Measurement of the Decay Rate of the Negative Positronium Ion

Consisting of a positron and two electrons, the negative ion of positronium is one of the simplest three-body systems with a bound state. Its constituents are stable, point-like particles, and due to the small particle masses, it is essentially free from perturbations by strong interaction effects. Together with the rather unique mass ratio, these properties make the Ps ion an interesting object for studying the quantum-mechanical three-body problem. Despite numerous theoretical investigations, the published experimental results are so far limited to a first observation and a single decay rate measurement. With a precision of 4.3%, its error is still an order of magnitude larger than the theoretical uncertainty. In this thesis, after giving a short review of the currently available theoretical results, a new determination of the decay rate is reported. This includes an exploratory experiment along the lines of the old one and a more precise measurement using an improved detection method. In the latter one, the error has been reduced to 0.8%. Moreover, the maximum precision that can be reached with the current set-up is investigated, and the prospects for further experiments at the new high-intensity positron source NEPOMUC at the FRM II research reactor in Munich are discussed