Third-order Zeeman effect in highly charged ions

The contribution of the third order in magnetic field to the Zeeman splitting of the ground state of hydrogenlike, lithiumlike, and boronlike ions in the range Z=6-82 is investigated within the relativistic approach. Both perturbative and non-perturbative methods of calculation are employed and found to be in agreement. For lithiumlike and boronlike ions the interelectronic-interaction effects are taken into account within the approximation of the local screening potential. The contribution of the third-order effect in low- and medium-Z boronlike ions is found to be important for anticipated high-precision measurements.