Global uniform asymptotics in the form of Airy functions for the problem of scattering on a repulsive Coulomb potential and Keplerian trajectories

Results announced in the authors' note [1] are presented in detail. For the scattering problem on a Coulomb potential we present an approach allowing us to construct an appropriate Lagrangian manifold formed by Keplerian orbits and to find an asymptotic representation for the solution by means of the Maslov canonical operator. Using resent results on an effective representation of the Maslov canonical operator in extended neighbourhoods of Lagrangian singularities (caustics) we can represent the asymptotic behaviour of the solution globally and uniformly as an Airy function of a complicated argument.