Non-local potentials and rotational bands of resonances in ion collisions

Sequences of rotational resonances (rotational bands) and corresponding ant iresonances are observed in ion collisions. In this paper we propose a desc ription which combines collective and single-particle features of cluster c ollisions. It is shown how rotational bands emerge in many-body dynamics, w hen the degeneracies proper of the harmonic oscillator spectra are removed by adding interactions depending on the angular momentum. These interaction s can be properly introduced in connection with the exchange forces and the antisymmetrization, and give rise to a class of non-local potentials whose spectral properties are analyzed in detail. In particular, we give a class ification of the singularities of the resolvent, which are associated with bound states and resonances. The latter are then studied using an appropria te type of collective coordinates, and a hydrodynamical model of the trappi ng, responsible for the resonances, is then proposed. Accordingly, we deriv e, from the uncertainty principle, a spin-width of the unstable states whic h can be related to their angular lifetime.