Effects of systematic errors in analyses of nuclear scattering data

The effects of systematic errors in elastic scattering differential cross-section data upon the assessment of quality fits to that data have been studied. First, to estimate the probability of any unknown systematic errors, select, typical, sets of data have been processed using the method of generalized cross validation; a method based upon the premise that any data set should satisfy an optimal smoothness criterion. Specified systematic errors should also be taken into account when high quality fits to data are sought. We have considered such effects due to the finite angular resolution associated with the data in some quite exceptional, heavy ion scattering data sets. Allowing angle shifting of the measured values gave new data sets that are very smooth. Furthermore, when such allowances for systematic errors are so taken into account, reasonable, but not necessarily statistically significant, fits to the original data sets can become so. Therefore, they can be plausible candidates for the {open_quote}{open_quote}physical{close_quote}{close_quote} descriptions of the scattering processes. In another case, the {ital S} function that provided a statistically significant fit to data, upon allowance for angle variation, became overdetermined. A far simpler {ital S} function form could then be found to describe the scattering process. The {ital S} functions so obtained have been used in a fixed energy inverse scattering study to specify effective, local, Schr{umlt o}dinger potentials for the collisions. An error analysis has been performed on the results to specify confidence levels for those interactions. {copyright} {ital 1996 The American Physical Society.}