Propagation Estimates and Asymptotic Completeness in Three-Body Long Range Scattering

In this work, we establish precise microlocalized propagation estimates in three-body problems and give a proof for the asymptotic completeness of waves operators in three-body long range scattering for a class of long range potentials of the form Va(xa) = V(1)a(xa) + V(2)a(xa) with V(1)a ≥ 0 decaying like O(|xa| −ϵ′) for some ϵ′ > 1/2 and V(2)a decaying like O(|xa| −γ) for some γ > 2(1 − ϵ′)/ϵ′.