In this contribution we present calculations performed for interacting electron systems within a non-perturbative formulation of the cluster theory. Extrapolation of the model to describe the time dependence of the interacting systems is feasible and planed. The theory is based on the unitary operator $e^{iS}$ ({\it S} is the correlation operator) formalism which, in this paper, is treated non perturbatively within many-particle correlations. The application of the derived equations to few-body systems is realized in terms of Generalized Linearization Approximations (GLA) and via the Cluster Factorization Theory (CFT). To check the reliability of the model we present two different applications. In the first we evaluate the transitions energies in Helium-, Lithium-, Beryllium-, and Boron-like Oxygen. The calculation aims to a precise determination of the satellite transitions which play an important role in plasma diagnostics. In a second we investigate a non-perturbative method to evaluate the charge radii of the Helium and Lithium isotopes by using the Isotopic Shift theory. We have found that our model leads naturally to components of $e^--e^+$ pair in the two-electron wave functions of the Helium isotopes and three-electron wave functions of the Lithium isotopes. The possible connection of these terms to the QED leading diagrams is postulated.
The effects of electron correlation and the Breit interaction on one- and two-electron one-photon transitions in double K hole states of He-like ions ($10\!\leq\!Z\!\leq\!47$)
