Orbiting resonances and bound states in molecular scattering

A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states. Then a single pole trajectory, that connects a rotational band of bound states and orbiting resonances, is obtained. These complex angular momentum singularities are derived through a geometrical theory of the orbiting. The downward crossing of the phase-- shifts through $\pi/2$, due to the repulsive region of the molecular potential, is estimated by using a simple hard--core model. Some remarks about the difference between diffracted rays and orbiting are also given.