  We consider collective laser cooling of atomic gas in the Festina lente
regime, when the heating effects associated with photon reabsorptions are
suppressed. We demonstrate that an appropriate sequence of laser pulses allows
to condense a gas of trapped bosonic atoms into the ground level of the trap in
the presence of collisions. Such condensation is robust and can be achieved in
experimentally feasible traps. We extend significantly the validity of our
previous numerical studies, and present new analytic results concerning
condensation in the limit of rapid thermalization. We discuss in detail
necessary conditions to realize all optical condensate in weak condensation
regime and beyond.
