content_image/400331.jpg content_image/400333.jpg content_image/400340.jpg
<img src='content_image/400331.jpg'>

<img src='content_image/400333.jpg'>

By using the perturbation theory we have obtained for the connected part of evolution operator average the contributions depicted in the Fig. 5. 

The contributions of the first, third and fourth dia- grams of Fig. 5 are enumerated below: 

<img src='content_image/400340.jpg'>

## IV. VACUUM DIAGRAMS 

In normal state the diagrams of Fig. 5 are changed. The direction of propagator lines and of the arrays at vertices points appear together with new coefficients be- fore the diagrams. This changing is demonstrated on the Fig. 6, where some of the diagrams of Fig. 5 are demon- strated. Vacuum diagrams in superconducting and nor- mal states contain the factor 1 $_{n}$, where n is the order of perturbation theory in which given diagram appears. This factor makes difficult the investigation of this contri- butions. In order to remove this coefficient it is necessary to use the trick of integration by constant of interaction V . The result of such integration is depicted on the Fig. 7. 

On the base of series expansions for renormalized prop- agators of the conduction c − electrons (see Fig. 1), lo- calized f − electrons (see Fig. 2) and definition of the correlation function Λ$_{αα}$ ′ ( x | x $^{′}$) we can prove that the contribution of the integrant of Fig. 7 in every order of perturbation theory can be presented itself as the prod- 

