Transition densities and form factors in the triangular alpha-cluster model of C-12 with application to C-12 + alpha scattering

Densities and transition densities are computed in an equilateral triangular alpha-cluster model for C-12, in which each alpha particle is taken as a Gaussian density distribution. The ground state, the symmetric vibration (Hoyle state), and the asymmetric bend vibration are analyzed in a molecular approach and dissected into their components in a series of harmonic functions, revealing their intrinsic structures. The transition densities in the laboratory frame are then used to construct form factors and to compute distorted-wave Born approximation inelastic cross sections for the C-12(alpha, alpha') reaction. The comparison with experimental data indicates that the simple geometrical model with rotations and vibrations gives a reliable description of reactions where alpha-cluster degrees of freedom are involved.