The algebraic cluster model: Three-body clusters (Q699066)

The paper deals with the cluster model of nuclei. A new method is introduced to study three-body clusters. Triangular configurations with \(D_{3h}\) point-group symmetry are analyzed. The spectrum, transition form factors, and \(B(E\lambda)\) values of \(^{12}C\) are investigated. It is concluded that the low-lying spectrum of \(^{12}C\) can be described by three alpha-particles at the vertices of an equilateral triangle, but not as a rigid structure. Large rotation-vibration interactions, Coriolis forces, and vibration-vibration interactions are needed. Other interpretations, such as the harmonic oscillator and a soft deformed oscillator with \(SO(6)\) hyperspherical symmetry, appear to be excluded by electron scattering data.