This contribution reviews the present status on the available constraints to the nuclear equation of state (EoS) around saturation density from nuclear structure calculations on ground and collective excited state properties of atomic nuclei. It concentrates on predictions based on self-consistent mean-field calculations, which can be considered as an approximate realization of an exact energy density functional (EDF). EDFs are derived from effective interactions commonly fitted to nuclear masses, charge radii and, in many cases, also to pseudo-data such as nuclear matter properties. Although in a model dependent way, EDFs constitute nowadays a unique tool to reliably and consistently access bulk ground state and collective excited state properties of atomic nuclei along the nuclear chart as well as the EoS. For comparison, some emphasis is also given to the results obtained with the so called {\it ab initio} approaches that aim at describing the nuclear EoS based on interactions fitted to few-body data only. Bridging the existent gap between these two frameworks will be essential since it may allow to improve our understanding on the diverse phenomenology observed in nuclei. Examples on observations from astrophysical objects and processes sensitive to the nuclear EoS are also briefly discussed. As the main conclusion, the isospin dependence of the nuclear EoS around saturation density and, to a lesser extent, the nuclear matter incompressibility remain to be accurately determined. Experimental and theoretical efforts in finding and measuring observables specially sensitive to the EoS properties are of paramount importance, not only for low-energy nuclear physics but also for nuclear astrophysics applications.

中文翻译：

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从原子核的基态和集体激发态性质得到的状态方程

该贡献回顾了从原子核的基态和集体激发态特性的核结构计算得出的关于饱和密度的核状态方程 (EoS) 可用约束的现状。它专注于基于自洽平均场计算的预测，可以将其视为精确能量密度泛函 (EDF) 的近似实现。EDF 源自有效相互作用，这些相互作用通常适用于核质量、电荷半径，并且在许多情况下，还适用于核物质特性等伪数据。尽管以依赖于模型的方式，EDF 现在构成了一种独特的工具，可以沿着核图以及 EoS 可靠且一致地访问原子核的体基态和集体激发态特性。为了比较，还强调了使用所谓的 {\it ab initio} 方法获得的结果，该方法旨在根据仅适用于少体数据的相互作用来描述核 EoS。弥合这两个框架之间的现有差距将是必不可少的，因为它可以提高我们对原子核中观察到的各种现象学的理解。还简要讨论了对核 EoS 敏感的天体物理物体和过程的观测示例。作为主要结论，核 EoS 对饱和密度的同位旋依赖性以及在较小程度上的核物质不可压缩性仍有待准确确定。寻找和测量对 EoS 特性特别敏感的可观测值的实验和理论工作至关重要，