α(Zα)2EFcorrection to hyperfine splitting in hydrogenic atoms

The electron self-energy correction of the order α(Zα${)}^2$ ${\mathit{E}}_{\mathit{F}}$ to the ground-state hyperfine splitting in hydrogenic atoms is calculated using a semianalytical method. The correction is divided into three parts by introducing two auxiliary parameters. The low-energy part corresponds to the nonrelativistic limit, where photon energy is of the order m${\mathrm{\alpha }}^2$, and the effective hyperfine interaction is given by ${\mathrm{\delta }}^3$(r). In the middle-energy part electron and photon momenta are of the order mα and m, respectively. This part is calculated using on-shell electron form factors. The high-energy part corresponds to the S-matrix amplitude for the forward scattering. The final value does not depend on auxiliary parameters and amounts to ΔE=(α/π)(Zα${)}^2$ ${\mathit{E}}_{\mathit{F}}$×17.122. It is larger than the previous value of Sapirstein ∼15.10(29) and significantly alters theoretical predictions. © 1996 The American Physical Society.