Symmetry energy and neutron matter equation of state at ${\rho }_0/3$ from the electric dipole polarizability in ${}^{48}$Ca, ${}^{68}$Ni and ${}^{208}$Pb

Abstract

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 $E_{\mathrm{sym}}(\rho )$ and the neutron matter equation of state $E_{\mathrm{PNM}}(\rho )$ 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 $E_{\mathrm{sym}}({\rho }_0/3)$ 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 $E_{\mathrm{sym}}({\rho }_0/3)=17.8_{-0.9(1.6)}^{+1.1(1.8)}\mathrm{MeV}$ and $E_{\mathrm{PNM}}({\rho }_0/3)=9.1_{-0.9(1.4)}^{+0.8(1.4)}\mathrm{MeV}$ 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.

Comments: 11 pages, 6 figures, comments are welcome