Impact-Parameter Theory Defined as a Constant-Collision-Velocity Semiclassical Limit of a Complete Quantum-Scattering Picture

A semiclassical limit, defined in terms of large mass and energy at fixed arbitrary collision velocity, is shown to be a simple formal prescription for obtaining a quantum treatment of the impact-parameter method and the eikonal approximation. In particular, for atomatom collisions, the resultant approximation is emphasized to be a proper strong-coupling equation for inelastic processes, as opposed to the adiabatic result of a large-mass limit at fixed energy.