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

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 $\left(\frac{\alpha }{\pi }\right){\left(Z\alpha \right)}^2\times (18.36\mathrm{}\pm 5)E_{\mathrm{F}}$ is found to be $\left(\frac{\alpha }{\pi }\right){\left(Z\alpha \right)}^2$ $(15.10\mathrm{}\pm 0.29)E_{\mathrm{F}}$. Theory and experiment are compared for muonium hyperfine splitting and consequences for the fine-structure constant are discussed.