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 cl assical deflection function when the conditions for a semiclassical analysi s of the quantum-mechanical scattering are met. Various interesting charact eristic features of the scattering are related to special features of the c lassical deflection function. The characteristic types of scattering discus sed are: interference. when the deflection function possesses more th:ln on e branch at a given angle: rainbow scattering, when the deflection function has a relative maximum or minimum; glory scattering, when the deflection f unction passes smoothly through 0 degrees or through an integral multiple o f +/- pi: and orbiting, when the deflection function possesses a singularit y. The consideration of the characteristic features of semiclassical scatte ring makes possible the analysis of an observed differential cross section to yield the classical deflection function, which in turn may be used to co nstruct the potential. (C) 1959 Academic Press.