Diagrams with Two External Coulomb Lines

Formally the contribution of diagram Fig. 7.4 is given by the standard quantum mechanical second order perturbation theory term. Summation over the intermediate states, which accounts for binding, is realized with the help 

As in the case of corrections of order a (Za) m, not only the diagrams in Fig. 7.3 with insertions of polarization operators in one and the same external Coulomb line but also the reducible diagrams Fig. 7.5 with polarization insertions in different external Coulomb lines generate corrections of order Respective contributions were calculated in [18] with the help of the subtracted Coulomb Green function from [20] 

2 Relativistic Corrections to the Leading Polarization Contribution with Exact Mass Dependence 

The leading electron polarization contribution in (7.7) was calculated in the nonrelativistic approximation between the Schrodinger-Coulomb wave functions. Relativistic corrections of relative order (Za) to this contribution may easily be obtained in the nonrecoil limit. To this end one has to calculate the expectation value of the radiatively corrected potential in (7.1) between the relativistic Coulomb-Dirac wave functions instead of averaging it with the nonrelativistic Coulomb-Schrodinger wave functions. 

This situation is radically different from the case of electronic hydrogen where inclusion of the electron loop in the photon propagator generates effectively a (5-function correction to the Coulomb potential (compare discussion in Sect. 2.2). 

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