Introduction

Significant advances in high-precision measurements of Zeeman splitting in highly charged ions have been achieved over the past quarter century. The corresponding leap in measurement precision, together with theoretical research, made it possible to determine the most accurate up-to-date electron mass determination. It is expected that in the near future high-precision g-factor measurements in hydrogen-, lithium- and boronlike ions will provide a high-precision tool for independent fine structure constant determination. New experiments on the g-factor of excited p-states enable separate measurement of the quadratic Zeeman effect. The quadratic Zeeman effect, studied for over eight decades, gains renewed importance in ultra-strong magnetic fields of magnetars and precision atomic clocks. Theoretical understanding of interelectronic interactions remains crucial for accurate interpretation of experimental data from projects like ALPHATRAP and ARTEMIS.

Methods

We present theoretical calculations of two-photon exchange corrections to the quadratic Zeeman effect in boron-like ions within the Breit approximation. This work extends previous theoretical treatments that established foundational calculations including leading-order terms, one-loop QED corrections, and one-photon-exchange contributions. The computational approach systematically addresses the dominant sources of uncertainty in quadratic Zeeman effect calculations for middle-Z boron-like systems.

Results and Discussion

Our calculations reveal that the two-photon exchange correction constitutes a significant contribution to the quadratic Zeeman effect in middle-Z boron-like ions. The results demonstrate that interelectronic interactions substantially influence the quadratic Zeeman splitting.

Conclusions

The two-photon exchange correction represents an advancement in the theoretical description of quadratic Zeeman effects in boron-like systems. Our results substantially reduce the theoretical uncertainty in quadratic Zeeman splitting calculations. These findings have direct implications for ongoing experiments with boron-like ions and contribute to improved understanding of atomic structure in magnetic fields.