Energy eigenvalue surfaces close to a degeneracy of unbound states: Crossings and anticrossings of energies and widths

The rich phenomenology of crossings and anticrossings of energies and widths, as well as the sudden change in shape of the S(E)-matrix pole trajectories, observed in an isolated doublet of resonances when one control parameter is varied, is fully explained in terms of sections of the energy eigenvalue surfaces in parameter space close to a degeneracy point.