  Measurements of energy separations in highly charged ions can in many cases
nowadays be performed with very high accuracy, an accuracy that sometimes
cannot be matched by the corresponding theoretical calcula- tions. Furthermore,
it has recently been demonstrated that there is a systematic deviation between
experimental and theoretical results for the K- alpha lines of medium-heavy
heliumlike ions. We have during a number of years been developing a general
procedure for energy-dependent perturbative calcu- lations, which opens up a
unique possibility of incorporating the energy- dependent QED perturbations
into the all-order many-body perturbation expansion in a rigorous way. Such an
expansion will yield several important effects, never before accounted for in
this type of analysis, which is expected to increase the theoretical accuracy
considerably. Calculation of some of these effects have been performed at our
laboratory in Gothenburg, and numerical results are given. Further work along
this line is now in progress. To what extent the improved procedure might
explain the discrepancy found by Chantler et al. remains to be seen.
