Electric Dipole Polarizability in ${}^{208}$Pb as a Probe of the Symmetry Energy and Neutron Matter around ${\rho }_0/3$

Abstract

It is currently a big challenge to accurately determine the symmetry energy $E_{\text{sym}}(\rho )$ and the pure neutron matter equation of state $E_{\text{PNM}}(\rho )$, even their values around saturation density ${\rho }_0$. We find that the electric dipole polarizability ${\alpha }_{\text{D}}$ in ${}^{208}$Pb can be determined uniquely by the magnitude of the $E_{\text{sym}}(\rho )$ or almost equivalently the $E_{\text{PNM}}(\rho )$ at subsaturation densities around ${\rho }_0/3$, shedding a light upon the genuine correlation between the ${\alpha }_{\text{D}}$ and the $E_{\text{sym}}(\rho )$. By analyzing the experimental data of the ${\alpha }_{\text{D}}$ in ${}^{208}$Pb from RCNP using a number of non-relativistic and relativistic mean-field models, we obtain very stringent constraints on $E_{\text{sym}}(\rho )$ and $E_{\text{PNM}}(\rho )$ around ${\rho }_0/3$. The obtained constraints are found to be in good agreement with the results extracted in other analyses. In particular, our results provide for the first time the experimental constraints on $E_{\text{PNM}}(\rho )$ around ${\rho }_0/3$, which are in harmony with the recent determination of $E_{\text{PNM}}(\rho )$ from microscopic theoretical studies and potentially useful in constraining the largely uncertain many-nucleon interactions in microscopic calculations of neutron matter.

5 pages, 3 figures. Accepted version to appear in PRC as a Rapid Communication

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