in the interpretation of the measurement [@wieman] of the parity violating amplitude in cesium, which restored an apparent deviation from the standard model of particle physics (see, e.g., [@Sush_ueh; @JBS_ueh; @KF2002; @MST2002; @SPVC2003; @SPTY2005; @rad_pot; @review]). There are other areas where full account of QED and many-body effects are required, including in the transition frequencies of many-electron highly-charged ions (see, e.g., [@blundell; @CCJS]) and in the spectra and chemical properties of superheavy elements [@Schwerdt_review]. Ongoing improvements in experimental precision and developments in many-body methods across a range of precision atomic applications necessitate the accurate treatment of combined many-body and QED effects in the generic atomic problem.

The one-loop radiative corrections are made up of the (local) vacuum polarization and the (non-local) self-energy terms. The vacuum polarization is dominated by the (lowest order in $Z\alpha$) Uehling potential, and incorporation of this potential into the many-body problem is relatively straightforward.

The rigorous, highly-accurate [*ab initio*]{} procedures for calculating QED self-energy corrections to properties of hydrogen-like and few-electron atoms and ions cannot be applied with the same success to more complex many-body systems (see, for example, the review [@mohr_review]). There are exact QED calculations performed in frozen atomic potentials (see, e.g., [@labzowsky; @sapcheng]), 