Abstract
The differential cross sections from the scattering of 350 MeV ${}^{7}$Li ions from ${}^{12}$C and from ${}^{28}$Si have been analyzed by both a global and a numerical inverse scattering theory. Statistically significant fits to both high quality data sets have been found from which the associated effective local interaction potentials between the colliding ions have been deduced. The interactions obtained by the different approaches are radically different. A priori physical information about the nature of realistic effective interactions is required to ascertain which, if any, is the most reasonable one for use in analyses of other reaction data from these systems.
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