Precise Optical Measurement of Lamb Shifts in Atomic Hydrogen

Abstract

We have measured the combination of hydrogen Lamb shifts $L_{1S}-5\mathrm{}{L}_{2S}+4\mathrm{}{L}_{4P}$ by comparing the frequencies of the $1S-2S$ and $2S-4P$ transitions. The measurement determines the $1S$ Lamb shift to be 8 172 827(51) kHz, the most precise value for any Lamb shift. The theoretical predictions for $L_{1S}$ are 8 172 802(30) and 8 172 654(40) kHz, corresponding to proton charge radius values of 0.862(12) and 0.805(11) fm, respectively.