Discrete two-variable expansions of physical scattering amplitudes

A model-independent method of performing energy-dependent scattering-amplitude analysis is presented. It makes use of previously developed two-variable expansions of scattering amplitudes but involves only summations and no integrals. The energy and angle dependence are displayed in known functions. The angle, as usual, figures in Legendre polynomials; the energy is contained in Gegenbauer polynomials, if the data analysis is performed over a finite energy region and in specifically constructed basis functions when the analysis concerns the entire energy region. The purpose of the expansions is to make it possible to analyze all data for a given two-body reaction simultaneously (for all energies and angles) and to store the obtained information in the expansion coefficients. These then characterize the dynamics of a specific reaction, rather than a certain kinematic situation.