Intensity and angular dependence of the scattering

It is of interest to consider first the intensity of the scattered light integrated over time (or frequency). The differential scattering cross-section is then 

Writing 5n(r, t) = 5nexp[i(q r—mt)] and substituting in (3.3.6) we obtain the free energy of elastic deformation of the system 

From the equipartition theorem (which is certainly valid in the present problem) 

On the other hand, the cross-section due to density fluctuation is given by the well known formula 

Thus the director fluctuations make the predominant contribution to the light scattering, as was first pointed out by de Gennes.  

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