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Algebraic potentials from SO(3,l) and SO(3,2) representations of scattering functions are deduced by matching to scattering functions obtained by fitting ,2 C-,2 C elastic-scattering differential cross sections. Their variations with energy suggest a simple mapping between algebraic and coordinate-space interactions.PACS numbers: 24.10.Ht, 21.60.Fw, 25.70.Cd Recent studies 1,2 have introduced techniques for defining S functions for elastic scattering from consideration of dynamical symmetry groups and their asymptotic properties. In particular the groups SO(3,7V) for TV 888 1 and 2 yield S functions that equate to scattering from modified Coulomb potentials, 2 and therefore these algebraic models are appropriate for use in the analysis of collisions between heavy ions. The models are valid even at high energies where the strong absorption model 3 has had success since most data reflect properties of the interaction in a sensitive radial region in the proximity of the strong-absorption radius, 4 and where the potential strengths are characteristically small in comparison with the Coulomb field strength. It has been shown 2 that the presence of a dynamical symmetry implies a par-