Relativistic gauge-invariant theory of determination of autoionization resonances parameters for atomicsystems with accouting for the plasma environment effects

We present the theoretical foundations of an advanced relativistic gauge-invariant theory for computing main energy, spectral characteristics of complex auto ionization resonances for atomic systems with simultaneous, quantitatively consistent consideration of the complex relativistic, interelectron exchange-correlation and plasma environment effects (in particular, the Debye plasma). The approach is based on the combination of a relativistic energy approach (S-matrix Gell-Mann and Low formalism), the relativistic gauge-invariant many-body perturbation theory with optimized Dirac-Fock-Sturm and Debye-Hückel approximations with accounting for the plasma environment effects with possible generalization on the presence of an additionalexternal electromagnetic field. The fundamental advantage of pt presented theory is the selection of the optimized Dirac-Fock-Sturm zeroth approximation and application of the consistent procedure for constructing a one-quasi particle representation (basis’s of relativistic wave functions) incompliance with the principle of gauge invariance, in particular, by minimizing a gauge-noninvariant contributions to the radioactive widths of the atomic (ionic) levels due to the complex exchange-correlation effects.