Ambiguities in strong absorptionlike [ital S] functions and in the corresponding potentials for heavy-ion collisions

A semiclassical (WKB) method within fixed energy inverse scattering theory has been used to analyze the differential cross section from the elastic scattering of 1449 MeV [sup 12]C ions off of [sup 208]Pb and of 1503 MeV [sup 16]O ions off of [sup 12]C. Excellent, statistically significant, fits to the [sup 12]C-[sup 208]Pb experimental data have been found using a McIntyre form for the scattering function but with diverse sets of parameter values. There are corresponding diverse interaction potentials. To fit the [sup 16]O-[sup 12]C data, a Regge pole term was needed to supplement the McIntyre form. Inversion of those scattering functions resulted in interaction potentials that vary noticeably within the sensitive radial regions. 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 for the [sup 12]C-[sup 208]Pb collision 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.