The Lamb Shift Experiment in Muonic Hydrogen

The subject of this thesis is the muonic hydrogen (µp) 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 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 2S(F=1) and 2P(F=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 hydrogen
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 long­live µp(2S) atoms with a lifetime
of 1.3 µs are formed. An incoming muon triggers a pulsed,
multi­stage laser system which delivers 0.2 mJ per pulse at 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 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. 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 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.