Accurate screened QED calculations in high-Zmany-electron ions

We describe a practical, rigorous, QED procedure for performing accurate calculations of the screened self-energy for high-Z ions based on a realistic local atomic potential. Using a basis-set algorithm, we show that the procedure involves a rapidly convergent partial-wave expansion that, in contrast to previous methods, requires explicit computation of only the first few partial waves. We apply the method to the 2s-2${\mathit{p}}_{1/2}$ transition of Li-like U, the 3s-3${\mathit{p}}_{3/2}$ transition of Na-like Pt, and the 4s-4${\mathit{p}}_{1/2}$ transition in Cu-like Bi. When combined with calculations of the screened Uehling vacuum-polarization term and earlier correlation calculations, the results agree with experiment to within several tenths of an eV.