Second order in mass ratio radiative-recoil corrections to hyperfine splitting in muonium

Radiative-recoil corrections to hyperfine splitting in muonium of order /spl alpha/(Z/spl alpha/)(m/M)/sup 2/E/sub F/ and of order (Z/sup 2//spl alpha/)(Z/spl alpha/)(m/M)/sup 2/E/sub F/ are calculated. An analytic expression [(-61n2-4/3)/spl alpha/(Z/spl alpha/)-12/17(Z/sup 2//spl alpha/)(Z/spl alpha/)](M/m)/sup 2/E/sub F/ is obtained. Numerically the correction is equal to -0.0351 kHz and is of the same order of magnitude as the planned accuracy of the experiment on measuring the hyperfine splitting which is now running at Los Alamos.