Uniform approximations for glory scattering and diffraction peaks

Semiclassical approximations are derived for the angular dependence of the scattering cross section σ(θ) for two cases, involving the forward and backward directions, where the classical scattering is infinite. The results are approximations uniform in angle and valid from the ordinary semiclassical region where σ(θ) is O(0) right round to θ = 0 or π for a glory σ(θ) is then O(-1) and the forward diffraction peak σ(θ) is O(-2) or larger, depending on the form of the long-range tail of the scattering potential. The formulae are all expressed in terms of the action functions along the paths of the classical problems.