Quantum seminar | 12 April 2023

Few-electron atomic systems such as light atoms and highly charged ions allow for theoretical predictions with an accuracy on the level of possible new physics effects beyond the Standard Model. Comparison with measurements provides determination of the fundamental constants and nuclear parameters. Theoretical description of these systems involves quantum electrodynamics for bound states. However, only the leading orders (up to second) of the perturbation theory in the coupling constant alpha can be taken into account within the rigorous QED approach, i.e. to all orders in the binding nuclear potential. Higher orders are considered within the quasi-relativistic quantum mechanics, e.g. Dirac-Coulomb-Breit equation. The contributions sought can be found either within some all-order method or within the perturbation theory. We present an efficient method based on the recursive formulation of the Rayleigh-Schrödinger perturbation theory that provides access to arbitrary high orders at a reasonable cost. Its numerical implementation is based on the finite basis set for the Dirac equation constructed from B-splines with the dual-kinetic-balance conditions. Special attention is paid to the contribution of the negative-energy states. The extension to the case of multiple perturbations is also considered. The results obtained within this method include various corrections to the binding energies, g factor and hyperfine splitting in highly charged ions.