  We consider a gas of ultracold two-level atoms confined in a cavity, taking
into account for atomic center-of-mass motion and cavity mode variations. We
use the generalized Dicke model, and analyze separately the cases of a
Gaussian, and a standing wave mode shape. Owing to the interplay between
external motional energies of the atoms and internal atomic and field energies,
the phase-diagrams exhibit novel features not encountered in the standard Dicke
model, such as the existence of first and second order phase transitions
between normal and superradiant phases. Due to the quantum description of
atomic motion, internal and external atomic degrees of freedom are highly
correlated leading to modified normal and superradiant phases.
