[en] A straightforward derivation based on an intuitive classical optical model description of collisions of the A*+A type leads to a simple semiclassical theory of direct/exchange scattering. The theory is shown to give an accurate description of low-energy He*--He collisions by comparison with exact quantum mechanical calculations, and is used as the basis for an analytical inversion procedure which yields both of the potential curves from a single angular distribution measurement. The inversion method is applied to our crossed beam measurements of He* (2 ¹S, 2 ³S)+He differential scattering at 0.94 kcal/mole nominal collision energy to derive the relevant potential curves at large internuclear distance. The success of the method depends strongly on the accurate inclusion of apparatus resolution effects in the analysis