We determine for the first time the magnetic dipole moment of a short-lived nucleus with part-per-million (ppm) accuracy. To achieve this 2-orders-of-magnitude improvement over previous studies, we implement a number of innovations into our $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) setup at ISOLDE at CERN. Using liquid samples as hosts, we obtain narrow, subkilohertz-linewidth, resonances, while a simultaneous in situ ${}^1\mathrm{H}$ NMR measurement allows us to calibrate and stabilize the magnetic field to ppm precision, thus eliminating the need for additional $\beta$-NMR reference measurements. Furthermore, we use ab initio calculations of NMR shielding constants to improve the accuracy of the reference magnetic moment, thus removing a large systematic error. We demonstrate the potential of this combined approach with the 1.1 s half-life radioactive nucleus ${}^{26}\mathrm{Na}$, which is relevant for biochemical studies. Our technique can be readily extended to other isotopic chains, providing accurate magnetic moments for many short-lived nuclei. Furthermore, we discuss how our approach can open the path toward a wide range of applications of the ultrasensitive $\beta$-NMR in physics, chemistry, and biology.

中文翻译：

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百万分之一精度的短寿命核的磁矩：朝着β检测NMR在物理，化学和生物学领域的新应用迈进

我们首次确定了寿命短的原子核的磁偶极矩，其精确度为百万分之一（ppm）。为了实现比以前的研究高2个数量级的改进，我们在我们的产品中实施了许多创新$\beta$核磁共振（$\beta$-NMR）设置在CERN的ISOLDE。使用液体样品作为宿主，我们可以获得窄的亚千赫兹线宽共振，同时可以原位同步 ${}^{\mathrm{1个}}\mathrm{H}$ NMR测量使我们能够将磁场校准并稳定到ppm精度，从而无需额外的 $\beta$-NMR参考测量。此外，我们使用NMR屏蔽常数的从头算来提高参考磁矩的精度，从而消除了较大的系统误差。我们证明了这种结合方法与1.1 s半衰期放射性核的潜力${}^{26}娜$，与生化研究有关。我们的技术可以很容易地扩展到其他同位素链，从而为许多短寿命核提供准确的磁矩。此外，我们讨论了我们的方法如何为超灵敏性的广泛应用开辟道路$\beta$-NMR在物理，化学和生物学中。