Quantum field theory of atoms interacting with photons .3. Scattering of weak cw light from cold samples of bosonic atoms

We study the coherent scattering of weak light from a system of cooled bosonic atoms in a trap. We derive and discuss in detail the scattering equation for such a process that describes multiple scatterings from different atoms. Our theory accounts for atom-atom interactions and determines the density profile of the atomic fields from the self-consistent Bogoliubov-Hartree method. We present two kinds of analytic solutions to the scattering equation using the on-shell approximation and the generalized diffraction theory. We discuss the validity of those approaches, and demonstrate that they both lead to similar results. Our studies indicate that the scattering cross sections exhibit non-lorentzian shapes with narrow features close to resonance. Coherent scattering occurs mainly in the forward direction, and the angular distribution is limited by the size of the atomic sample in the trap. We present results for various ranges of relevant parameters such as trap size, interaction strength, number of atoms, and temperature, etc.