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 $1/{\alpha }_{\mathrm{D}}$ in ${}^{48}\mathrm{Ca}$, ${}^{68}\mathrm{Ni}$, and ${}^{208}\mathrm{Pb}$ to the symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$ and the neutron matter equation of state $E_{\mathrm{PNM}}\left(\rho \right)$ at a subsaturation density of $\rho ={\rho }_0/3$, with ${\rho }_0$ being the saturation density. Combined with predictions from nonrelativistic Skyrme energy-density functionals (EDFs), our results reveal strong linear correlations between $1/{\alpha }_{\mathrm{D}}$ and both $E_{\mathrm{sym}}({\rho }_0/3)$ and $E_{\mathrm{PNM}}({\rho }_0/3)$. In particular, the $1/{\alpha }_{\mathrm{D}}-E_{\mathrm{PNM}}({\rho }_0/3)$ correlation for ${}^{208}\mathrm{Pb}$ is found to be nearly model independent. A Bayesian analysis of the measured values of ${\alpha }_{\mathrm{D}}$ in ${}^{48}\mathrm{Ca}$, ${}^{68}\mathrm{Ni}$, and ${}^{208}\mathrm{Pb}$ yields quantitative constraints of $E_{\mathrm{sym}}({\rho }_0/3)=17.8_{-0.9\left(1.6\right)}^{+1.1\left(1.8\right)}\mathrm{MeV}$ and $E_{\mathrm{PNM}}({\rho }_0/3)=9.1_{-0.9\left(1.4\right)}^{+0.8\left(1.4\right)}\mathrm{MeV}$ at the 68% (90%) confidence level, respectively. The extracted value of $E_{\mathrm{PNM}}({\rho }_0/3)$ exceeds most predictions from microscopic many-body theories, suggesting a mild tension between nuclear EDF-based constraints derived from ${\alpha }_{\mathrm{D}}$ data and results from ab initio calculations.

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• Asymmetric nuclear matter
• Equations of state of nuclear matter
• Giant resonances
• Symmetry energy