Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method

A second-order supersymmetric transformation is presented, for the two-channel Schr"odinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the potential matrix analytically. The iteration of a few such transformations allows a precise fit of realistic mixing parameters in terms of a Pade expansion of both the scattering matrix and the effective-range function. The method is applied to build an exactly-solvable potential for the neutron-proton ${}^3{S}_1$-${}^3{D}_1$ case.