Rainbow Extinction, Orbiting and Regge Poles

International audienceWe discuss the elastic scattering 4He + 24Mg at 50 MeV as a good example of a whole range of phenomena that compete in heavy ion reactions and can be identified in elastic scattering data. The reaction is dominated by deep optical potentials and shows all characteristics of a strongly refractive scattering: Fraunhofer diffractive oscillations at very forward angles, shallow Airy oscillation forward to a rainbow bump, significant increase of the cross section at large angles. Primitive evaluation of the deflection function indicates a strong orbiting singularity. The lowest order eikonal expansion of the scattering phase suggests a typical rainbow pattern, though the rainbow angle lies far beyond the physical angular range. The semiclassical uniform multireflection expansion of the scattering amplitude tells that the strong refractive effects associated with orbiting are carried by the internal barrier component which retains contributions from trajectories refracted by the spherical well. A complementary analysis in terms of unitary Regge pole amplitudes shows that the effects associated with the break in the exponential decay of the rainbow tail could be interpreted as simple diffraction due to pole(s) in the S-matrix. This strengthen the conjecture that orbiting and Regge poles are dual aspects of heavy ion scattering. The similarity with the Fresnel clothoide for light diffraction is exemplified with a schematic model that allows an almost exact calculation of the scattering amplitude