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We investigate the behavior of a bound electron–hole excitation in an energy region where the response of the system is highly resonant and shows strong collective behavior. Formulae for calculating discrete energy levels and wavefunctions are presented for the case where the perturbation is strong enough to change the nodal structure of the perturbed wavefunctions relative to that of the unperturbed wavefunctions. This change in nodal structure requires a renaming of the associated atomic states. Neglect of such renaming is shown to have been at the root of a recent controversy between differing interpretations, based on alternative calculational procedures, of the 4d-subshell photoionization spectra of Ba and La. It is demonstrated explicitly that these alternative calculational procedures are equivalent and that their interpretations are consistent.