al.*]{} [@derev_relax] to include the effects on valence $d$ levels. Inclusion of relaxation corrections leads to several orders of magnitude enhancement of the Uehling correction to the $d$-level binding energies.

We study also the effect of second- and higher-order many-body perturbation theory on the Uehling correction to valence binding energies through inclusion of the second-order and all-orders correlation potentials. We have found significant corrections to Uehling shifts for all orbitals.

The underlying mechanisms leading to the large many-body effects are studied and calculations are performed for the series of alkali-metal atoms Na through to the superheavy element E119. This work serves as a preliminary study of the more general QED-many-body interplay, where the full radiative corrections (including the larger self-energy) are considered. Since the Uehling potential may be determined to very high precision and is a local operator which may readily be included into atomic many-body codes, the study of the many-body effects is not hindered by any complexity arising from the QED terms themselves. While the form of the self-energy terms is more sophisticated than Uehling, and the radiative shift is generally larger and of opposite sign, the short range of the interaction means that the same many-body enhancement 