Criticism of the Gaussian approximation

In spite of appealing features, the Gaussian approximation has a very serious defect it predicts a size exponent v = 2/d which is too big, in contradiction to the results of computer simulations and experiments for real polymers. 

This phenomenon can be analysed as follow. When a chain swells, the interaction between links is reduced, but simultaneously the entropy diminishes, and there is a balance between these two effects. But, in the framework of the Gaussian approximation, the entropy is calculated exactly as a consequence, the fact that the calculated swelling is too large implies that the interaction energy is overestimated. 

we observe that for a Gaussian chain, the probability distribution of the end-to-end vector is 

For such a model, the probability of contact of the points Mj belonging to the chain is proportional to 

In the same way, and for the same reasons, the Gaussian approximation predicts that the closure probability pN of a finite chain is proportional to JV Td. 

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