Theory of the Lamb Shift in Hydrogen and Light Hydrogen-Like Ions

Theoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high-precision determination of the proton charge radius drastically reduces the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two-and three-loop QED effects, which calls for further advances in their calculations. The present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen-like ions with the nuclear charge number up to Z = 5 is reviewed. Theoretical errors due to various effects are critically examined and estimated.