Correlations in many electron systems: theory and applications

In this contribution, we present calculations performed for interacting electron systems within a nonperturbative formulation of the cluster theory. Extrapolation of the model to describe the time dependence of the interacting systems is feasible and planned. The theory is based on the unitary operator eiS (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 and via the cluster factorization theory. 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 for a precise determination of the satellite transitions that play an important role in plasma diagnostics. In the second application we investigate a nonperturbative method to evaluate the charge radii of the helium and lithium isotopes by using the isotopic shift theory. We 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 quantum electrodynamics leading diagrams is postulated.PACS Nos.: 31.10.+z, 31.30.Gs, 32.30.–r