  The purpose of this paper is twofold. First, we compare, in detail, the
derivation of the Casimir-Polder interaction using time-ordered perturbation
theory, to the matching of the scattering amplitude using quantum
electrodynamics. In the first case, a total of twelve time-ordered diagrams
need to be considered, while in the second case, one encounters only two
Feynman diagrams, namely, the ladder and crossed-ladder contributions. For
ground-state interactions, we match the contribution of six of the time-ordered
diagrams against the corresponding Feynman diagrams, showing the consistency of
the two approaches. Second, we also examine the leading radiative correction to
the long-range interaction, which is of relative order O(alpha^3). In doing so,
we uncover logarithmic terms, in both the interatomic distance as well as the
fine-structure constant, in higher-order corrections to the Casimir-Polder
interaction.
