Anharmonicities of giant dipole excitations

The role of anharmonic effects on the excitation of the double giant dipole resonance is investigated in a simple macroscopic model. Perturbation theory is used to find energies and wave functions of the anharmonic oscillator. The cross sections for the electromagnetic excitation of the one- and two-phonon giant dipole resonances in energetic heavy-ion collisions are then evaluated through a semiclassical coupled-channel calculation. It is argued that the variations of the strength of the anharmonic potential should be combined with appropriate changes in the oscillator frequency, in order to keep the giant dipole resonance energy consistent with the experimental value. When this is taken into account, the effects of anharmonicities on the double giant dipole resonance excitation probabilities are small and cannot account for the well-known discrepancy between theory and experiment.