Self-consistent calculation of responses

We now return to the problem of a dense chain system where weak perturbations Wm(r ) are applied on all sites. Our assumption will be to write the responses us the response of ideal chains, with the chains experiencing not only external potentials W but also a self-consistent potential U (which will be a linear function of 5 ). 

However, the main domain of iq pl ution of the RPA is not the semi-dilute regime (where inside each blob, an ideal chain pictuie is not acceptable) but rather the melt regime, where the total concentration is 

Let us first state our assumption in detail, writing as a function of 

It is essential to note that the self-consistent potential U isthe same for all n (just as it is in the semi-dilute case of eq. (IX.63)). This expresses the chemical identity of all monomers and reduces our self-consistent problem considerably. There is only one unknown function U, and we can obtain it explicitly ftom the condition of constant total concentrations eq. (IX.64). Inserting eq. (IX.64) into eq. (IX.66) we get  

Finally, if we use this self-consistent potential in eq. (IX.66), we arrive at the explicit form for the response functions 

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