Elastic Scattering using artificial confining potentials

It is shown that the discrete energies of a scattering Hamiltonian calculated under the influence of an artificial confining potential can be used to determine its phase shifts. Two potentials that have the same discrete energy under the influence of the confining potential will have exactly the same phase shift at that energy when the confining potential is removed. This result can be exploited by a variety of techniques to determine the phase shifts of many-body scattering problems. Results for both model problems and real physical systems such as $e^{\pm}$-H, $e^{\pm}$-He, Ps-H, and Ps-He are presented.