Double-beta processes play a key role in the exploration of neutrino and weak interaction properties, and in the searches for effects beyond the standard model. During the last half century many attempts were undertaken to search for double-beta decay with emission of two electrons, especially for its neutrinoless mode $0\nu 2{\beta }^{-}$, the latter having still not been observed. Double-electron capture (2EC) was not yet in focus because of its in general lower transition probability. However, the rate of neutrinoless double-electron capture $0\nu 2\mathrm{EC}$ can experience a resonance enhancement by many orders of magnitude when the initial and final states are energetically degenerate. In the resonant case, the sensitivity of the $0\nu 2\mathrm{EC}$ process can approach the sensitivity of the $0\nu 2{\beta }^{-}$ decay in the search for the Majorana mass of neutrinos, right-handed currents, and other new physics. An overview of the main experimental and theoretical results obtained during the last decade in this field is presented. The experimental part outlines search results of 2EC processes and measurements of the decay energies for possible resonant $0\nu 2\mathrm{EC}$ transitions. An unprecedented precision in the determination of decay energies with Penning traps has allowed one to refine the values of the degeneracy parameter for all previously known near-resonant decays and has reduced the rather large uncertainties in the estimate of the $0\nu 2\mathrm{EC}$ half-lives. The theoretical part contains an updated analysis of the electron shell effects and an overview of the nuclear-structure models, in which the nuclear matrix elements of the $0\nu 2\mathrm{EC}$ decays are calculated. One can conclude that the decay probability of $0\nu 2\mathrm{EC}$ can experience a significant enhancement in several nuclides.

中文翻译：

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无中微子双电子俘获

Double-beta过程在探索中微子和弱相互作用特性以及寻找超出标准模型的效应中起着关键作用。在过去的半个世纪中，人们进行了许多尝试来寻找具有两个电子发射的双β衰变，尤其是其无中微子模式$0\nu 2{\beta }^{-}$，但尚未观察到后者。由于双电子捕获（2EC）通常具有较低的跃迁几率，因此尚未成为焦点。但是，无中微子双电子俘获率$0\nu 2\mathrm{欧共体}$当初始状态和最终状态发生能量简并时，可以经历许多数量级的共振增强。在共振情况下，$0\nu 2\mathrm{欧共体}$ 过程可以接近 $0\nu 2{\beta }^{-}$衰落，寻找马约拉纳中微子质量，右旋电流和其他新物理学。概述了该领域最近十年获得的主要实验和理论结果。实验部分概述了2EC过程的搜索结果以及衰减能量的测量，以寻找可能的共振$0\nu 2\mathrm{欧共体}$过渡。潘宁阱确定衰变能量的空前精确性，使人们能够为所有先前已知的近共振衰变改进简并参数的值，并减少了估算的相当大的不确定性。$0\nu 2\mathrm{欧共体}$半衰期。理论部分包含对电子壳效应的最新分析，以及核结构模型的概述，其中原子核的基体元素$0\nu 2\mathrm{欧共体}$计算衰减。可以得出这样的结论：$0\nu 2\mathrm{欧共体}$ 会在几种核素中经历明显的增强。