Radiative transition probabilities in atoms are normally calculated from
nonrelativistic wave functions and the electric dipole transition operator.
The theory of relativistic corrections to nonrelativistic energies is
well established in terms of the Breit interaction, but the same is not
true for relativistic corrections to transition probabilities.
Our objectives are first, to start from operators derived
from quantum electrodynamics for the lowest-order relativistic
corrections and verify that they yield the same results as from solutions
to the Dirac equation for the case of hydrogen. And second, apply the same
operators (including two-electron corrections) to the case of electric
dipole transitions in heliumlike ions. In both cases, relativistic
corrections become increasingly important with increasing nuclear charge.