Nuclear Giant Resonance States and the Related Problems

本项目的目的是：1.从巨Gamow-Teller共振态确定依赖于核自旋的Landau-Migdal参数的值；2.用与模型无关的求和规则理解双巨共振态；3.研究相对论和非相对论核模型之间的关系.对于目的1，我们从最近的实验中确定了该参数的值，并证明结果实际上与目的3有关.对于目的2，我们导出了各种与模型无关的求和规则，不仅适用于最近实验观察到的双巨共振态.也适用于三重巨共振态。我们还独立地推导了它们的激发能和跃迁强度之间的一些恒等式。对于目的3，我们已经证明了以前的相对论原子核模型存在严重的问题。它们在现象学上很好地解释了巨共振态的结构，但违反了求和规则。为了使相对论模型满足求和规则，我们需要对核反应函数的发散度进行适当的重整化。我们以Gamow-Teller求和规则为例，提出了一种适当的重整化方法。我们期望目前的结果是下一个目标3项目的良好起点。

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.