Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems

A general quantum electrodynamic method for derivation of nuclear recoil corrections in hydrogenic systems, which are exact in the nuclear charge parameter $Z\alpha$, is introduced. The exemplary derivation is presented for the $O(m\mathrm{/}M)$ nuclear pure recoil correction to the hyperfine splitting. The obtained result is verified by comparison to the known $(Z\alpha {)}^5$ contribution