EXERCISE 9.1. The static density correlation function, Cnn (r), for an equilibrium fluid can be written Cn (r) = (1/N) dr' (n(r' +r)n(r')), where the density phase function is defined n(r,q)=6(q-r). The static structure factor for the fluid is defined as Sn(k) =dre Cnn (r). Show that in the limit Noo and Voo with n = N/V = constant, the static structure factor when written in terms of the pair correlation function has the form

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Snn (k) 1+n6(k) +- 470qdqsin(kg) (82(9) 1).