Unfolding a degeneracy point: crossings and anticrossings of unbound states in parameter space

Some geometric and topological properties of a degeneracy of unbound states are investigated in the scattering of a beam of particles by a double barrier potential well with two regions of trapping. We find that, near and at a degeneracy of unbound states, the surfaces representing the resonance eigenwave numbers as functions of the control parameters of the system have the topology of the Riemann surfaces of the square root of the difference of two complex, regular functions of the control parameters. (Author)