb from RCNP using a number of non-relativistic and relativistic mean-field models, we obtain very stringent constraints on $E_{\text{sym}}(ρ)$ and $E_{\text{PNM}}(ρ)$ around $ρ_0/3 $. The obtained constraints are found to be in good agreement with the results extracted in other analyses. In particular, our results provide for the first time the experimental constraints on $E_{\text{PNM}}(ρ)$ around $ρ_0/3 $, which are in harmony with the recent determination of $E_{\text{PNM}}(ρ)$ from microscopic theoretical studies and potentially useful in constraining the largely uncertain many-nucleon interactions in microscopic calculations of neutron matter.