Complex local potential by Marchenko inversion of partly real and partly complex phase shift

By using the (in general complex) phase shifts for elastic neutron-deuteron scattering in the quartet channel, calculated by means of the exact few-body theory, as input in the fixed-l inverse scattering theory of Marchenko, we construct equivalent local two-body potentials. The latter, though being complex and energy independent, nevertheless reproduce the input phase shifts, which are real below and complex above the deuteron breakup threshold, to a high accuracy. It is even more remarkable that the scattering wave functions (with real boundary conditions) for energies in the elastic regime, calculated with these potentials, are real outside the range of the force, and to a very good approximation real also in the interior region