  We investigate the possibility of a Dicke-type superradiant phase transition
of an atomic gas with an extended model which takes into account the
short-range depolarizing interactions between atoms approaching each other as
close as the atomic size scale, which interaction appears in a regularized
electric-dipole picture of the QED of atoms. By using a mean field model, we
find that a critical density does indeed exist, though the atom-atom contact
interaction shifts it to a higher value than it can be obtained from the bare
Dicke-model. We argue that the system, at the critical density, transitions to
the condensed rather than the "superradiant" phase.
