  We investigate the effects of a movable mirror (cantilever) of an optical
cavity on the superradiant light scattering from a Bose-Einstein condensate
(BEC) in an optical lattice. We show that the mirror motion has a dynamic
dispersive effect on the cavity-pump detuning. Varying the intensity of the
pump beam, one can switch between the pure superradiant regime and the Bragg
scattering regime. The mechanical frequency of the mirror strongly influences
the time interval between two Bragg peaks. We found that when the system is in
the resolved side band regime for mirror cooling, the superradiant scattering
is enhanced due to coherent energy transfer from the mechanical mirror mode to
the cavity field mode.
