Recoil corrections in highly charged ions

A recently introduced Bethe-Salpeter formalism is applied to the calculation of recoil corrections to the energy levels of all n=1, 2, and 3 states of hydrogenic ions. Finite basis set techniques are shown to allow the accurate evaluation of expressions that sum all orders of Z alpha, which are rederived in the formalism using combinatoric techniques. A comparison of the all-order results with one-loop calculations and known terms of the perturbation expansion in Z alpha is made. Good agreement of the results of the present work with previous calculations is shown, and a discussion of issues that will have to be treated for the many-electron case, where highly accurate experiments have been carried out, is given.