**Authors: **O.Yu. Khetselius, I.N. Serga, D.E. Sukharev, A.N. Shahman

**Year: **2015

**Issue: **19

**Pages: **195-200

**Abstract**

It is presented an effective relativistic approach to the description of the energy and spectral characteristics of the pion atoms, based on the Klein-Gordon-Fock equation, model of optimized optical strong pion-nucleon interaction potential and method of the relativistic many-particle perturbation theory with the “0” Hamiltonian of the Dirac- Breit -Kohn-Sham approximation ( approximation to the formal precision QED perturbation theory) and correct accounting for the relativistic, radiation QED effects, the finite size nuclear effects plus the nuclear quadrupole deformation correction and electron shielding effect (electromagnetic unit). The bare interaction potential in the system is represented as the sum of the optical strong π

^{–}– N interaction potential, relativistic Coulomb potential describing the interaction of the pion with the nucleus as amended by the Breit-Rosenthal-Crawford-Schawlow correction on the final size of a nucleus, generalized radiation potential, taking into account the main QED effect of vacuum polarization, etc., and the self-consistent potential of the surviving electron shells. For a number of heavy π^{–}– А, including,^{181 }Ta,^{197}Au,^{203}Tl,^{208}Pb,^{209}Bi, etc there are presented the values of the shifts and widths for the 4f, 3d levels due to the strong π^{–}– N interaction, including the corrections, ‘directly related to the effect of the nuclear quadrupole deformation. For a number of π^{–}– А the data on the shifts and widths of the energy levels in a spectrum are presented for the first time.

**Tags: **Klein-Gordon-Fock equation; shift and width of energy levels due to the strong π- - N interaction; the optical potential of π- - N interaction

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