标题： 原子核集体激发的有效场论 显示英文标题

标题： Effective field theories for collective excitations of atomic nuclei

摘要： 集体运动模式作为控制原子核低能激发的相关自由度出现。 这些模式——转动、配对转动和振动——在能量上与非集体激发分离，使得能够在有效场论的框架下描述它们。 转动和配对转动分别是有限变形核和有限超流核中旋转对称性和相位对称性自发破缺产生的 Nambu-Goldstone 模式残余。 这种对称性破缺严重限制了低能拉格朗日量的结构，从而明确了本质内容并简化了描述。 通过有效场论的方法揭示了原子核集体激发的本质，并且这一方法在考虑破缺尺度的情况下得以定义。 这允许系统地改进计算并估计和量化不确定性。 集体激发的有效场论已被用于计算感兴趣的能谱、跃迁概率和其他矩阵元。 特别是，对于无中微子双贝塔衰变的核矩阵元的预测随之带有量化不确定性。 本综述总结了这些结果，并将通过有效场论的方法与著名的模型和从头算计算进行了比较。 显示英文摘要

摘要： Collective modes emerge as the relevant degrees of freedom that govern low-energy excitations of atomic nuclei. These modes - rotations, pairing rotations, and vibrations - are separated in energy from non-collective excitations, making it possible to describe them in the framework of effective field theory. Rotations and pairing rotations are the remnants of Nambu-Goldstone modes from the emergent breaking of rotational symmetry and phase symmetries in finite deformed and finite superfluid nuclei, respectively. The symmetry breaking severely constrains the structure of low-energy Lagrangians and thereby clarifies what is essential and simplifies the description. The approach via effective field theories exposes the essence of nuclear collective excitations and is defined with a breakdown scale in mind. This permits one to make systematic improvements and to estimate and quantify uncertainties. Effective field theories of collective excitations have been used to compute spectra, transition rates, and other matrix elements of interest. In particular, predictions of the nuclear matrix element for neutrinoless double beta decay then come with quantified uncertainties. This review summarizes these results and also compares the approach via effective field theories to well-known models and ab initio computations.