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 diffe rence of the ''unperturbed'' energies or of the widths leads always to a cr ossing of either the energies or the widths of the "perturbed'' system. A p articularly 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. (C) 1999 Elsevier Science B. V. All rights reserved.