such that there are ‘many’ active partial waves. ‘Many’ here means sufficient, even with $S^J_{l'l}$ for a single energy, to yield a precise reproduction of the potential.

The test was carried out as follows: one of the authors applied the optical model parameters of Hatanaka [*et al*]{} to the standard spin-1 scattering code DDTP [@ddtp], reading out the $S$-matrix onto a file. A second author, knowing only the target and the energy, then applied IMAGO to find the potential from these $S$-matrix elements. The inversion was carried out with a starting potential which contained only real and imaginary central potential components. These were guessed from general systematics without specific knowledge of Hatanaka’s potential. Since with IMAGO there is complete freedom to choose the starting potential and inversion basis, it is worthwhile to test the inversion method starting with no more information about the potential than might be available in a ‘for real’ case.

When a converged solution was found, the potentials obtained were compared with the known potentials with results shown in Figure 1. The solid lines represent the ‘target’ potential, i.e. the potential from which the $S$-matrix was calculated using DDTP. The short dashes represent the potential found by 