Additional radiative-recoil corrections to muonium and positronium hyperfine splitting

A compact expression for one-loop radiative corrections to lepton lines in positronium and muonium hyperfine splitting is presented. It is valid for hyperfine-splitting contributions of order α2E/sub F/, including the effects of recoil to all orders. For muonium, known nonrecoil parts of this contribution are easily evaluated analytically, as is a previously calculated radiative-recoil contribution of order α2E/sub F/(m/sub e//m/sub μ/)ln(m/sub μ//m/sub e/). Nonlogarithmic radiative-recoil corrections obtained by numerical evaluation of this expression yield new contributions of 2.64 +- 0.07 kHz for muonium and -11.12 +- 0.02 MHz for positronium