Supersymmetry between Phase-Equivalent Coupled-Channel Potentials

Abstract

With supersymmetric quantum mechanics, a coupled-channel potential is determined which is phase equivalent to a given one, and whose bound spectrum is identical except for one arbitrary bound state which is removed. The bound state is suppressed by a first supersymmetric transformation and the original scattering matrix is recovered with a second transformation. The resulting potential presents an ${r}^{\ensuremath{-}2}$ singularity at the origin in some channels. The method is applied to the removal of the nonphysical state of the deep $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ neutron-proton Moscow potential and transforms it into a shallow potential with a repulsive core.