Extraction of spin-orbit potentials from scattering data via inversion

We present an approximate global inversion procedure which allows the determination of the central and the spin-orbit potential from scattering data at fixed energy involving one spin-half particle. The procedure assumes that the contribution of the spin-orbit potential to the phase shifts can be evaluated in second order Distorted Wave Born Approximation. The method works best for relatively high incident energies and relatively weak spin-orbit potentials. First tests show that, for energies above 50 MeV, typical forms of nucleon-nucleus optical potentials can be reconstructed satisfactorily.