On three-body scattering cross sections

Abstract

Using a Hilbert space version of the Faddeev method. The authors prove finiteness and continuity as a function of the energy of the total scattering cross section for three quantum mechanical particles with two-body initial states. It is assumed that the pair potentials are locally in L^q(R³) for some q > 3/2 and decay as mod x mod ^{−2- delta} at infinity.