Bayesian inference of the symmetry energy and the neutron skin in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Ca</mml:mi><mml:mprescripts/><mml:none/><mml:mn>48</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Pb</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>208</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> from CREX and PREX-2
Zhen Zhang, Lie-Wen Chen
Abstract
Using the recent model-independent determination of the charge-weak form factor difference $\mathrm{\ensuremath{\Delta}}{F}_{\mathrm{CW}}$ in $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ by the CREX and PREX-2 collaborations together with some well-determined properties of doubly magic nuclei, we perform Bayesian inference of the symmetry energy ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ and the neutron skin thickness $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ of $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ within the Skyrme energy density functional (EDF). We find the inferred ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ and $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ separately from CREX and PREX-2 are compatible with each other at $90%$ C.L., although they are inconsistent at $68.3%$ C.L. with CREX (PREX-2) favoring a very soft (stiff) ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ and rather small (large) $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$. By combining the CREX and PREX-2 data, we obtain a soft symmetry energy around saturation density ${\ensuremath{\rho}}_{0}$ and thinner $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ of $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$, which are found to be closer to the corresponding results from CREX alone, implying the PREX-2 is less effective to constrain the ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ and $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ due to its lower precision of $\mathrm{\ensuremath{\Delta}}{F}_{\mathrm{CW}}$. Furthermore, we find the Skyrme EDF results inferred by combining the CREX and PREX-2 data nicely agree with the measured dipole polarizabilities ${\ensuremath{\alpha}}_{D}$ in $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ as well as the neutron matter equation of state from microscopic calculations. The implications of the inferred soft ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ around ${\ensuremath{\rho}}_{0}$ are discussed.