Prog. Theor. Phys. Vol. 114 No. 4 (2005) pp. 805-812
Sum Rules of the Multiple Giant Resonance States
1Department of Physics, Faculty of Science, Chiba University,
Chiba 263-8522, Japan
2Department of Applied Physics, Fukui University, Fukui 910-8507, Japan
3Dipartimento di Fisica, Università di Milano, and INFN,
Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy
(Received April 13, 2005)
Various sum rules for multiple giant dipole resonance states
are derived. For the triple giant dipole resonance states,
the energy-weighted sum of the transition strengths
requires a model to be related to those of the single and double giant
dipole resonance states.
It is also shown that the non-diagonal matrix elements of the double
commutator between the dipole operator and the nuclear Hamiltonian
give useful identities for the excitation energy
and transition strength of each excited state.
Using those identities, the relationship between width of the single
dipole state and those of the multiple ones is qualitatively discussed.
These results, it is stressed, may be useful in the study of other
systems than dipole excitations in nuclei, as well as in the problem of
anharmonicities of collective motions.
DOI : 10.1143/PTP.114.805
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