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Although quantum mechanical expressions for the scattering cross sections related to corresponding oscillator strengths have been derived, the original derivation in terms of classical electromagnetic fields by Rayleigh still gives a proper quantitative expression for the cross section. Fluctuations, or inhomogeneities, in the dielectric constant of a gas are held responsible for the scattering of light. The effects of density, temperature, molecular (re)-orientation, and the role of kinetics, causing elastic and inelastic scattering have primarily an effect on the spectral distribution of the scattered light. These phenomena give rise to splitting into several scattering components with Raman, Brillouin and Rayleigh-wing contributions, besides the central component, usually referred to as the Cabannes peak.
The original Rayleigh expression for the total scattering cross section comprising all elastic and inelastic contributions directly relates to the index of refraction and through this relationship all phenomena of Rayleigh scattering have hitherto been analyzed quantitatively.