th / 0 10 80 02 v 1 1 A ug 2 00 1 The mean energy , strength and width of triple giant dipole resonances

We investigate the mean energy, strength and width of the triple giant dipole resonance using sum rules. We point out that the excitation operator for the triple giant dipole resonance must be modified from the naive choice D 3. With the modified excitation operator, the strength and mean energy calculated in the Tomonaga model agree with the harmonic limit and the width is larger than √ 3 times that of the giant dipole resonance. Had we adopted the naive choice, we would have obtained unphysical results for these quantities. Assuming the absence of a charge exchange component in the nuclear interaction, we derive model independent relationships between the mean energies and strengths of multiple giant dipole resonances, which are an extension of relations derived previously for the double giant dipole resonance. The study of the double giant dipole resonance in nuclei has received a considerable amount of attention over the last 15 years [1]. Both the pion double charge exchange 1