Optical-depth scaling of light scattering from a dense and cold atomic $^{87}$Rb gas

We report investigation of near-resonance light scattering from a cold and dense atomic gas of $^{87}$Rb atoms. Measurements are made for probe frequencies tuned near the $F=2to F=3$ nearly closed hyperfine transition, with particular attention paid to the dependence of the scattered light intensity on detuning from resonance, the number of atoms in the sample, and atomic sample size. We find that, over a wide range of experimental variables, the optical depth of the atomic sample serves as an effective single scaling parameter which describes well all the experimental data.