We have measured the ground-state g-factor of boronlike argon 40 Ar 13+ with a fractional uncertainty of 1.4 × 10 −9 with a single ion in the newly developed Alphatrap double Penning-trap setup. The here obtained value of g = 0.663 648 455 32(93) is in agreement with our theoretical prediction of 0.663 648 12(58). The latter is obtained accounting for quantum electrodynamics, electron correlation, and nuclear effects within the state-of-the-art theoretical methods. Our experimental result distinguishes between existing predictions that are in disagreement, and lays the foundations for an independent determination of the fine-structure constant.

Relativistic calculations of the second-and third-order contributions in magnetic field to the Zeeman splitting in boronlike ions are presented for the wide range of nuclear charge numbers Z = 6-92. The interelectronic-interaction correction of the first order in 1/Z is evaluated to all orders in αZ. The higherorder corrections in 1/Z are taken into account approximately by means of effective screening potentials.The obtained results are important for interpretation of experimental data on the Zeeman splitting in boronlike ions, in particular, for the ARTEMIS experiment presently implemented at GSI. 32.60.+i Investigations of the g factor of highly charged ions can serve for stringent tests of the boundstate QED, the determination of fundamental constants and of nuclear parameters, see, e.g., Refs.[1-4]. Meanwhile, the precision of the g-factor measurements in Penning traps has reached the level of 10 −9 -10 −11 [1,[5][6][7][8][9][10]. Achievement of the comparable theoretical accuracy requires consideration of the QED diagrams up to the second order in α, higher-order correlation contributions, and various nuclear effects, see Ref.[4] and more recent works [11][12][13][14][15][16][17]. The long-term combined experimental and theoretical efforts have provided the most accurate up-to-date value of the electron mass [18][19][20]. Recent measurement for two lithium-like calcium isotopes [21] is sensitive to the relativistic nuclear recoil effect indicating the potential to access bound-state QED effects beyond the Furry picture [14,15]. Further investigations with few-electron ions can provide an independent determination of the fine structure constant [22][23][24].The nonlinear effects in magnetic field play an important role in boronlike ions [25,26]. Due to the mirror symmetry, the second-order effect does not influence the ground-state Zeeman splitting in hydrogenlike, lithiumlike, and boronlike ions. However, it becomes observable in the Zeeman splitting of the 2 P 3/2 state of boronlike ions, which can be measured by the laser-microwave double-resonance spectroscopy [25,27]. Moreover, the quadratic effect gives a tiny correction to the fine-structure transition energies, which are measured with an increasing precision [28][29][30][31].The third-order effect contributes to the Zeeman splitting of any state, although in hydrogenlike and lithiumlike ions it is negligible at the present level of accuracy. In boronlike ions the nonlinear contributions are strongly enhanced due to the mixing of the fine-structure components.The first high-precision g-factor measurement in boronlike ion was performed for Ar 13+ at the MPIK with the laser spectroscopy [32]. The ARTEMIS experiment at GSI implements the laser-microwave double-resonance technique to reach the ppb precision for the g factors of the ground 2 P 1/2 and the first excited 2 P 3/2 states in boronlike argon [25,33]. The new Penning-trap experiment at the MPIK in Heidelberg, called ALPHATRAP [34], primarily aims at the g factor of heavy few-electron ions, inc...