Abstract The knowledge of the level density is necessary for understanding nuclear reactions involving excited nuclear states. In particular, it is an important element in description of astrophysical processes and in technological applications. This review article explains main ideas of physics forming the level density in complex nuclei that grows very fast due to combinatorial complexity of total excitation energy shared by many constituents. This can be translated into a language of statistical physics by the Darwin–Fowler method. We briefly go through the historical development from the nuclear Fermi-gas model to the self-consistent mean field including the pairing effects. At the next step we introduce the ideas of thermalization in a closed mesoscopic system and quantum chaos with very complicated eigenfunctions. This is supported by the experience of the shell model in a limited orbital space that either provides an exact solution or uses the Monte Carlo approach. The statistical method of moments allows one to avoid the exact diagonalization keeping intact the quality of the results. We discuss the popular “constant temperature model” that describes well available data and the shell-model results; it is shown that its success cannot be explained by the phase transition from superfluid to a normal phase. The interpretation is suggested, supported by the numerical studies, in terms of dynamical chaotization including the collective enhancement of the level density. The role of incoherent collision-like interactions is stressed as a necessary element of the thermalization process.

中文翻译：

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核能级密度、热化、混沌和集合性

摘要 能级密度的知识对于理解涉及激发核态的核反应是必要的。特别是，它是描述天体物理过程和技术应用的重要元素。这篇评论文章解释了物理学的主要思想，在复杂核中形成能级密度，由于许多成分共享的总激发能的组合复杂性，这种密度增长非常快。这可以通过达尔文-福勒方法翻译成统计物理学的语言。我们简要回顾了从核费米气体模型到包括配对效应在内的自洽平均场的历史发展。在下一步中，我们将介绍封闭介观系统中的热化思想和具有非常复杂的本征函数的量子混沌。这得到了壳模型在有限轨道空间中的经验的支持，该模型提供了精确的解决方案或使用蒙特卡罗方法。矩的统计方法可以避免精确的对角化，保持结果的质量不变。我们讨论了流行的“恒温模型”，它描述了可用的数据和壳模型结果；结果表明，它的成功不能用从超流体到正常相的相变来解释。在数值研究的支持下，建议根据动态混沌化（包括水平密度的集体增强）进行解释。非相干碰撞类相互作用的作用被强调为热化过程的必要元素。