A link between scattering resonances and dilation analytic resonances in few body quantum mechanics

Abstract

We study the (2 cluster)→(2 cluster) scattering amplitudes for classes of two, three, and four particle dilation analytic Schrödinger operators whose two-body potentials fall off exponentially. As functions of the energy, these amplitudes are shown to have meromorphic continuations on certain Riemann surfaces. We prove that all poles of these continuations are necessarily bound states or dilation analytic resonances [i.e., eigenvalues ofH(θ) for some θ].