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

Abstract

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).