Abstract
We discuss the regions forbidden to classical scattering trajectories by repulsive potentials. We give explicit results for the asymptotic form of these regions, far from the scattering center, in terms of the scattering angle function. We account for divergent total cross sections on the basis of these results.
Editor's Note: This article presents an intuitive approach to infinite cross sections by way of the “scattering shadow” of a repulsive potential. The authors apply classical scattering theory to repulsive power-law and Yukawa potentials, present numerical methods for calculating the envelope of trajectories that define the shadow, and derive analytic expressions for its asymptotic behavior. Scattering shadows clearly illustrate the physical origin of infinite cross sections. As such, the approach complements traditional analyses of scattering cross sections based on the impact parameter or differential cross section, common in texts and courses on classical scattering and quantum mechanics.