A scaling law for light scattering from dense and cold atomic ensembles

We calculate the differential cross section of polarized light scattering from a cold and dense atomic ensemble. The regularities in the transformation of the cross section when increasing the size of the atomic ensemble are analyzed numerically. We show that for typical experimental conditions, an approximate scaling law can be obtained. Very good agreement is found in a comparison with experimental data on the size dependence of a dense and cold cloud of 87$Rb atoms.