Atomic interaction effects in the superradiant light scattering from a Bose-Einstein condensate

We investigate the effects of the atomic interaction in the Superradiant Rayleigh scattering from a Bose-Einstein condensate driven by a far-detuned laser beam. We show that for a homogeneous atomic sample the atomic interaction has only a dispersive effect, whereas in the inhomogeneous case it may increase the decay of the matter-wave grating.