Abstract
The relation of the phenomenological algebraic cluster model, i.e., of the vibron model and its extensions, to the microscopic description is discussed. Based on this connection a semimicroscopic approach is formulated, in which the internal cluster degrees of freedom are treated in terms of the SU(3) shell model, and the relative motion is described by the vibron model. For a two-cluster system this model has a group structure of U ST C 1 (4)⊗ U C 1 (3)⊗ U R (4)⊗ U C 2 (3)⊗ U ST C 2 (4), and the phenomenological interactions are obtained in terms of the group generators. The model space is constructed to be free from the Pauli-forbidden states and spurious center of mass motion, similar to that of the SU(3) cluster model. Three examples, the 12C + α, the 12C + 12C and the 14C + α systems are presented to demonstrate various aspects of the semimicroscopic algebraic cluster model.
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