Abstract
We postulate a Gaussian three-body potential amongα particles and adjust its parameters so that, when it is added to the Ali-Bodmerα-α potential, a good fit to experimental energies of low-lying 0+ and 2+ states of12C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-α system. The 3-α potential improved results found with the Ali-Bodmer potential alone. We find the 0 2 + state to be a (non-rigid) linear chain and the ground state to be a triangle ofα particles.
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