  We calculate the one-photon exchange contribution to the interatomic
interaction potential between electrically neutral, identical atoms, one of
which is assumed to be in an excited state, by matching the scattering matrix
(S matrix) element with the effective Hamiltonian. This approach allows us to
use covariant perturbation theory, where the two possible time orderings of
emission and absorption are summarized in a single Feynman amplitude. Our
results encompass the full retardation correction to the one-photon exchange
van-der-Waals potential. We employ the temporal gauge for the virtual photon
propagator. Based on the Feynman prescription, we obtain the imaginary part of
the interaction energy, which leads to an interaction-induced correction to the
decay rate. Our results lead to precise formulas for the distance-dependent
enhancement and suppression of the decay rates of entangled superradiant and
subradiant Dicke state, as a function of the interatomic distance. We apply the
result to an example calculation involving two hydrogen atoms, one of which is
in the ground state, the other in an excited P state.
