Requirements of scattering data for model-independent analyses

A primary step in many attempts to ascertain the interaction potential between two colliding quantal systems is to define a ''physical'' S matrix (or scattering phase shifts) from measured data. We study applications of a controlled random search method of defining such S matrices. This method is model independent and should yield a global minimum form of the S matrix in the sense of a mean square variance in relation to the data. In practice, that is a difficult prospect. In this study, Woods-Saxon potentials, typical of those used in nuclear scattering data analyses, have been used to define the analytic input data for S-matrix analyses. The requirements on that input data with respect to recovery of the known underlying S matrix and the generating interaction potential reveal that a maximum amount of experimentally available data with very high precision is needed to achieve a reliable insight into the nuclear interaction. We found that such sufficient data exceed in both number and precision those given in most published results of actual nuclear scattering experiments. While discussion in this paper is restricted to the elastic scattering of two nuclei, the results have relevance to any other quantum scattering system