Abstract
The degree of freedom of α cluster exists widely in light α conjugate nuclei, which not only plays essential roles in the synthesis of elements and abandance of elements in nuclear astrophysics but also serves as the natural laboratory to test various new many-body theories and nuclear force due to the available high precision data. This article briefly summarizes the different theoretical approaches for alpha-cluster and compares the results of 12C Hoyle state with these approaches. All the theories support the structure of Hoyle state with a more extended size compared with ground state. However, a consensus has not be reached about how α clusters stay inside Hoyle state, where several candidate states are possible, such as a condensate state, a gas or crystalline arrangements of the α-particles. Further more, we also introduce the new experimental measurements of a decay and collective excitation of rotational band. In order to pin down the existence form of a in Hoyle state, a deeper knowledge of the collective excitation of cluster is needed. The essential progress can only be possible by high combination of new data with high precision and new many-body theory, where the roles of nucleon-nucleon correlation, cluster-cluster correlation and continuum are needed to be included reasonably.
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