Nuclear shape effect on the g factor of hydrogenlike ions

The nuclear shape correction to the g factor of a bound electron in the 1S state is calculated for a number of nuclei in the range of charge numbers from Z=6 up to Z=92. The leading relativistic deformation correction has been derived analytically, and also its influence on one-loop quantum electrodynamic terms has been evaluated. We show the leading corrections to become significant for mid-Z ions and for very heavy elements to even reach the 10(-6) level.