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

中文翻译：

---

贝叶斯框架中中子表层和纯中子物质的核对称能

我们提出了核对称能量大小的推论 $J$， 斜率 $升$，和曲率 ${钾}_{\mathrm{符号}}$结合钙、铅和锡同位素的中子表皮数据，以及我们关于纯中子物质的最佳理论信息。贝叶斯框架用于从手性有效场理论计算中始终结合纯中子物质状态方程的先验知识。中子蒙皮使用扩展的 Skyrme 能量密度函数以完全量子 Skyrme-Hartree-Fock 方法建模，允许独立变化$J$, $升$， 和 ${钾}_{\mathrm{符号}}$不影响对称核物质状态方程。量化使用不同物理探针获得的中子蒙皮数据的效果。我们认为，鉴于现有数据，合并正交误差是获得每个核素统一误差的更合适的方法，并且这样做我们获得了 95% 的可信值$J=31.3\begin{array}{c}+4.2\\ -5.9\end{array}\mathrm{电动汽车}$, $升=40\begin{array}{c}+34\\ -26\end{array}\mathrm{电动汽车}$， 和 ${钾}_{\tau }=升-6{钾}_{\mathrm{符号}}=-444\begin{array}{c}+100\\ -84\end{array}\mathrm{电动汽车}$ 使用无信息先验 $J$, $升$， 和 ${钾}_{\mathrm{符号}}$， 和 $J=31.9\begin{array}{c}+1.3\\ -1.3\end{array}\mathrm{电动汽车}$, $升=37\begin{array}{c}+9\\ -8\end{array}\mathrm{电动汽车}$， 和 ${钾}_{\tau }=-480\begin{array}{c}+25\\ -26\end{array}\mathrm{电动汽车}$使用纯中子物质 (PNM) 先验。我们还表明，之间的非正相关$J$ 和 $升$中子表皮诱导数据与核液滴模型一致。单独的中子蒙皮数据显示出对对称能量参数的限制，与单独从手性有效场理论获得的那些参数一样严格，并且当结合使用时，95% 的可信区间减少了 4-5 倍。还表明，文献中使用的大多数核相互作用具有不饱和密度依赖性，这与 PNM 先验和中子蒙皮数据的组合不一致。我们展示了杰斐逊实验室即将进行的违反奇偶校验电子散射实验的铅和钙中子皮的测量结果，美因茨超导加速器应获得总误差范围$\mathrm{\Delta }升\approx 50\mathrm{电动汽车}$ 和 $\mathrm{\Delta }{钾}_{\tau }\approx 240\mathrm{电动汽车}$ 对于无信息先验和 $\mathrm{\Delta }升\approx 30\mathrm{电动汽车}$ 和 $\mathrm{\Delta }{钾}_{\tau }\approx 100\mathrm{电动汽车}$对于 67% 可信范围的 PNM 先验。在这些实验之前，我们根据现有的关于锡的中子表皮的数据对钙和铅的中子表皮进行了预测。$0.166\pm 0.008$ 调频和 $0.169\pm 0.014$ fm，分别使用无信息先验和 $0.167\pm 0.008$ 调频和 $0.172\pm 0.015$ fm，分别使用 PNM 先验。