Multiple-Scattering Expansions for Nonrelativistic Three-Body Collision Problems. IV. Application of the Faddeev-Watson Expansion to Scattering Processes

The high-energy limit of the differential scattering cross section, according to the exact Born approximation can have either an $E^{-2\mathrm{}}$ or an $E^{-6\mathrm{}}$ energy dependence, depending on the scattering angle and masses of the system. When the target is made of equal-mass particles having charges which are equal but opposite in sign, the first-order Born approximantion predicts a zero for the elastic scattering amplitude. This anomalous behavior does not appear in the first-order Faddeev-Watson multiple-scattering approximation. An application of the first-order Faddeev-Watson multiple-scattering approximation to a three-body Coulomb system with arbitrary masses is considered. The three-body scattering amplitude is derived and expressed in terms of an integral consisting of contributions coming from (a) the two-body bound-state poles in the initial and final wave functions, (b) the branch-point singularities in the off-shell two-body Coulomb $T$ matrices, and (c) the intermediate two-body bound- and antibound-state poles.