On the determination of the reaction cross section from elastic scattering

In the scattering between heavy ions often a strong Coulomb excitation of the low-lying states occurs. In this paper the authors study its effect on the determination of the reaction cross section from elastic scattering data. Emphasis is put on the question whether the analysis of the sum of Coulomb excited states and elastic scattering gives a consistent value of the reaction cross section. This in heavy-ion scattering often corresponds to the experimental situation. The simple quarter-point recipe is not reliable. The application of the usual optical model to the sum of elastic and inelastic scattering gives the reaction cross section as the flux going into the other channels. It should not be applied to strictly elastic scattering. The model independent sum-of-differences method is a reliable procedure. An extension of this method is derived that allows general conclusions: to yield correct reaction cross sections a model for elastic scattering has to describe the forward angles appropriately. In principle fitting the data is not needed when the generalized sum-of-differences method is used. (Auth.)