Ambiguities in strong absorption S-functions and corresponding potentials for heavy ion collisions

A semiclassical (WKB) method within fixed energy inverse scattering theory has been used to analyse the differential cross section from the elastic scattering of 1449 MeV12C ions off of 208Pb. Excellent, statistically significant, fits to the experimental data have been found using a McIntyre form for the scattering function but with diverse sets of parameter values. Inversion of those scattering functions resulted in interaction potentials for this system that are also quite diverse. In addition, conventional optical model potentials have been obtained with which direct solution of the Schroedinger equations result in similar excellent fits to the data. It is shown that these large ambiguities in the potentials are due, in the main, to the limited angular range of the cross-section data and although the corresponding cross-section shapes beyond the measured scattering angle range vary over many orders of magnitude, it is unlikely that experiments can be made sensitive enough to select from among them because those cross sections are so small. 23 refs., 3 tabs., 6 figs