Extracting resonance parameters from experimental data on scattering of charged particles

Abstract

A method of extracting resonance parameters from scattering data is outlined for scattering that involves Coulomb interactions. This is done for single-channel scattering, as well as multi-channel scattering. Within the outlined model, a set of experimental data points are fitted using a multi-channel S-matrix. The resonance parameters are located as poles of the S-matrix on an appropriate sheet of the Riemann surface of the energy. The proper analytic structure of the S-matrix is ensured, since it is constructed in terms of explicit analytic functions from which the functions depending on the Sommerfield parameters and channel momenta, responsible for the branching of the Riemann surfaces, are factorised. The fashion in which the S-matrix is thus constructed, allows the location of multi-channel and single channel resonances, their partial widths, as well as to obtain the scattering cross sections, even for channels for which no data is available. Pseudo-data for a single- and two-channel model is generated using appropriate potentials for which the resonance parameters are known exactly. Fitting the data appropriately produces resonance parameters which are then compared with the exact values. The feasibility of the proposed model is thus shown.