Experiment to measure the Lamb shift in muonic hydrogen

Abstract

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 ?E (2 S1/2(F=1)–2 P3/2(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 theµp(2P ? 1S) transition.