Relativistic and QED effects to the g factor of Li-like ions

New perspectives for testing QED effects via g factor of highly charged ions motivated numerous investigations on this subject during the last years. High-precision measurements of the g factor of light H-like ions [1, 2] provided a new determination of the electron mass to an accuracy which is four times better than that of the previously accepted value (see Ref. [3] and references therein). The analysis of corresponding experimental data stimulated a variety of accurate theoretical calculations (see, e.g., Refs. [4, 5, 6, 7, 8, 9] and references therein). Investigation of ions with more than one electron is anticipated in the nearest future. In particular, measurements of the g factor of Li-like calcium are currently in progress by the Mainz-GSI collaboration. An extension of these studies to higher Z systems will provide access to an independent determination of the fine structure constant [10]. The accuracy of theoretical values for the g factor of high-Z H-like ions is presently limited by nuclear effects. The uncertainty induced by them in the high-Z region is comparable with the binding QED correction of second order in α. At present nuclear structure effects do not allow for a theoretical description at the required level of accuracy. This represents a serious obstacle towards any further improvement of theoretical predictions and for identification of two-loop QED effects in future experiments. However, in Ref. [11] it was shown that the uncertainty due to nuclear effects can be significantly reduced in a specific combination of the g factors of Hand Li-like ions with the same nucleus. Below we briefly summarize the most accurate results for different contributions and for total values of the g factor of Li-like ions within the range Z = 6 – 92 obtained in Refs. [12, 13]. The total value of the ground-state g factor of a Li-like ion is conveniently written as