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 being still not observed. Double-electron capture (2EC) was not in focus so far because of its in general lower transition probability. However, the rate of neutrinoless double-electron capture ($0\nu 2$EC) can experience a resonance enhancement by many orders of magnitude in case the initial and final states are energetically degenerate. In the resonant case, the sensitivity of the $0\nu 2$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. We present an overview of the main experimental and theoretical results obtained during the last decade in this field. The experimental part outlines search results of 2EC processes and measurements of the decay energies for possible resonant $0$2EC 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 $0\nu 2$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 $0\nu 2$EC decays are calculated. One can conclude that the decay probability of $0$2EC 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（$0\nu 2{\beta }^{-}$），但仍未观察到后者。到目前为止，双电子捕获（2EC）尚未成为人们关注的焦点，因为它通常具有较低的跃迁几率。但是，无中微子双电子的捕获率（$0\nu 2$如果初始状态和最终状态发生剧烈退化，则EC）可能会经历多个数量级的共振增强。在共振情况下，$0\nu 2$EC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。我们概述了该领域在过去十年中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可能的共振$ 0 $ 2EC跃迁的衰减能量测量。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。$0\nu 2$EC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$0\nu 2$计算EC衰减。可以得出结论，$ 0 $ 2EC的衰变概率可以在几个核素中得到显着提高。