QED corrections to one-electron energy levels

The energy difference between the 2 i/2 and 2pi/2 levels in hydrogen and in hydrogenlike ions (the Lamb shift) includes contributions from radiative corrections, reduced mass, nuclear recoil, and finite nuclear size. These corrections are discussed here and in the following two subsections. 

The largest contribution to the Lamb shift in one-electron atoms or ions arises from the electron self-energy and can be expressed in terms of a slowly varying functions F nlj, aZ) and G nlj, aZ) through 

The function H aZ) in Eq. (51) gives the remainder of FsEinlj, aZ) not represented by the analytical expressions above. It can be inferred from the precise numerical values given by Jentschura et al. [8] for Z from 1 to 5 and from Mohr [9, 10, 11, 12] and Mohr and Kim [13] for higher Z. Finite nuclear size corrections to FsE nlj, aZ) have been accurately evaluated by Mohr and Soff [14]. A similar expansion for the much smaller two-loop corrections GsE(nfj, aZ) is given in Refs. [15, 16]. The leeiding term in that expemsion is 

The next largest correction to the Lamb shift is the vacuum polarization correction illustrated by the Feynman diagram given in the right panel of Fig. 1. We write the vacuum-polarization correction as 

The dominant contribution to Fyp can be obtained as the expectation value of the Uehling potential [17] 

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