Corrections toO(α7mc2) fine-structure splittings in helium

The times-order external-potential Bethe-Salpeter formalism is reformulated in a Schrödinger-like equation and in a form suitable for calculation of contributions arising from the relativistic momentum region. O(${\mathrm{\alpha }}^7$ ${\mathit{mc}}^2$) corrections to the fine structure of helium arising from the relativistic momentum region due to exchange diagrams are derived and presented. They are expressed in the form of expectation values of nonrelativistic operators. These off-leading-order contributions arising from the relativistic momentum region are not sensitive to any experiment in hydrogen, positronium, or muonium but they are larger than experimental errors in the measurements of fine structure in helium. Therefore, they provide a test of corrections of this kind, which has not been carried out in any other bound-state system. © 1996 The American Physical Society.