The value of vacuum-polarization amplitude is investigated in the region of positronium bound-state poles, where the naive Feynman-graph expansion fails. The corresponding contribution to positronium-ground-state splitting is explicitly evaluated up to order α⁶. The previously given result for the α⁶ lnα^-1 term coming from fourth-order vacuum-polarization corrections to the one-photon annihilation diagram is confirmed and put on a sounder basis. The α⁶ term is found to receive, besides the obvious contribution from α² vacuum-polarization term, an additional α⁶-contribution which can be considered as generated by an infinite series of terms of higher nominal order in α.
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Barbieri et al. (1973) studied this question.
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