Nuclear symmetry energy from neutron skins and pure neutron matter in a Bayesian framework

We present an inference of the nuclear symmetry energy magnitude $J$, slope $L$, and curvature ${K}_{\mathrm{sym}}$ from combining neutron skin data on calcium, lead tin isotopes, our best theoretical information about pure matter. A Bayesian framework is used to consistently incorporate prior knowledge matter equation state chiral effective field theory calculations. Neutron skins are modeled in a fully quantum Skyrme-Hartree-Fock approach using extended Skyrme energy-density functional which allows for independent variation without affecting symmetric state. The effect obtained with different physical probes quantified. argue that, given existing data, errors quadrature more appropriate way obtain unified each nuclide, doing so we 95% credible values $J=31.3\begin{array}{c}+4.2\\ \ensuremath{-}5.9\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=40\begin{array}{c}+34\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, ${K}_{\ensuremath{\tau}}=L\ensuremath{-}6{K}_{\mathrm{sym}}=\ensuremath{-}444\begin{array}{c}+100\\ \ensuremath{-}84\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ uninformative priors ${K}_{\mathrm{sym}}$, $J=31.9\begin{array}{c}+1.3\\ \ensuremath{-}1.3\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=37\begin{array}{c}+9\\ \ensuremath{-}8\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, ${K}_{\ensuremath{\tau}}=\ensuremath{-}480\begin{array}{c}+25\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ (PNM) priors. also show that nonpositive correlation between $J$ $L$ induced by consistent droplet model. alone shown place limits parameters as stringent those alone, when combined intervals reduced factor 4--5. It majority interactions literature have subsaturation density dependencies inconsistent combination PNM data. measurements calcium upcoming parity-violating electron scattering experiments at Jefferson Lab Mainz Superconducting Accelerator should total error ranges $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}50\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}240\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}30\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ 67% bounds. Ahead experiments, make predictions based $0.166\ifmmode\pm\else\textpm\fi{}0.008$ fm $0.169\ifmmode\pm\else\textpm\fi{}0.014$ fm, respectively, $0.167\ifmmode\pm\else\textpm\fi{}0.008$ $0.172\ifmmode\pm\else\textpm\fi{}0.015$