Three-Alpha Structure of12C in the Boson Model

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Abstract
Theoretical works on few-body dynamics of the three-alpha system are reviewed on the basis of the recent success in describing important low-lying states of 12C in the Faddeev formalism. In order to assert the boson 3α-model are realistic, choice of the α-α potential is the most crucial point; the α-α potential should be selected to reproduce the substantial aspect of the a-a interaction obtained microscopically. The results calculated from such a potential are compared with those from the repulsive core potential mainly for energy properties, to see how the properties of the 3α system depend on the difference of the potentials which reproduce the 2α data equally well. It is shown that the boson 3α-model can describe the coexistence of both the shell-model-like structure and the well-developed cluster structure, if we employ suitable α-α potentials and solve the three-body problem exactly. Mechanism of energy gain and alpha-reduced-width amplitudes are discussed, and the structures of the wave-functions are clarified. Correspondence to the results obtained in the microscopic approach is shown to be fairly good, if we remove the superfluous states with the large redundant components arising from approximate treatment of the Pauli principle. Thus 12C can be regarded as a prototype in studying dynamics of three-boson systems with internal structure.

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