Cooperative scattering and radiation pressure force in dense atomic clouds

We consider the collective scattering by a cloud of $N$ two-level atoms driven by an uniform radiation field. Dense atomic clouds can be described by a continuous density and the problem reduces to deriving the spectrum of the atom-atom coupling operator. For clouds much larger than the optical wavelength, the spectrum is treated as a continuum, and analytical expressions for several macroscopic quantities, such as scattered radiation intensity and radiation pressure force, are derived. The analytical results are then compared to the exact $N$-body solution and with those obtained assuming a symmetric timed Dicke state. In contrast with the symmetric timed Dicke state, our calculations takes account of the back action of the atoms on the driving field leading to phase shifts due to the finite refraction of the cloud