Neutrinoless double beta ($0\nu \beta \beta$) decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element ($M^{0\nu }$) associated with the given $0\nu \beta \beta$transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of $M^{0\nu }$ for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of $M^{0\nu }$. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of $M^{0\nu }$ considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.

中文翻译：

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0νββ衰变矩阵元的核壳模型计算现状

中微子双beta（$0\nu \beta \beta$）衰变搜索目前是实验物理学的主要焦点之一。对这种衰减的观察将对我们对中微子的内在本质的理解具有重要的意义，并阐明标准模型的局限性。该过程的速率取决于未知的中微子有效质量和核基质元素（${\mathrm{中号}}^{0\nu }$）与给定的 $0\nu \beta \beta$过渡。后者只能通过理论计算来提供，因此需要对${\mathrm{中号}}^{0\nu }$实验计划的成功。这种需求驱使理论上的核物理学界提供最可靠的计算方法。${\mathrm{中号}}^{0\nu }$。在解决多体核问题的各种计算模型中，壳模型被广泛认为是原子核微观描述的基本框架。在这里，我们回顾了最新的和高级的壳模型计算${\mathrm{中号}}^{0\nu }$考虑光中微子交换通道的实验核。我们报告有关模型空间和壳模型核哈密顿量变化的理论计算的敏感性。