Abstract This work focuses on developing an efficient numerical method to solve the relativistic hydrogen-like atom in a finite magnetic field. To this end, we derive and implement an algorithm based on Gaussian-type orbitals that exploits fermionic symmetry to accelerate the calculations and to distinguish states of different character. This is then used to investigate a novel type of mixing regime between internal and external magnetic interactions. Finally, we assess the implications for the core region of heavy elements, where spin-orbit coupling is much stronger than the effects of external magnetic fields, and the consequences for quantum chemical calculations on heavy atoms in the vicinity of white dwarfs.
Menges et al. (Mon,) studied this question.