The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order density functional approximation is applied to determination of the energy and spectral parameters of the Auger decay for the Na, Si, Ge, Ag solids. The results are compared with reported experimental results as well as with those obtained by alternative theoretical schemes. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the zeroth approximation of relativistic many-body perturbation theory, which significantly affects the agreement of theory and experiment.