The role of complex trajectories in elastic scattering

Abstract

Undulations in differential elastic cross sections have previously been attributed to interference between the amplitudes of classical trajectories having the same observed scattering angle. From this point of view, oscillations resulting from a monotonically repulsive central potential are hard to understand, since in this case there is no interference from real trajectories. We have examined in detail the complex trajectories for the potential energy function 4r⁻¹², and found that there are complex impact parameters with real positive and negative scattering angles. We showed that the semiclassical formulation of Ford and Wheeler is accurate, provided that the first complex stationary phase point for negative scattering angles is included.