This Master's thesis investigates a method to measure atomic nuclei with record precision using muonic atom X-ray spectroscopy. In particular, 6Li is measured experimentally. The method used is independent from the previous most precise measurement of the 6Li nuclear charge radius which uses electron scattering. Measuring low-Z elements using muonic X-ray transitions requires excellent detectors which have so far been mostly optimised for higher energies. This project investigates methods to reach precision requirements for low-Z elements which can yield insight into nuclear structure models, and uses a Silicon Drift Detector (SDD) which is here characterised in detail and found to allow for significantly improved results over previous attempts. So far, the SDD and developed calibration scheme demonstrates a 3.7 eV precision compared to the target 0.5 eV. It appears to be limited by detector resolution, which also makes curve fitting difficult for complex line structures. A new method for generating calibration lines, X-ray fluorescence, is tested and shows good promise for future use. The planned use of a Metallic Magnetic Microcalorimeter will potentially improve results significantly, having a much-improved resolution over SDD's. Preliminary experimental results find ΔEµLi-6, 2p-1s = 18780.6 ± 15.7 eV, which is a factor of 4 improvement over the previous best measurement of this transition and the world's most precise measurement to date. While the uncertainty is larger than seen in designated calibration runs, it demonstrates the ability to perform high-precision muonic atom spectroscopy. With new detector technologies, this thesis finds no immediate obstacles to the target 0.5 eV precision.

Scanning Electron Microscopy combined with Energy Dispersive X-ray Spectroscopy (SEM-EDS) is a widely applied elemental microanalysis method. The integration of silicon drift detectors (SDDs) has notably enhanced EDS performance, enabling precise elemental identification due to its large sensitive area and low output capacitance.  Accurate simulations of SDDs can provide insights that enable the design and optimization of future models without the need for costly and time-consuming experimental iterations. Moreover, the current model-based quantification methods for EDS applications have reached their maximum predictive accuracy. As such, creating a more accurate simulation model could help achieve a higher level of precision in these quantification models, which would be immensely valuable for all EDS applications.  With this objective in mind, a simulation framework for modeling SDDs in EDS was developed based on Geant4, Allpix Squared, and COMSOL Multiphysics. The simulation encompasses the entire physics pipeline, including characteristic X-ray emission from the target sample and its absorption in the detector. The generated charge carriers within the detector are propagated through the internal electric field of the SDD, and their individual charge contribution is measured to simulate EDS spectra. The simulated model was compared to existing literature and in-house experimental measurements, showing strong agreement in the case of a well-tuned SDD. Limitations of the simulation framework are discussed, and further research to enhance accuracy and speed is explored.