The Lamb Shift Experiment in Muonic Hydrogen
The subject of this thesis is the muonic hydrogen (\xb5p) Lamb shift experiment being performed at the Paul Scherrer Institute, Switzerland. Its goal is to measure the 2S-2P energy difference in \xb5p atoms by laser spectroscopy and to deduce the proton root \xadmean\xad square (rms) charge radius with 10-3 precision, an order of magnitude better than\npresently known. This would make it possible to test bound-state quantum electrodynamics (QED) in hydrogen at the relative accuracy level of 10-7, and will lead to an improvement in the determination of the Rydberg constant by more than a factor of seven. Moreover it will represent a benchmark for QCD theories.\n\nThe experiment is based on the measurement of the energy difference between the 2S(F=1) and 2P(F=2) levels in \xb5p atoms to a precision of 30 ppm, using a pulsed laser tunable\nat wavelengths around 6 \xb5m. Negative muons from a unique low energy muon beam are stopped at a rate of 70 s-1 in 0.6 hPa of hydrogen gas. Highly excited \xb5p atoms are formed, and most of them promptly deexcite to the ground state within 100 ns. However, there is a roughly 1% probability that long\xadlive \xb5p(2S) atoms with a lifetime of 1.3 \xb5s are formed.\nAn incoming muon triggers a pulsed, multi\xadstage laser system which delivers 0.2 mJ per pulse at 6 \xb5m with 55 s-1 repetition rate. It consists of two XeCl excimer lasers followed by dye lasers which pump an oscillator \xadamplifier frequency \xadcontrolled Ti:Sa laser. Its 6 ns long pulse at 708 nm is then frequency shifted to 6 \xb5m via third Stokes production in a Raman cell filled with hydrogen. The laser pulse has a delay of about 1.5 \xb5s with respect to the prompt muon cascade. \n\nIf the laser is on resonance, it induces 2S-2P transitions. The subsequent deexcitation to the 1S state emits a 1.9 keV Lyman-alpha x ray which is detected by large area avalanche photo diodes. The resonance frequency, and hence the Lamb shift and the proton radius, are determined by measuring the intensity of these x rays as a function of the laser wavelength.\n\nA search for the 2S-2P resonance line was performed in November 2003 when a broad range of laser frequencies was scanned (49.7409 - 49.8757 THz), corresponding to proton radii between 0.844 and 0.905 fm. The result of the data analysis is that no significant 2S-2P resonance was observed. The negative result is with high probability due to the low statistics and not to an incorrect search region.\n \nThe first part of this thesis reports on the present status of the Lamb shift theory in \xb5p. Following, there is a detailed description of the apparatus and analysis of the data. An estimate of the present and future laser-\xadinduced event rates are given, together with a study of the present and future background. In the Appendices are discussed: the energy levels in hydrogen, the proton radius definition, the relevance of this experiment, the 2S state population and lifetime, and the spectroscopic properties of the 2S-2P transition.