Bounds on the total scattering cross-section for N-body systems

Abstract

We consider quantum-mechanical nonrelativistic N particle scattering systems with pair potentials decreasing at infinity more rapidly than r⁻². Let σ̅_α (λ ) be the total scattering cross-section, at energy λ , for scattering initiated in a two-body channel α . We derive explicit bounds, in terms of the pair potentials, for weighted averages of σ_α (λ ) over a range of energies and discuss some interesting features of these bounds, in particular their implications for the high-energy behaviour of σ_α (λ ).