**Authors: **A.A. Svinarenko, A.V. Glushkov, A.V. Ignatenko, V.V. Buyadzhi, A.V. Smirnov

**Year: **2015

**Issue: **19

**Pages: **224-229

**Abstract**

In the paper we give a review of a new generalized energy approach (Gell-Mann and Low S-matrix formalism) combined with the relativistic multi-quasiparticle (QP) perturbation theory (PT) with the Dirac-Kohn-Sham zeroth approximation and accounting for the exchange-correlation, relativistic corrections to studying autoionization resonances in the complex atomic spectra. As application, we list the energies and widths of the number of the Rydberg resonances in helium. There are presented the results of comparison of our theory data for some helium autoionization resonances with the available experimental data and those results of other theories, including, method of complex rotation by Ho, algebraic approach by Wakid-Callaway, diagonalization method by Senashenko-Wague etc. Besides, we present new data on the energies of the configurations 1s5s, 1s5p, 1s5d, 1s5f, 1s5g terms in the spectrum of the ion Kr XXXV, as well as the corresponding values of the lifetimes of these states, calculated on the basis of the relativistic energy approach.

**Tags: **new spectral data; spectroscopy of autoionization resonances

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