| Summary: | The question of a possible finite neutrino mass is one of the most investigated and controversial topics in particle physics and cosmology. The most promising direct ex periments for determining the neutrino mass are based on the study of the /-decay of molecular tritium. The mass of the neutrino is deduced by analysing the shape of the continuous energy spectrum of the electrons emitted in the /3-decay. In this thesis, the molecular physics issues facing these experiments are investigated. Theoretical final state probability distributions of the daughter molecule are calculated to satisfy the higher resolution requirements and increased sensitivity of the future ex periments. Transition probabilities to the six lowest electronically bound states of 3HeT+ are calculated. Rotational excitation of the daughter molecule is considered and probabilities obtained for the /-decay of T2 in the first four rotational states. Isotope contamination from DT and HT molecules is also investigated, and the probability distributions for 3HeD+ and 3HeH+ are calculated. The sensitivity of the initial temperature, ortho:para ratio and isotopic composition of the source is considered. Estimates of the error in the value of the neutrino mass deduced from fitting theoretical spectra, due to uncertainties in temperature, ortho:para ratio of T2 and percentage of DT molecules, are obtained. The R-matrix method is used to treat the electronic continuum of 3HeT+. Reso nances converging to the first eight excited target states are obtained, and the transition probabilities to these resonances and background continuum are calculated. Endpoint effects due to the decay of other possible species in the source - T_, T, T+, T2", Tg and T - are also investigated. It is hoped that this data will be used as part of the forthcoming KATRIN experi ment.
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