Using isosbestic points to extract interactions from structure factors

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Inverting scattering experiments to obtain effective interparticle interactions for particles in solution is generally a poorly conditioned problem. More accurate potentials can be obtained through the use of isosbestic points, values of k where the scattering intensity I(k) or the structure factor S(k) is invariant to changes in potential well-depth. These points also suggest a new extended corresponding states principle for particles in solution based on the particle density or packing fraction, the second osmotic virial coefficient, and a new measure of potential range.