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Eigenchannel R-matrix calculations for photodetachment of H– up to the H(n = 6) threshold provide complete theoretical confirmation of observed high-lying, doubly excited state spectra. Long-range multipole interactions beyond the reaction volume are found to play an important role. Similar calculations for Li– photodetachment up to the Li(n = 6) threshold predict analogous resonance structures. These results indicate that recent advances in understanding two-electron correlations in H– and He have application to many electron systems.