Structure of Resonance States in Three-Alpha Systems

Geometrical structures of low-energy states in the \({}^{12}\) ${}^{12}$ C nucleus are investigated using density distributions obtained from three \(\alpha \) $\alpha$ -particle wave functions calculated for a set of phenomenological \(2\alpha \) $2\alpha$ - and \(3\alpha \) $3\alpha$ potentials by Faddeev technique. Calculated shapes of triangles that three \(\alpha \) $\alpha$ -particles form are classified to either an equilateral triangle, an isosceles triangle, or a mixture of these with various sizes, which may characterize the excitation mechanism of the states