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An electronic Hamiltonian appropriate for describing core-hole processes is derived and its properties are discussed. Based on this Hamiltonian a many-body theory is presented, and a useful linked-cluster theorem is proven. A distinction between relaxation and correlation terms can be made in each order of the perturbation expansion. Under certain well-defined conditions the core-ionization process can be visualized as a Franck-Condon transition between two multidimensional potential-energy surfaces in an abstract bosonic space. The corresponding approximation, the boson approximation, is discussed and applied to the water molecule.
Cederbaum et al. (Tue,) studied this question.