Feshbach and pseudopotential theories. A useful analogy

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Abstract
An analogy is drawn between the well-known Feshbach theory on one hand, and on the other the reputedly cruder pseudopotential technique for two-electron atomic and molecular systems. We show how both formalisms can be treated on an equal footing by using a generalized Phillips–Kleinman formalism for the second. Among other benefits stemming from this analogy, the simplicity and versatility of pseudopotential methods can be used to considerably simplify the calculation of positions (couplings) and widths involving two-electron autoionizing atomic (molecular) states.