Iteration-variational method and its application to quantum-electrodynamic calculations in one- and two-electron atoms

Abstract

A new variational method is presented which permits a direct and rapidly convergent calculation of almost divergent sums over complete sets of intermediate states, using a finite-basis-set representation. The formalism for first-order perturbation calculations of infinite sums for two-electron systems is presented and the technique is used to calculate the first-order perturbation correction to the Bethe logarithm in two-electron systems. Estimates of higher-order coefficients in the $\frac{1}{Z}$ expansion are given.