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Supersymmetric inversion of effective-range expansions

A complete and consistent inversion technique is proposed to derive an accurate interaction potential from aneffective-range function for a given partial wave in the neutral case. First, the effective-range function is Tayloror Pade expanded, which allows high precision fitting of the experimental scattering phase shifts with a minimalnumber of parameters on a large energy range. Second, the corresponding poles of the scattering matrix areextracted in the complex wave-number plane. Third, the interaction potential is constructed with supersymmetrictransformations of the radial Schrodinger equation. As an illustration, the method is applied to the experimentalphase shifts of the neutron-proton elastic scattering in the 1S0 and 1D2 channels on the [0–350] MeV laboratoryenergy interval.