Vincent Debierre

We present theoretical results on hydrogen atoms and hydrogen-like ions.
Concerning atoms, we explore in detail the van der Waals interactions between a ground-state and an excited-state atom, focusing especially (but not exclusively) on excited $s$ states. The appearance of oscillating long-range ($1/R^2$) tails in the large-separation limit is highlighted. The role of quasi-degenerate, and lower-lying excited states, is described in detail.
Concerning ions, we discuss the computation of a set of two-loop QED corrections to the bound electron g-factor. These corrections involve the so-called ‘magnetic loop’ sub-diagram, which, at the lowest non-vanishing order, involves the light-by-light scattering process. Preliminary results indicate that these corrections can be observable at high-Z, provided that the presumably larger, two-self-energy-loops corrections are computed and benchmarked first. With the development of experimental facilities aiming at very high-precision measurements of $g$-factors in heavy highly charged ions, such exotic QED corrections as presented here, can become relevant for the determination of fundamental constants.