An inversion scheme is presented to derive the potentials of algebraic scattering theory from the corresponding S functions. Representative heavy ion scattering data of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions on ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, accurately fitted by McIntyre strong absorption type S functions, are employed to obtain exact algebraic potentials and to generalize the analytical shapes proposed previously by Alhassid et al. The coordinate space potentials corresponding to a number of S functions are also obtained via semiclassical inversion.

• Received 26 February 1993

DOI:https://doi.org/10.1103/PhysRevC.47.2827