Depolarization shift of the superradiant phase transition

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.