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

TL;DR

This study uses electric dipole polarizability measurements in various nuclei to constrain the symmetry energy and neutron matter equation of state at subsaturation density, revealing strong correlations and providing quantitative bounds.

Contribution

It demonstrates model-independent correlations between dipole polarizability and nuclear matter properties, and constrains these properties using a Bayesian analysis of experimental data.

Findings

Strong linear correlations between $1/\alpha_D$ and $E_{sym}(\rho_0/3)$ and $E_{PNM}(\rho_0/3)$.

Model-independent $1/\alpha_D$--$E_{PNM}(\rho_0/3)$ correlation for $^{208}$Pb.

Quantitative constraints on symmetry energy and neutron matter EOS at $\rho_0/3$ from experimental data.

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 $E_{\rm{sym}}(\rho)$ 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.