Recent advances in nuclear structure theory have significantly enlarged the accessible part of the nuclear landscape via ab initio many-body calculations. These developments open new ways for microscopic studies of light, medium-mass and heavy nuclei as well as nuclear matter and represent an important step towards a systematic and comprehensive understanding of atomic nuclei across the nuclear chart. While remarkable agreement has been found between different many-body methods for a given nuclear Hamiltonian, the comparison with experiment and the understanding of theoretical uncertainties are still important open questions. The observed discrepancies to experiment indicate deficiencies in presently used nuclear interactions and operators. Chiral effective field theory (EFT) allows to systematically derive contributions to nucleon-nucleon (NN), three-nucleon (3N) and higher-body interactions including estimates of theoretical uncertainties. While the treatment of NN interactions in many-body calculations is well established, the calculation of 3N interactions and their incorporation in ab initio frameworks is still a frontier. This work reviews in detail recent and current developments on the derivation and implementation of improved 3N interactions and provides a comprehensive introduction to fundamental methods for their practical calculation and representation. We further give an overview of novel and established methods that facilitate the inclusion and treatment of 3N interactions in ab initio nuclear structure frameworks and present a selection of the latest calculations of atomic nuclei as well as nuclear matter based on state-of-the-art nuclear NN and 3N interactions derived within chiral EFT. Finally, we discuss ongoing efforts, open questions and future directions.

中文翻译：

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三核力：原子核和致密物质的实现和应用

核结构理论的最新进展通过从头计算的多体计算显着扩大了核景观的可访问部分。这些发展为轻、中质量和重原子核以及核物质的微观研究开辟了新的途径，并代表朝着在整个核图中系统和全面地了解原子核迈出的重要一步。虽然对于给定的核哈密顿量，不同的多体方法之间已经发现了显着的一致性，但与实验的比较和对理论不确定性的理解仍然是重要的开放问题。观察到的实验差异表明目前使用的核相互作用和操作员存在缺陷。手性有效场论 (EFT) 允许系统地推导出对核子 - 核子 (NN) 的贡献，三核子 (3N) 和更高体相互作用，包括理论不确定性的估计。虽然在多体计算中对 NN 相互作用的处理已经很好地建立，但 3N 相互作用的计算及其在 ab initio 框架中的结合仍然是一个前沿。这项工作详细回顾了改进的 3N 相互作用的推导和实现的近期和当前发展，并提供了对其实际计算和表示的基本方法的全面介绍。我们进一步概述了新的和已建立的方法，这些方法有助于在从头算核结构框架中包含和处理 3N 相互作用，并基于最先进的技术提出一系列最新的原子核和核物质计算手性 EFT 中衍生的核 NN 和 3N 相互作用。最后，我们讨论正在进行的工作、开放性问题和未来的方向。