  We extend the semiclassical model of the collective atomic recoil laser
(CARL) to include the quantum mechanical description of the center-of-mass
motion of the atoms in a Bose-Einstein condensate (BEC). We show that when the
average atomic momentum is less than the recoil momentum $\hbar\vec q$, the
CARL equations reduce to the Maxwell-Bloch equations for two momentum levels.
In the conservative regime (no radiation losses), the quantum model depends on
a single collective parameter, $\rho$, that can be interpreted as the average
number of photons scattered per atom in the classical limit. When $\rho\gg 1$,
the semiclassical CARL regime is recovered, with many momentum levels populated
at saturation. On the contrary, when $\rho\le 1$, the average momentum
oscillates between zero and $\hbar\vec q$, and a periodic train of $2\pi$
hyperbolic secant pulses is emitted. In the dissipative regime (large radiation
losses) and in a suitable quantum limit, a sequential superfluorescence
scattering occurs, in which after each process atoms emit a $\pi$ hyperbolic
secant pulse and populate a lower momentum state. These results describe the
regular arrangement of the momentum pattern observed in recent experiments of
superradiant Rayleigh scattering from a BEC.
