QED theory of the nuclear recoil effect on the atomicgfactor

The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in $\alpha Z$ and to first order in $m/M$ is formulated. The complete $\alpha Z$-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order $(\alpha {Z)}^{2}m/M$ for an arbitrary state of a hydrogenlike atom.