ABSTRACT
The experimentally established universal character of the crossinganticrossing properties of the energies and widths of an isolated doublet of resonances, observed when the control parameters of the system are varied, is explained in terms of the topological properties of the universal unfolding of the degeneracy point of the two unbound states in parameter space. This result generalizes a theorem of von Neumann and Wigner for bound states to the case of unbound states. We will illustrate these results with a numerical computation of the surfaces representing the complex resonance energy eigenvalues and the unfolding of the degeneracy point of an isolated doublet of resonances as function of the control parameters of the system in the scattering of a beam of particles by a double barrier potential with two regions of trapping
