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.

The T₁ relaxation time measured in nuclear magnetic resonance experiments contains information about electric field gradient (EFG) fluctuations around a nucleus, but computer simulations are typically required to interpret the underlying dynamics. This study uses classical molecular dynamics (MD) simulations and quantum chemical calculations to investigate EFG fluctuations around a Na⁺ ion dissolved in the ionic liquid 1-ethyl 3-methylimidizolium tetrafluoroborate, [Im₂₁][BF₄], to provide a framework for future interpretation of NMR experiments. Our calculations demonstrate that the Sternheimer approximation holds for Na⁺ in [Im₂₁][BF₄] and the anti-shielding coefficient is comparable to its value in water. EFG correlation functions, C_EFG(t), calculated using quantum mechanical methods or from force field charges are roughly equivalent after 200 fs, supporting the use of classical MD for estimating T₁ times of monatomic ions in this ionic liquid. The EFG dynamics are strongly bi-modal with 75-90 % of the decorrelation attributable to inertial solvent motion and the remainder to a highly distributed diffusional processes. Integral relaxation times, <τ_EFG>, were found to deviate from hydrodynamic predictions and were non-linearly coupled to solvent viscosity. Further investigation showed that Na⁺ is solvated by four tetrahedrally arranged [BF₄]^- anions and directly coordinated by ~6 fluorine atoms. Exchange of [BF₄]^- anions is rare on the 25-50 ns timescale and suggests that motion of solvent-shell [BF₄]^- are the primary mechanism for the EFG fluctuations. Different couplings of [BF₄]^- translational and rotational diffusion to viscosity are shown to be the source of the non-hydrodynamic scaling of <τ_EFG>.

Recently there has been an increased interest to apply the sensitive $\beta$-decay asymmetry detected nuclear magnetic resonance ($\beta$-NMR) technique to biological studies. A liquid-sample $\beta$-NMR setup was build at ISOLDE to allow such investigations and to use the resolution gain of liquid-state NMR in nuclear physics. As part of this setup a magnetic field locking system, a set of printed circuit board shimming coils, a sample exchange system, a set of compact $\beta$-detectors and a custom experimental vacuum chamber were developed. The main magnetic field was stabilized down to the ppm level by the locking system while allowing the direct determination of the absolute magnetic field. The homogeneity of the magnetic field was improved to $\le$ 5 ppm over the sample volume by the shimming coils. Time spent on changing samples was reduced by a factor of five by the liquid sample exchange system. During experiments it was possible to continuously observe the liquid sample thanks to the custom chamber and compact $\beta$-detectors. The absolute field determination allows for a novel way to reference $\beta$-NMR measurements, removing the need for time consuming reference measurements. The improved accuracy and resolution resulting from these innovations allows the study of the distribution of nuclear magnetization and (bio)chemicals using high-accuracy liquid-sample $\beta$-NMR.

A better understanding of the molecular interactions and, consequently, the structure-property relationships in protic ionic liquids (PIL) can help create more accurate property prediction models and enhance the efficiency of their various applications. This approach is especially relevant in understanding the PIL-H₂O mixtures. Depending on the application, water molecules can be considered as not only an impurity in PILs but also a dopant or even a cosolvent. Our study investigated density, viscosity, electrical conductivity, and derived properties like thermal expansion coefficients, excess molar volume, and excess viscosity of low-toxic alkanolammonium- and carboxylate-based PIL-H₂O mixtures. One- (1D) and two-dimensional (2D) nuclear magnetic resonance spectroscopy was employed to elucidate the distribution of water molecules within the PIL structure. In addition, critical aggregation concentrations (CAC) of PIL-H₂O mixtures were determined based on the physicochemical properties and ¹H longitudinal relaxation times. The results showed that the strength of PIL-H₂O interactions depends on the anion, while the cation affects the position of water in the PIL solvent network. Overall, our study provides valuable insight into the molecular modeling and property prediction of this type of PIL, a promising and currently underexplored subclass of ionic liquids.