Problem: The structure factor for dilute systems

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For a dilute system of identical nano-objects, it can be assumed that the relative phase between two of the objects, \(\exp(i {\mathbf q} \cdot ({\mathbf R}_J-{\mathbf R}_{K}))\), assumes a random value.

Derive from this assumption that \(S(q) = 1\) for dilute systems.