Nuclear recoil correction to the hyperfine splitting in atomic systems

We consider leading $O(m/M)$ nuclear recoil corrections to the hyperfine splitting in light atomic systems. Due to the singularity of hyperfine interactions, the electromagnetic form factors of the nucleus have to be introduced as a function of the four-momentum square, which goes beyond the Hamiltonian description of the system. We present a compact formula for $O\left(Z\alpha \right)$ recoil corrections and indicate the importance, especially for light atoms, of a more realistic description of the nuclear structure effects.