Feshbach-type projection method for multiply excited resonances

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Abstract
A procedure for the Feshbach projection is presented. Although projection operators are not explicitly used within this procedure, it is completely equivalent to an explicit use of idempotent projectors, provided that both the target-state wave functions and the trial function of the entire system are of the configuration-interaction type. The Feshbach-projection-operator method is extended to the case of triply excited resonances (i.e., to an infinite number of open channels). Projectors are given explicitly for three-electron systems and for N-electron systems with the double-ionization threshold described by the (N-2)-electron one-determinant function. For configuration-interaction wave functions a procedure similar to that for doubly excited states is proposed.