  In this paper we analyze the dynamics of single-excitation states, which
model the scattering of a single photon from multiple two level atoms. For
short times and weak atom-field couplings we show that the atomic amplitudes
are given by a sum of decaying exponentials, where the decay rates and Lamb
shifts are given by the poles of a certain analytic function. This result is a
refinement of the "pole approximation" appearing in the standard
Wigner-Weisskopf analysis of spontaneous emission. On the other hand, at large
times, the atomic field decays like $O(1/t^3)$ with a known constant expressed
in terms of the coupling parameter and the resonant frequency of the atoms.
Moreover, we show that for stronger coupling, the solutions also feature a
collection of oscillatory exponentials which dominate the behavior at long
times. Finally, we extend the analysis to the continuum limit in which atoms
are distributed according to a given density.
