AI 中文总结
研究在斯凯姆能量密度泛函框架下，利用核密度分布的第四径向矩\(R_4\)及其与\(R_2\)的比值\(R_{4/2}\)，通过对100个斯凯姆泛函模型预测的统计分析，来约束亚饱和密度下的核状态方程。
AI 中文摘要
近期实验进展很快能精确提取核电荷密度分布的均方根半径及第四径向矩。核密度分布的第四径向矩\(R_4\equiv\sqrt[4]{\left<r^4\right>}\)对核表面厚度是敏感探针。本文在斯凯姆能量密度泛函框架下，研究\(R_4\)在亚饱和密度下约束核状态方程的效用。通过对100个斯凯姆泛函模型预测的统计分析，证明了在\(\text{}^{48}\text{Ca}\)和\(\text{}^{208}\text{Pb}\)等代表性核中，\(\rho = 0.08 \text{ fm}^{-3}\)处的每粒子能量曲率\(K(\rho)\)与\(R_4\)（或\(R_{4/2}=R_4/R_2\)）有强相关性。确定\(R_{4/2}\)对密度尾部敏感，可作为测试斯凯姆泛函空间中亚饱和\(K(\rho)\)的有效代理。例如，在\(^{48}\text{Ca}\)或\(^{208}\text{Pb}\)中，\(R_{4/2}\)精度达0.5%或更高时，可将\(0.08\) fm\(^{-3}\)处对称物质每粒子能量的曲率约束在20 MeV以内。
英文摘要
Recent experimental advances could soon allow the accurate extraction of not only the root-mean-square radius but also the fourth radial moment of the nuclear electric charge density distribution. The fourth radial moment of the nuclear density distribution, $R_4\equiv\sqrt[4]{\left<r^4\right>}$, provides a sensitive probe of the nuclear surface thickness, as it is more susceptible to the large-$r$ distributions than the root-mean-square radius ($R_2$). In this work, we examine the utility of $R_4$ for constraining the nuclear equation of state (EoS) at subsaturation densities, specifically for the proton distribution and within the framework of Skyrme energy density functionals. Using a statistical analysis based on predictions from one hundred Skyrme functional models, we demonstrate strong correlations between the energy per particle curvature $K(ρ)$ at $ρ= 0.08 \text{ fm}^{-3}$ and $R_4$ (or the ratio $R_{4/2}=R_4/R_2$) in representative nuclei such as $\text{}^{48}\text{Ca}$ and $\text{}^{208}\text{Pb}$. We establish that $R_{4/2}$, being sensitive to the density tail, serves as an efficient proxy for sub-saturation $K(ρ)$ within the tested Skyrme functional space. Knowledge of $R_{4/2}$ within 0.5\% precision or better, for example in $^{48}$Ca or $^{208}$Pb, could constrain the curvature of the energy per particle of symmetric matter at $0.08$ fm$^{-3}$ within 20 MeV or less.
