A new parameterization of the multi-channel S-matrix in terms of the Jost functions is used to fit non-relativistic two-body Coulomb scattering data. The S-matrix is written in terms of the Jost matrices which are written in a semi-analytic form where all the factors responsible for the branching of the Riemann energy surface are explicitly factorised.

The method is tested on a two-channel model using a set of artificially generated data-points.The model is then applied to the single channel scattering of 12C with the alpha particle (energy range 1-6 MeV), where the resonance parameters as well as other important scattering parameters relevant to astrophysics are successfully determined.