Quantifying the Impact of Molecular Effects on Tritium β-Decay

The Karlsruhe Tritium Neutrino (KATRIN) Experiment directly measures the neutrino mass-scale with a target sensitivity of 0.3 eV/c² by determining the shape change in the beta spectrum near the endpoint. The Rear Wall is used to maintain a homogeneous starting potential distribution over the full magnetic flux tube volume in the gaseous tritium source. During operation, tritium is circulated from the gaseous source and through the beamline. In this process, small amounts of tritium adsorb on the Rear Wall. Because the Rear Wall tritium has different conditions such as temperature than those of the gaseous source tritium, the Rear Wall tritium has a different spectrum than that of the gaseous source tritium. This Rear Wall tritium spectrum is superimposed onto the spectrum from the gaseous source, and thus is treated as a background. Not accounting for this background tritium spectrum from the adsorbed tritium results in a neutrino mass squared bias of order 10⁻³ eV². This thesis will discuss this background tritium spectrum, the efforts made to model it, and the size of its systematic contribution to KATRIN’s neutrino mass results. Since modern tritium-based experiments use a molecular source and molecular excitations modify the beta spectrum, one must also understand these “final-state” excitations precisely in order to properly analyze the spectral shape. Historical mass spectroscopy measurements in the 1950’s (Snell[1] and Wexler[2]) disagreed with im proved theoretical calculations from the 1990’s (Saenz[3]). The Tritium Recoil-Ion Mass Spectrometer (TRIMS) experiment is a coincidence time-of-flight mass spec trometer designed to test the theory used in the neutrino-mass analysis. The main open threads this thesis seeks to connect are: 1. is it possible to mathematically rec oncile the results of 1950’s mass spectroscopy measurements [1][2], 1990’s theoretical calculations[3], and the 2020 TRIMS results[4]? and 2. Can the quasibound HeH⁺ and HeT⁺ ions predicted by theory be successfully modeled via simulation? This thesis seeks to address the first open thread through extensive Liouville theorem cal culations with the experimental and theoretical results. This thesis will address the second open thread through its description of the development of a new python-based TRIMS simulation called PyTRIMS to simulate and model dissociation in flight.