Abstract
The contribution of the root mean square (RMS) proton charge radius to the Lamb shift (2S-2P energy difference) in muonic hydrogen (μp) amounts to 2%. Apart from the uncertainty on this charge radius, theory predicts the Lamb shift with a precision on the ppm level. We are going to measure δE (2S 1/2 (F = 1)-2P 3/2 (F = 2)) in a laser resonance experiment to a precision of 30 ppm (i.e., 10% of the natural linewidth) and to deduce the RMS proton charge radius with 10 -3 relative accuracy, 20 times more precise than presently known. The most important requirement for the feasibility of such an experiment, namely the availability of a sufficient amount of long-lived metastable μp atoms in the 2S state, has been investigated in a recent experiment at PSI. Our analysis shows that in the order of one percent of all muons stopped in low-pressure hydrogen gas form a long-lived μp(2S) with a lifetime of the order of 1 μs. The technical realization of our experiment involves a new high-intensity low-energy muon beam, an efficient low-energy muon entrance detector, a randomly triggered 3-stage laser system providing the 0.5 mJ, 7 ns laser pulses at 6.02 μm wavelength, and a combination of a xenon gas-proportional-scintillation-chamber (GPSC) and a microstrip-gas-chamber (MSGC) with a CsI-coated surface to detect the 2 keV X-rays from the μp(2P → 1S) transition.