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.
