The mean energy, strength and width of the double giant dipole states

Model-independent sum rules for an excitation strength of the "double" giant dipole resonance state are derived. The strength is given in terms of that for the "single" giant dipole resonance state. The width and the mean energy of the double giant resonance state relative to those of the single giant dipole resonance state are estimated rather model-independently without assuming independent phonon excitations. The mean energy of the double giant dipole state is twice that of the single giant dipole resonance state, while the width is larger than 2 times that of the single giant dipole state. The mean energy and the width are consistent with experiments. The relationship between these results and those of the folding model is briefly discussed.