  The theory of the g factor of an electron bound to a deformed nucleus is
considered non-perturbatively and results are presented for a wide range of
nuclei with charge numbers from Z=16 up to Z=98. We calculate the nuclear
deformation correction to the bound electron g factor within a numerical
approach and reveal a sizable difference compared to previous state-of-the-art
analytical calculations. We also note particularly low values in the region of
filled proton or neutron shells, and thus a reflection of the nuclear shell
structure both in the charge and neutron number.
