content_image/338901.jpg content_image/338902.jpg content_image/338903.jpg content_image/338904.jpg
The zero-order contribution Δ E (0) $_{scrSE}$, depicted on Fig. 2(a), is the difference between the SE corrections calculated with and without the screening potential 

<img src='content_image/338901.jpg'>

Here, the subscript “C” labels the energies and wave functions calculated with the Coulomb potential of the nucleus only, while Σ( ε ) denotes the unrenormalized self-energy operator. The contribution of the diagrams depicted in Fig. 2(b) is conveniently divided into irreducible and reducible parts [63]. The irreducible part is represented by the expression 

where the sum over b runs over all core electron states, P is the permutation operator, giving rise to the sign ( − 1) P of the permutation, Δ = ε$_{P a}$ − ε$_{a}$ , and I ( ω ) is the interelectronic- interaction operator defined in the Coulomb gauge by Eqs. (8) and (9). The expression for the reducible part is given by 

<img src='content_image/338902.jpg'>

<img src='content_image/338903.jpg'>

The vertex part, corresponding to Fig. 2(c), is given by 

<img src='content_image/338904.jpg'>

where u = 1 − i 0 preserves the proper treatment of poles of the electron propagators. Expres- sions (18)-(21) suffer from ultraviolet divergences. To cancel these divergences explicitly we have employed the renormalization scheme presented in details in Refs. [4, 64]. The infrared divergences which occur in some terms of the expressions (20) and (21) are regularized by introducing a nonzero photon mass and canceled analytically. 

