Abstract
Sum rules are applied to studying soft multipole excitations in halo nuclei. The soft modes are considered as relative oscillations between the halo neutrons and the core part of a halo nucleus. It is shown by using the di-neutron cluster model that the excitation energies depend linearly on the separation energy of halo neutrons, while the transition strengths are inversely proportional to the separation energy. These relationships hold qualitatively in the independent-particle model. An analytic formula for the transition density is obtained for the dipole mode and compared with the results of microscopic RPA calculations.
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