Vanishing rainbows near orbiting and the energy dependence of rainbow scattering: Relation to properties of the potential

Abstract

The energy threshold behavior of elastic rainbow scattering near the transition to orbiting is derived. Analysis of the energy dependence of the rainbow angle shows that the full range from high energies down to orbiting can be fitted with two parameters. Thus measurements of the rainbow angle can give essentially only two pieces of information about the potential. For potentials of common shapes such measurements are sensitive to regions of the potential just beyond the minimum and give information about the shape of the potential in this range. However, neither a minimum nor a point of inflection in the potential is necessary for rainbow scattering.