Low-Energy Parametrization of Scattering Observables in n -Dimensional Quantum Systems

A rigorous theory for low-energy scattering in quantum systems in n dimensions, $n>~2$, with general, possibly long-range, interactions is presented. It gives new insights into lowenergy phenomena; e.g., for $n=2$ the controversy around the existence of scattering parameters is resolved. Furthermore, the important role of a parametrization of scattering observables in the study of spin-polarized quantum systems is illustrated. For $n=3$, an analytic expansion of the phase shift and scattering length for charged, finite-size particle scattering, around their neutral counterparts, is derived.