镜像$\beta$跃迁的$\mathcal{F}t$值及允许核$\beta$衰变中弱磁感应电流
$\mathcal{F}t$ values of the mirror $β$ transitions and the weak magnetism induced current in allowed nuclear $β$ decay
AI总结：
本研究更新了镜像β衰变的Ft值，通过核壳模型计算弱磁性矩阵元并与实验对比，扩展至A=75核，为精确测量和新物理探索提供指导。
摘要：
近年来，核$\beta$衰变中的一系列关联测量已达到1\\%及以下的精度，预计在不久的将来将达到更高的精度。在这些精度水平上，由强相互作用引起的反冲项等高阶修正以及辐射修正，在将这些结果解释为新物理或提取$V_{ud}$夸克混合矩阵元时，不能再被忽视。我们在此更新了$T=1/2$镜像$\beta$衰变的$\mathcal{F}t$值，并概述了当前对最重要的反冲项——弱磁性——在$T=1/2$镜像$\beta$跃迁及更高同位旋多重态中大量$\beta$衰变中的实验和理论知识。决定弱磁性的矩阵元在核壳模型中计算，并与实验数据交叉验证，显示出总体良好的一致性。此外，我们表明，从适当形变的核势中可以获得进一步的见解，特别是对于镜像$T=1/2$衰变。这些结果为弱磁性的大小提供了新的认识，将可用信息扩展到质量高达$A=75$的核的$\beta$跃迁。这为正在进行和新的精确核$\beta$衰变关联测量的规划和解释提供了重要指导，这些测量旨在寻找新物理或在镜像$\beta$衰变中提取$V_{ud}$夸克混合矩阵元。对弱磁性的更详细了解也可能对与反应堆中微子问题相关的进一步理论工作具有意义。
英文摘要：
In recent years a number of correlation measurements in nuclear $β$ decay have been performed reaching a precision of the order of 1\% and below and it is expected that even higher precision will be reached in the near future. At these levels of precision higher-order corrections due to e.g. recoil terms induced by the strong interaction and radiative corrections cannot necessarily be neglected anymore when interpreting these results in terms of new physics or extracting a value for the $V_{ud}$ quark-mixing matrix element. We provide here an update of the $\mathcal{F} t$ values of the $T=1/2$ mirror $β$ decays as well as an overview of current experimental and theoretical knowledge of the most important recoil term, weak magnetism, for both the $T=1/2$ mirror $β$ transitions and a large set of $β$ decays in higher isospin multiplets. The matrix elements determining weak magnetism were calculated in the nuclear shell model and cross-checked against experimental data, showing overall good agreement. Additionally, we show that further insight can be obtained from properly deformed nuclear potentials, in particular for mirror $T=1/2$ decays.. The results provide new insights in the size of weak magnetism, extending the available information to $β$ transitions of nuclei with masses up to $A =$ 75. This provides important guidance for the planning and interpretation of ongoing and new precise correlation measurements in nuclear $β$ decay searching for new physics or to extract the $V_{ud}$ quark-mixing matrix element in mirror $β$ decays. This more detailed knowledge of weak magnetism can also be of interest for further theoretical work related to the reactor neutrino problem.
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