alpha(Z alpha)(2)E(F) correction to hyperfine splitting in hydrogenic atoms

The electron self-energy correction of the order alpha(Z alpha)(2)E(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 alpha(2), and the effective hyperfine interaction is given by delta(3)(r). In the middle-energy part electron and photon momenta are of the order m 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 Delta E=(alpha/pi)(Z alpha)(2)E(F)x17.122. It is larger than the previous value of Sapirstein similar to 15.10(29) and significantly alters theoretical predictions.