  The compressibility limit of a cold gas confined in a magneto-optical trap
due to multiple scattering of light is a long-standing problem. This scattering
mechanism induces long-range interactions in the system, which is responsible
for the occurrence of plasma-like phenomena. In the present paper, we
investigate the importance of the long-range character of the mediated
atom-atom interaction in the equilibrium and dynamical features of a
magneto-optical trap. Making use of a hydrodynamical formulation, we derive a
generalized Lane-Emden equation modeling the polytropic equilibirum of a
magneto-optical trap, allowing us to describe the cross-over between the two
limiting cases: temperature dominated and multiple-scattering dominated traps.
The normal collective modes of the system are also computed.
