Nuclear Giant Resonance States and the Related Problems

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The purposes of the project are1.Determination of the value of Landau-Migdal parameter, which depends on the nuclear spin, from the giant Gamow-Teller resonance states,2.Understanding of the double giant resonance states with model-independent sum rules, and3.Investigation of the relationship between relativistic and non-relativistic nuclear models.As to the purpose 1, we determined the value of the parameter from recent experiment, and have shown that the result is, in fact, related to the purpose 3.As to the purpose 2, we have derived various model-independent sum rules not only for double giant resonance states which are recently observed experimentally, but also for triple giant resonance states. We have also derived model-independently some identities between their excitation energies and transition strengths.As to the purpose 3, we have showed that the previous relativistic nuclear models have a serious problem. They explain phenomenologically well the structure of giant resonance states, but violate the sum rules. In order for the relativistic models to satisfy the sum rules, we need to renormalize the divergence of the nuclear response functions properly. We propose a method of proper renormalization by taking as an example the Gamow-Teller sum rule. We expect that the present result is a good starting point of the next project for the purpose 3.