title: Development of the β-NMR technique towards the study of hyperfine anomalies in short-lived nuclei
Creators: name: Jankowski, Marcus
Publisher: name: UNSPECIFIED
Year: 2024

description: The knowledge of magnetic dipole moments of atomic nuclei is very valuable for nuclear structure research. Because this nuclear property depends to a large degree on the configuration of the unpaired nucleons in the nucleus, it can serve as a reference to benchmark the model predictions and assess its underlying assumptions. If magnetic moments are determined with great precision, one can address small effects, such as the hyperfine anomaly, which arises from the finite size of the nucleus, and particularly the distribution of nuclear magnetisation. Obtaining information on the hyperfine anomaly can help to constrain nuclear structure models. The importance of experimentally determined magnetic moments and the quest for reaching higher precision can therefore not be underestimated. 

β-detected nuclear magnetic resonance (β-NMR) is a powerful spectroscopic technique that is used to determine the nuclear magnetic moments of short-lived β-emitting nuclei with great precision. Such studies are conducted at the VITO beamline at the ISOLDE facility at CERN. This setup has recently undergone several major upgrades to further enhance its resolution, including the installation of a 4.7 T superconducting magnet and a new data acquisition system. The latter system was a major part of the work conducted for this thesis and is presented in detail. It uses a field-programmable gate array to characterise the detected β particles in real-time by a selection of their properties, such as time of arrival or signal integral. The properties are saved for all individual β events, enabling a flexible in-depth data analysis. In addition, a new method of evaluating the β-NMR spectra was developed. It considers the frequency and the time dependency of the measured signals and allows for a more comprehensive representation of the recorded data through a two-dimensional fit.

This thesis presents the first β-NMR studies on short-lived 47K using the newly upgraded experimental setup. The magnetic moment µI=1.936182(19) µN was derived from these measurements. It was possible to reduce the uncertainty to 10 ppm, which is two orders of magnitude smaller than in the literature. The differential hyperfine anomaly between stable 39K and 47K was also determined at 39∆47=0.360(9) %. This precisely measured differential hyperfine anomaly is then compared to the theoretical hyperfine anomaly obtained by combining atomic (Hartree-Fock) and nuclear (Density Functional Theory) theoretical approaches. It is shown that in contrary to the magnetic moments alone, which cannot pinpoint the relative contributions of spin and orbital angular momentum to the total magnetic moment of 39K and 47K, their differential hyperfine anomaly provides a strong constraint on the composition of the magnetic moment. This analysis points to the conclusion that consistency is achieved when the orbital contribution to the magnetic moment of both 39K and 47K remains unchanged, but their spin contributions are lowered with respect to the calculated values. Ongoing theoretical efforts and further studies on other K isotopes and other isotopic chains will show whether this conclusion is more universal. In summary, as shown here, precise measurements of the hyperfine anomaly in unstable nuclei should allow to test nuclear structure models, to increase the ability of such models to predict magnetic moments, and finally to improve understanding of the magnetic moment operator.