Perturbed Orbital Contribution to the Two-Loop Lamb Shift in Hydrogen

A part of the two-loop Lamb shift called the perturbed orbital term is evaluated with exact Dirac-Coulomb propagators. It is shown to be the most nonperturbative function of Zα yet encountered in QED, so much so that even at Z0ex0ex=0ex0ex1 the leading term in its Zα expansion is of the opposite sign from the complete answer. The higher order contributions are -71(1)0ex0exkHz to the ground state Lamb shift in hydrogen and -8.9(1) and -346(1)0ex0exkHz to the n0ex0ex=0ex0ex2 Lamb shift in hydrogen and He⁺, respectively.