The Lamb Shift Experiment in Muonic Hydrogen

The subject of this thesis is the muonic hydrogen (μ−p) Lamb shift experiment being performed at the Paul Scherrer Institute, Switzerland. Its goal is to measure the 2S − 2P energy difference in μp atoms by laser spectroscopy and to deduce the proton root–mean– square (rms) charge radius rp with 10 −3 precision, an order of magnitude better than presently 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. The experiment is based on the measurement of the energy difference between the 2SF=1 1/2 and 2P F=2 3/2 levels in μp atoms to a precision of 30 ppm, using a pulsed laser tunable at wavelengths around 6 μm. Negative muons from a unique low–energy muon beam are stopped at a rate of 70 s−1 in 0.6 hPa of H2 gas. Highly excited μp 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–lived μp2S atoms with a lifetime of 1.3 μs are formed. An incoming muon triggers a pulsed, multi–stage laser system which delivers 0.2 mJ per pulse at λ ' 6 μm with 55 s−1 repetition rate. It consists of two XeCl excimer lasers followed by dye lasers which pump an oscillator–amplifier frequency–controlled Ti:Sa laser. Its 6 ns long pulse at 708 nm is then frequency shifted to 6 μm via third Stokes production in a Raman cell filled with hydrogen. The laser pulse has a delay of about 1.5 μs with respect to the prompt muon cascade. If the laser is on resonance, it induces 2S−2P transitions. The subsequent deexcitation to the 1S state emits a 1.9 keV Kα x ray which is detected by large area avalanche photodiodes. The resonance frequency, and hence the Lamb shift and rp, are determined by measuring the intensity of these x rays as a function of the laser wavelength. A 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. The first part of this thesis reports on the present status of the Lamb shift theory in μp. Following, there is a detailed description of the apparatus and analysis of the data. An estimate of the present and future laser–induced event rates are given, together with a study of the present and future background. In the Appendices are discussed: the energy levels in H, the proton radius definition, the relevance of this experiment, the 2S state population and lifetime, and the spectroscopic properties of the 2S − 2P transition.