  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.
