Radiative corrections in hydrogen higher orders

The coefficient C41 and C40 are defined by the expressions given in the preceding Sec.3.1 and the other coefficients are  

The general expression for Ceo is not known, though the values Ceo n) are known up to n = 4 [14]. The recent accuracy of the experiment requires also that we take into account the corrections of the order ma aZ), ma aZ) and partly ma aZ). All these corrections can be evaluated in the first order in the nuclear potential V, i.e. with the free - electron formfactors. 

The nonperturbative interaction of the free electron with the electromagnetic field (i.e. the most general vertex contribution) can be expressed in the form  

Fi(g ), F2 ) are called Dirac and Pauli formfactors correspondingly. For the corrections of the order ma (aZ) the result is (see [9] and the references therein)  

Expressions (198), (199) correspond to the two-loop corrections to the graph Fig.lOa. The two-loop corrections to the graph Fig.lOb give  

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