The inverse scattering problem and the equivalent local potential

We examine the role of the non-locality of the potential in the two-body scattering by taking the nucleon-Σ system as an example. We employ a non-local potential for the nucleon-Σ channel which has the characteristic features of the quark model and reproduces the phase shifts of widely used local potentials. We use inverse scattering methods to obtain the equivalent local potential from the non-local potential, and show that the obtained local potential has a strong short range repulsion.