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 $2\mathrm{/}{r}^2$ and $6\mathrm{/}{r}^2$ in natural units, for the ${}^3{S}_1$ and ${}^1{S}_0$ channels respectively. The simplest solution in the ${}^3{S}_1$ 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 ${}^3{S}_1$-${}^3{D}_1$ coupled channel problem with the coupled channel Marchenko inversion method.