Neutron-proton scattering and singular potentials

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 $2/r^2$ and $6/r^2$ 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.

Comments: 39 pages. Extended version. Title changed, presentation improved and a new appendix on the coupled channel problem added