Symmetry energy and neutron matter equation of state at $ρ_0/3$ from the electric dipole polarizability in $^{48}$Ca, $^{68}$Ni and $^{208}$Pb
Based on the quasiparticle random phase approximation implemented via the finite amplitude method, we employ a set of representative relativistic mean-field models to investigate the sensitivity of the inverse electric dipole polarizability $1/α_{\mathrm{D}}$ in $^{48}\mathrm{Ca}$, $^{68}\mathrm{Ni}$, and $^{208}\mathrm{Pb}$ to the symmetry energy $E_{\rm{sym}}(ρ)$ and the neutron matter equation of state $E_{\rm{PNM}}(ρ)$ at a subsaturation density of $ρ= ρ_0/3$. Combined with predictions from nonrelativistic Skyrme energy density functionals (EDFs), our results reveal strong linear correlations between $1/α_{\mathrm{D}}$ and both $E_{\rm{sym}}(ρ_0/3)$ and $E_{\rm{PNM}}(ρ_0/3)$. In particular, the $1/α_{\mathrm{D}}$--$E_{\rm{PNM}}(ρ_0/3)$ correlation for $^{208}\mathrm{Pb}$ is found to be nearly model-independent. A Bayesian analysis of the measured values of $α_{\rm{D}}$ in $^{48}\mathrm{Ca}$, $^{68}\mathrm{Ni}$, and $^{208}\mathrm{Pb}$ yields quantitative constraints of $E_{\mathrm{sym}}(ρ_0/3) = 17.8^{+1.1(1.8)}_{-0.9(1.6)}~\mathrm{MeV}$ and $E_{\mathrm{PNM}}(ρ_0/3) = 9.1^{+0.8(1.4)}_{-0.9(1.4)}~\mathrm{MeV}$ at the 68\% (90\%) confidence level, respectively. The extracted value of $E_{\mathrm{PNM}}(ρ_0/3)$ exceeds most predictions from microscopic many-body theories, suggesting a mild tension between nuclear EDF-based constraints derived from $α_{\mathrm{D}}$ data and results from \textit{ab initio} calculations.