Crossing and anticrossing of energies and widths for unbound levels

The crossing and anticrossing properties of the energies and widths of two unbound levels under the influence of a symmetrical complex interaction are investigated. It is found that a sufficiently large variation of the difference of the “unperturbed” energies or of the widths leads always to a crossing of either the energies or the widths of the “perturbed” system. A particularly interesting result is that for a real off diagonal interaction there is a joint crossing of the “unperturbed” energies and of either the “perturbed” energies or the “perturbed” widths.