content_image/361569.jpg content_image/361570.jpg content_image/361571.jpg content_image/361572.jpg content_image/361573.jpg content_image/361574.jpg content_image/361575.jpg content_image/361576.jpg content_image/361577.jpg
is the unperturbed wave function. The time-Fourier transform of the Green function is defined as 

<img src='content_image/361569.jpg'>

The Feynman rules for the Green function are given in Ref. [49]. The energy shift Δ E$_{a}$ and the Green function g ( E ) are to be expanded as a power series in α , 

<img src='content_image/361570.jpg'>

<img src='content_image/361571.jpg'>

Then from Eq. (3) we find the first-, second- and third-order te rms of the energy shift, 

<img src='content_image/361572.jpg'>

<img src='content_image/361573.jpg'>

<img src='content_image/361574.jpg'>

Equation (9) and the Feynman rules for g ( E ) yield the formal expressions for the total contribution of the two-loop diagrams presented in Fig. 3. Consequently replacing each electron propagator according to Eq. (2) we obtain the formal expressions for the two-electron one-loop diagrams displayed in Figs. 1 and 2. 

For brevity we introduce the operator 

<img src='content_image/361575.jpg'>

where α µ = (1 , α ) are the Dirac matrices, and D$_{µν}$ is the photon propagator. It is given by 

in the Feynman gauge and by 

<img src='content_image/361576.jpg'>

<img src='content_image/361577.jpg'>

