Neutron-proton scattering and singular potentials

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/r(2) and 6/r(2) in natural units, for the S-3(1) and S-1(0) channels, respectively. The simplest solution in the S-3(1) 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 S-3(1)-D-3(1) coupled channel problem with the coupled channel Marchenko inversion method.