Existence and analyticity of many body scattering amplitudes at low energies

We study elastic and inelastic (2 cluster) - (2 cluster) scattering amplitudes for N-body quantum systems. For potentials falling off like r⁻^-1-E we prove that below the lowest 3-cluster threshold these amplitudes exist, are continuous and that asymptotic completeness holds. Moreover, if potentials fall off exponentially we prove that these amplitudes can be meromorphically continued in the energy, with square root branch points at the 2 cluster thresholds.