Multiple-Scattering Expansions for Nonrelativistic Three-Body Collision Problems. VIII. Eikonal Approximation for the Faddeev-Watson Multiple-Scattering Expansion

The Faddeev-Watson multiple-scattering (FWMS) expansion is investigated in the eikonal approximation. For the case with the classical trajectories taken to lie along straight lines, the second-order FWMS expansion reduces to the well-known Glauber-eikonal approximation. Application of the second-order FWMS expansion in the eikonal approximation is carried out for elastic and inelastic ($e$, H) scattering with the classical trajectories taken as intersecting two straight-line segments. The result suggests that there is a substantial cancellation between the first-order and second-order terms in the FWMS expansion for pair Coulomb interactions.