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

Abstract

Sequences of rotational resonances (rotational bands) and corresponding antiresonances are observed in ion collisions. In this paper we propose a description which combines collective and single-particle features of cluster collisions. It is shown how rotational bands emerge in manybody dynamics, when the degeneracies proper of the harmonic oscillator spectra are removed by adding interactions depending on the angular momentum. These interactions 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 classification of the singularities of the resolvent, which are associated with bound states and resonances. The latter are then studied using an appropriate type of collective coordinates, and a hydrodynamical model of the trapping, responsible for the resonances, is then proposed. Accordingly, we derive, from the uncertainty principle, a spin-width of the unstable states which can be related to their angular lifetime.

Unified scheme for describing time delay and time advance in the interpolation of rotational bands of resonances

“…In order to summarize rapidly the hydrodynamical model of the vortices, we move back to the expression of the current density, introduced in section 3: i.e., j = i{χ∇χ * − χ * ∇χ}, where χ is the wavefunction (see also Ref. [13]). Assuming a semiclassical approximation, we write χ = A √ 2 e iΘ (A = constant); accordingly, we have: j = A 2 ∇Θ.…”

“…In a previous paper [13] -hereafter referred as I -we have studied ion collisions treating the composed structure of the clusters by means of the Jacobi coordinates and of the related SU (n)group algebra. We proved that rotational bands emerge by removing the SU (n) degeneracies by introducing forces that depend on the relative angular momentum of the clusters: i.e., non-local potentials.…”

Time delay and time advance in resonance theory

“…At this point, however, we strongly remark that there does not exist a one-to-one correspondence between time advance, compositeness of the interacting particles and Pauli exchange forces, as we shall explain with more details and examples in a remark in Section 3. Coming back to the Pauli exchange forces, we note that it is precisely the Pauli antisymmetrization which leads us to introduce non-local potentials [8], which depend on the angular momentum. Then performing for this enlarged class of potentials the analytic continuation of the partial scattering amplitudes from integer values of the angular momentum ℓ to complex-valued angular momenta λ ∈ C, a peculiar feature, which is absent in the case of local Yukawian potentials, comes out: the scattering amplitude can have pole singularities both in the first and in the fourth quadrant of the CAM plane.…”

Transition from resonances to surface waves in pi^+-p elastic scattering

“…In Ref. [20,29] we have developed a detailed analysis of the resonance-echo process in connection with ion collision. In the present situation the phenomenon is quite similar: when the pion and the proton get in contact and successively penetrate each other, the composing quarks come into play.…”

“…If the walls are not completely reflecting, the lifetime of the resonance is finite. In fact, there is a wide phenomenological evidence of rotational bands of resonances in non-relativistic ion collisions [20], where the CAM theory can be applied effectively, and a clear evidence of Regge trajectories can be obtained [21]. In these rotational bands one can plot L(L + 1) versus E (see Fig.…”