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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 β-detected nuclear magnetic resonance (β-NMR) setup at ISOLDE at CERN. Using liquid samples as hosts, we obtain narrow, subkilohertz-linewidth, resonances, while a simultaneous in situ ^{1}H NMR measurement allows us to calibrate and stabilize the magnetic field to ppm precision, thus eliminating the need for additional β-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}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 β-NMR in physics, chemistry, and biology.

This paper reports on the hyperfine-structure and radioactive-decay studies of the neutron-deficient francium isotopes ^{202–206}Fr performed with the Collinear Resonance Ionization Spectroscopy (CRIS) experiment at the ISOLDE facility, CERN. The high resolution innate to collinear laser spectroscopy is combined with the high efficiency of ion detection to provide a highly sensitive technique to probe the hyperfine structure of exotic isotopes. The technique of decay-assisted laser spectroscopy is presented, whereby the isomeric ion beam is deflected to a decay-spectroscopy station for alpha-decay tagging of the hyperfine components. Here, we present the first hyperfine-structure measurements of the neutron-deficient francium isotopes ^{202–206}Fr, in addition to the identification of the low-lying states of ^{202,204}Fr performed at the CRIS experiment.

With increasing demand for accurate calculation of isotope shifts of atomic systems for fundamental and nuclear structure research, an analytic energy derivative approach is presented in the relativistic coupled-cluster (CC) theory framework to determine the atomic field shift and mass shift (MS) factors. This approach allows the determination of expectation values of atomic operators, overcoming fundamental problems that are present in existing atomic physics methods, i.e. it satisfies the Hellmann–Feynman theorem, does not involve any non-terminating series, and is free from choice of any perturbative parameter. As a proof of concept, the developed analytic response relativistic CC theory has been applied to determine MS and field shift factors for different atomic states of indium. High-precision isotope-shift measurements of ${}^{104-127}$ In were performed in the 246.8 nm (5p ^2 P _3/2 $\to $ 9s ^2 S _1/2 ) and 246.0 nm (5p ^2 P _1/2 $\to $ 8s ^2 S _1/2 ) transitions to test our theoretical results. An excellent agreement between the theoretical and measured values is found, which is known to be challenging in multi-electron atoms. The calculated atomic factors allowed an accurate determination of the nuclear charge radii of the ground and isomeric states of the ${}^{104-127}$ In isotopes, providing an isotone-independent comparison of the absolute charge radii.