| Summary: | In atomic and many-particle physics, Green functions often occur as <i>propagators</i> to formally represent the (integration over the) complete spectrum of the underlying Hamiltonian. However, while these functions are very crucial to describing many second- and higher-order perturbation processes, they have hardly been considered and classified for complex atoms. Here, we show how relativistic (many-electron) Green functions can be approximated and systematically improved for few- and many-electron atoms and ions. The representation of these functions is based on <i>classes</i> of virtual excitations, or so-called <i>excitation schemes</i>, with regard to given bound-state reference configurations, and by applying a multi-configuration Dirac-Hartree-Fock expansion of all atomic states involved. A first implementation of these approximate Green functions has been realized in the framework of <span style="font-variant: small-caps;">Jac</span>, the Jena Atomic Calculator, and will facilitate the study of various multi-photon and/or multiple electron (emission) processes.
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