The shift of the constant energy level after the interaction of particles with the polarizing phonons

The shift of the electron energy level due to its interaction with the polarizing phonons is investigated here for the particles whose energy does not depend on the wave vector. We also analyze the influence of the value of the constant of electron - phonon interaction and other parameters of the problem on the electron energy change. The methods of Green's functions, presented by the the Feynman diagrams and  using the double permutations, are present here. The paper contains the analysis of the columns of the corresponding double permutations, the analytical expressions of which form the mass operator presented by the chain fractions.  We received the expressions for admissibles and inadmissibles columns for phonon components of double permutations. The numerical calculations allow to conclude about the energy shift and how it depends on the parameters.

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