Abstract
We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko's method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of the form 2/r² and 6/r² in natural units, for the ³S₁ and ¹S₀ channels respectively. The simplest solution in the ³S₁ channel contains three parameters only but reproduces all features of the potential and bound state wave function within one percent error. We also consider the ³S₁-³D₁ coupled channel problem with the coupled channel Marchenko inversion method.