  We analyse the effects of atom-atom collisions on collective laser cooling
scheme. We derive a quantum Master equation which describes the laser cooling
in presence of atom-atom collisions in the weak-condensation regime. Using such
equation, we perform Monte Carlo simulations of the population dynamics in one
and three dimensions. We observe that the ground-state laser-induced
condensation is maintained in the presence of collisions. Laser cooling causes
a transition from a Bose-Einstein distribution describing collisionally induced
equilibrium,to a distribution with an effective zero temperature. We analyse
also the effects of atom-atom collisions on the cooling into an excited state
of the trap.
