Muonium and positronium potentials with radiative corrections are derived from the scattering operator, and general results for the spectra of these systems to order α³R_∞ are obtained. We also compare our results with those obtained earlier with the Bethe-Salpeter approach, and find a discrepancy in the case of the $1S$ state. Our theoretical results are in good agreement with the available experimental data.
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Gupta et al. (1989) studied this question.
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