High-precision calculation of the Zeeman splitting of lithiumlike ions: g factor and nonlinear contributions

The bound-electron g factor of highly charged ions provides a sensitive probe of relativistic, correlation, and quantum electrodynamic (QED) effects [1, 2]. Recent progress in both experiment and theory has highlighted the need for accurate predictions for few-electron systems, including lithiumlike ions, where interelectronic interaction plays a dominant role. In this work, we present a unified theoretical investigation of the g factor for the ground state and the lowest excited 2p_1/2 and 2p_3/2 states of lithiumlike ions over a broad range of nuclear charge numbers.

Interelectronic interaction is treated within bound-state QED. The first-order correction is calculated rigorously to all orders in αZ, while the two-photon-exchange term is evaluated using the Breit approximation supplemented with negative-energy contributions. Higher-order terms are obtained via the recursive formulation of perturbation theory. One-loop QED corrections, self-energy and vacuum polarization, are computed employing finite-basis B-spline techniques, and leading nuclear-recoil effects are included using effective operators. All calculations are performed within the extended Furry picture using several screening potentials to estimate the uncalculated higher-order many-electron contributions.

For the ground and excited states, we obtain significantly improved values of the interelectronic-interaction contribution, with uncertainties reduced by up to an order of magnitude compared with earlier theoretical predictions [3, 4]. For the excited 2p_j states, we additionally calculate the quadratic and cubic Zeeman contributions, which become essential for the interpretation of high-precision spectroscopy [5].

Our calculations provide the most accurate theoretical predictions for the g factor of lithiumlike ions to date. The achieved precision meets the requirements of ongoing and planned high-precision measurements and strengthens the capabilities of bound-state QED tests in strong fields.

1. D. A. Glazov et al., Atoms 11, 119 (2023)
2. S. Sturm et al., Annalen Der Physik 525, 620 (2013)
3. D. V. Zinenko et al., Phys. Rev. A 107, 032815 (2023)
4. D. V. Zinenko et al., arXiv:2505.09567 (2025)
5. D. von Lindenfels et al., Phys. Rev. A 87, 023412 (2013)