B Scattering function in RPA

To find the coefficients xi and xy, we substitute the power expansion (5.64a) into the material conservation laws (5.27a) and (5.27b), and compare term by term. The results are summarized as follow. The 0-th term yo should be the solution of the equation 

For instance, if association takes place only within the A component, we find. 0 = 

To derive the RPA scattering function in a compact form, we here introduce vector notations. Let x be an S2-component columnar vectorial whose (o ,/)-th component is defined by t given in (5.54), so that we can write x = [t ]. Similarly let e be the columnar vector whose components are all unity. We have by definition 

We now consider linear response 8pf) of the density to an arbitrary external field acting on each monomer with strength Uf. Linear response theory gives 

It is assumed to act uniformly on all species of monomers in a bulk system 

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