  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
${}^3S_1$ and ${}^1S_0$ channels respectively. The simplest solution in the
${}^3S_1$ 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 ${}^3S_1$-${}^3D_1$ coupled channel problem with the coupled
channel Marchenko inversion method.
