Dependence of Proton Optical-Model Parameters upon Experimental Uncertainties

Abstract

The dependence of proton optical-model parameters upon experimental uncertainties has been studied for four types of errors. These were errors in over-all normalization, errors affecting the shape of the angular distribution, errors in incident energy, and errors in scattering angle. By varying the data, it is found that the optical-model parameters are affected differently by the four types of errors; this suggests that a single, over-all assigned error is inadequate for error analysis in optical-model studies. The minimum-$\chi 2$ criterion is critically examined as a criterion for obtaining optimum optical-model parameters. The role of the experimental errors in the theoretical analysis is studied. Because the errors associated with the individual cross sections that form an angular distribution are not independent, we conclude that these data do not make up a collection of several independent random samples, but that, collectively, they resemble a single random sample. This conclusion is statistically important in the study of reaction mechanisms using results of optical-model analysis.