α(Zα)2EFBinding Corrections to Hyperfine Splitting in Hydrogenic Atoms

Abstract

A perturbative expansion of the electron's Dirac Coulomb propagator around a nonrelativistic form is used to evaluate the one-loop nonrecoil corrections to ground-state hyperfine splitting in hydrogenic atoms. A contribution previously estimated as $(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}}){(Z\ensuremath{\alpha})}^{2}\ifmmode\times\else\texttimes\fi{}(18.36\ifmmode\pm\else\textpm\fi{}5){E}_{\mathrm{F}}$ is found to be $(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}}){(Z\ensuremath{\alpha})}^{2}$ $(15.10\ifmmode\pm\else\textpm\fi{}0.29){E}_{\mathrm{F}}$. Theory and experiment are compared for muonium hyperfine splitting and consequences for the fine-structure constant are discussed.