Both the incompressibility $K_A$ of a finite nucleus of mass $A$ and that ($K_{\infty }$) of infinite nuclear matter are fundamentally important for many critical issues in nuclear physics and astrophysics. While some consensus has been reached about $K_{\infty }$, accurate theoretical predictions and experimental extractions of $K_{\tau }$ characterizing the isospin dependence of $K_A$ have been very difficult. We propose a differential approach to extract $K_{\tau }$ and $K_{\infty }$ independently from the $K_A$ data of any two nuclei in a given isotope chain. Applying this method to the $K_A$ data from isoscalar giant monopole resonances (ISGMR) in even-even Pb, Sn, Cd, and Ca isotopes taken by Garg et al. at the Research Center for Nuclear Physics (RCNP), Osaka University, Japan, we find that the ${}^{106}\mathrm{Cd}\text{−}{}^{116}\mathrm{Cd}$ and ${}^{112}\mathrm{Sn}\text{−}{}^{124}\mathrm{Sn}$ pairs having the largest differences in isospin asymmetries in their respective isotope chains measured so far provide consistently the most accurate up-to-date $K_{\tau }$ value of $K_{\tau }=-616\pm 59$ MeV and $K_{\tau }=-623\pm 86$ MeV, respectively, largely independent of the remaining uncertainties of the surface and Coulomb terms in expanding $K_A$, while the $K_{\infty }$ values extracted from different isotopes chains are all well within the current uncertainty range of the community consensus for $K_{\infty }$. Moreover, the size and origin of the “soft Sn puzzle” is studied with respect to the “stiff Pb phenomenon.” It is found that the latter is favored due to a much larger (by $\approx 380$ MeV) $K_{\tau }$ for Pb isotopes than for Sn isotopes, while $K_{\infty }$ from analyzing the $K_A$ data of Sn isotopes is only about 5 MeV less than that from analyzing the Pb data.

中文翻译：

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富中子核不可压缩性的微分分析

两者的不可压缩性 ${钾}_{\mathrm{一种}}$ 质量有限的原子核 $\mathrm{一种}$ 然后 （${钾}_{\infty }$) 的无限核物质对于核物理学和天体物理学中的许多关键问题具有根本的重要性。虽然已经达成了一些共识${钾}_{\infty }$, 准确的理论预测和实验提取 ${钾}_{\tau }$ 表征同位旋依赖性 ${钾}_{\mathrm{一种}}$已经很困难了。我们提出了一种差分方法来提取${钾}_{\tau }$ 和 ${钾}_{\infty }$ 独立于 ${钾}_{\mathrm{一种}}$给定同位素链中任意两个原子核的数据。将此方法应用于${钾}_{\mathrm{一种}}$来自 Garg等人在偶数 Pb、Sn、Cd 和 Ca 同位素中的等标量巨单极子共振 (ISGMR) 的数据。在日本大阪大学核物理研究中心 (RCNP)，我们发现${}^{106}\mathrm{光盘}\text{-}{}^{116}\mathrm{光盘}$ 和 ${}^{112}锡\text{-}{}^{124}锡$ 迄今为止测量的各自同位素链中同位旋不对称性差异最大的对始终提供最准确的最新数据 ${钾}_{\tau }$ 的价值 ${钾}_{\tau }=-616\pm 59$ MeV 和 ${钾}_{\tau }=-623\pm 86$ MeV，分别在很大程度上独立于表面和库仑项在膨胀过程中的剩余不确定性 ${钾}_{\mathrm{一种}}$，而 ${钾}_{\infty }$ 从不同同位素链中提取的值都在当前社区共识的不确定范围内 ${钾}_{\infty }$. 此外，还针对“硬铅现象”研究了“软锡拼图”的大小和起源。发现后者受到青睐，因为它更大（由$\approx 380$ 兆伏） ${钾}_{\tau }$ 铅同位素比锡同位素多，而 ${钾}_{\infty }$ 从分析 ${钾}_{\mathrm{一种}}$ Sn同位素的数据仅比分析Pb数据的数据少约5 MeV。