Ionization of core electrons

Making use of the physical properties of core electrons the Hamiltonian of the system can be simplified. To study electronic processes involving core electrons, e.g., their ionization, one can work with a reduced effective Hamiltonian operating in valence space only. It accounts for the response of the valence electrons to the presence of a core hole. Because of the two possible spin quantum numbers of the remaining core electron, the effective Hamiltonian has 2×2 matrix form which complicates the evaluation of the ionization spectrum. An elegant transformation is introduced to diagonalize the operator matrix giving rise to a scalar effective Hamiltonian. With its help an exact linked cluster theorem for the core Green’s function, which is directly related to the spectrum, is derived. The resulting cluster function is analyzed in some detail.