The size of the proton from the Lamb shift in muonic hydrogen

A measurement of the Lamb shift (2S-2P energy difference) in muonic hydrogen (μp, the exotic hydrogen atom made from one proton and one negative muon μ^-) has been on the physicists´ wish list for more than 40 years. Muonic hydrogen is a unique system to study the finite size (rms charge radius) r_p of the proton. Due to its 200 times larger mass, the muon´s Bohr radius in μp is about 200 times smaller than the corresponding electron Bohr radius in regular hydrogen H. This enhances finite size effects by about 200³ in μp, compared to H. The finite size contribution to the Lamb shift in muonic hydrogen is as large as 2% of the total 2S Lamb shift (Fig. 1 a).