Deep l-independent potentials from supersymmetric inversion

Central potentials, independent of both the energy and the angular momentum l, are constructed from elastic phase shifts. The ambiguities of a fixed- l inversion are exploited to fit the phase shifts of other partial waves. The fitted quantities are the energy and normalization constant of forbidden bound states, and the small-distance behavior of the potential. The method is based on supersymmetric transformations of the radial Schrodinger equation. It is applied to the alpha+alpha collision in nuclear physics, and to the e(-)+Ne collision in atomic physics.