Algebraic approach for α-cluster structure in ¹²C and ¹⁶O

We investigate the properties of the states observed around the α-cluster breakup threshold region in ¹²C and ¹⁶O. We apply the orthogonality condition model (OCM), where the model space is given by the SU3 algebra. From bases of this SU3 configuration, two algebraic approaches of the symplectic (sp) method and μ-truncation method are introduced. In ¹²C, we show that the sp-quanta are important to understand the mechanism of the appearance of the large E0 transition strength. With these methods, both strong- and weak-coupling configurations are taken into account at the same time. Therefore, the properties of gas-like and linear-chain states are investigated easily. In ¹⁶O, a simpler truncation utilizing the μ quanta is applied. Here, the energy levels and the linear-chain (L. C.) configurations are investigated.