Semiclassical description of scattering (Reprinted from Annals of Physics, vol 7, pg 259-286, 1959)

The quantum-mechanical scattering amplitude can be simply related to the classical deflection function when the conditions for a semiclassical analysis of the quantum-mechanical scattering are met. Various interesting characteristic features of the scattering are related to special features of the classical deflection function. The characteristic types of scattering discussed are: interference. when the deflection function possesses more th:ln one branch at a given angle: rainbow scattering, when the deflection function has a relative maximum or minimum; glory scattering, when the deflection function passes smoothly through 0 degrees or through an integral multiple of +/- pi: and orbiting, when the deflection function possesses a singularity. The consideration of the characteristic features of semiclassical scattering makes possible the analysis of an observed differential cross section to yield the classical deflection function, which in turn may be used to construct the potential. (C) 1959 Academic Press.