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We calculate hard spin-independent contributions to energy levels in muoniumand positronium which are due to radiatively corrected electron factorinsertion in two-photon exchange diagrams. Calculation of these corrections ismotivated by the new round of precise measurements of spin-independenttransition frequencies in muonium and positronium.

Two-Loop Electron Factor Contribution to Lamb Shift in Muonium and Positronium