The notion of interacting elementary particles for low and medium energy nuclear physics is associated with definitions of potential operators which, inserted into a Lippmann-Schwinger equation, yield the scattering phase shifts and observables. In principle, this potential carries the rich substructure consisting of quarks and gluons and thus may be deduced from some microscopic model. In this spirit we propose a boson exchange potential from a nonlinear quantum field theory. Essentially, the meson propagators and form factors of conventional models are replaced by amplitudes derived from the dynamics of self-interacting mesons in terms of solitary fields. Contrary to deduction, we position the inversion approach. Using Gel'fand-Levitan and Marchenko inversion we compute local, energy-independent potentials from experimental phase shifts for various partial waves. Both potential models give excellent results for on-shell NN scattering data. In the off-shell domain we study both potential models in (p, pγ) Bremsstrahlung, elastic nucleon-nucleus scattering and triton binding energy calculations. It remains surprising that for * Contribution to the International Conference on Inverse and Algebraic Quantum Scattering Theory, Lake Balaton '96.