Saddles and trajectories, and poles and surface waves in heavy-ion elastic scattering

摘要: Abstract The terms I m ± ( θ ) of the Poisson summation formula are used to describe and classify oscillatory structures heavy-ion elastic cross sections coming from a strong-absorption model. method stationary phase, which relates these branches deflection function, is shown be inadequate replaced by saddle-point in plane complex angular momenta. positions saddle points found fairly independent parametrisation define certain “active” regions contribute scattering amplitude. may thought as corresponding trajectories nuclear potential. If possesses poles many contributions can simply expressed residues nearest real axis. One leading parametric has an energy dependence similar that dominant Regge pole generated optical Poles lying above axis give rise surface waves, i.e. they damped progress around surface. These possess classically equivalent paths sense correspond deflections less than π. Terms below have no classical equivalent, increase can, then, only being diffractive. Some useful formulae for section given limiting case sharp cut-off discussed.