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 $E_{ \rm{ sym}}(\rho)$ and the neutron matter equation of state $E_{ \rm{ PNM}}(\rho)$ at a subsaturation density of $\rho = \rho_0/3$. Combined with predictions from nonrelativistic Skyrme energy density functionals (EDFs), our results reveal strong linear correlations between $1/\alpha_{ \mathrm{ D}}$ and both $E_{ \rm{ sym}}(\rho_0/3)$ and $E_{ \rm{ PNM}}(\rho_0/3)$. In particular, the $1/\alpha_{ \mathrm{ D}}$--$E_{ \rm{ PNM}}(\rho_0/3)$ correlation for $^{ 208}\mathrm{ Pb}$ is found to be nearly model-independent. A Bayesian analysis of the measured values of $\alpha_{ \rm{ D}}$ in $^{ 48}\mathrm{ Ca}$, $^{ 68}\mathrm{ Ni}$, and $^{ 208}\mathrm{ Pb}$ yields quantitative constraints of $E_{ \mathrm{ sym}}(\rho_0/3) = 17.8^{ +1.1(1.8)}_{ -0.9(1.6)}~\mathrm{ MeV}$ and $E_{ \mathrm{ PNM}}(\rho_0/3) = 9.1^{ +0.8(1.4)}_{ -0.9(1.4)}~\mathrm{ MeV}$ at the 68\% (90\%) confidence level, respectively. The extracted value of $E_{ \mathrm{ PNM}}(\rho_0/3)$ 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 \textit{ ab initio} calculations.
Categories: nucl-th