Alpha (Z alpha )2EF correction to hyperfine splitting in hydrogenic atoms.

Abstract

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