  We generalize the formalism proposed by Dalibard, Dupont-Roc and
Cohen-Tannoudji [the DDC formalism] to the fourth order of the coupling
constant, which can be used to study the interatomic interaction of two
ground-state atoms coupled with the vacuum scalar fields. We show that the
interatomic potential can be attributed to the joint effect of both vacuum
fluctuations and the radiation reaction of atoms. Remarkably, the formulae we
derived for the contributions of vacuum fluctuations and the radiation reaction
to the interatomic potential upon which future research on fourth-order effects
in particular circumstances can be based differ from those in the existing
literature [Phys. Rev. D 95, 085014 (2017)].
