To solve the strong CP problem in QCD, a global U(1) Peccei–Quinn symmetry is postulated [1, 2]. Its spontaneous breaking gives rise to a pseudo-Nambu–Goldstone boson, the axion, which eliminates CP violation in strong interactions [3, 4]. Extensions of the Standard Model predict the emergence of new particles [5]. For example, additional U(1) gauge symmetries can lead to the appearance of a dark photon—a massive vector particle that acts as a mediator of interactions within the dark sector. As the dark matter problem remains one of the key issues in modern physics, the study of axions and dark photons opens new possibilities for reconciling cosmological data with experimental results [6].

Despite the success of the Standard Model, its incompleteness drives the development of precision methods, with measurements of the bound-electron g factor and energy spectra in highly charged ions (HCIs) playing a central role. Significant progress has been achieved in HCI research in these areas [7, 8]. The strong Coulomb field of the HCI nucleus enhances relativistic and quantum electrodynamic effects, while their simple electronic structure enables high-precision calculations. High-precision measurements of the HCI g factor [9-12], when compared with theoretical predictions, provide opportunities to detect deviations arising from new physics [13-15].

In this work, we investigate the interaction of bound electrons, mediated by new physics models (such as axions, dark photons, and others), and its impact on the energy levels and g factors of few-electron ions. The study is devoted to assessing the contribution of these effects that emerge from the exchange of virtual axions or dark photons between electrons. This approach opens up the possibility of establishing stringent constraints on the parameters of the considered models. We also examine systems and configurations in which corrections associated with new physics are enhanced.