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The algebraic molecular model is used in $^{12}$C to construct densities andtransition densities connecting low-lying states of the rotovibrationalspectrum, first and foremost those belonging to the rotational bands based onthe ground and the Hoyle states. These densities are then used as basicingredients to calculate, besides electromagnetic transition probabilities,nuclear potentials and formfactors to describe elastic and inelastic$\alpha$+$^{12}$C scattering processes. The calculated densities and transitiondensities are also compared with those obtained by directly solving the problemof three interacting alpha's within a three-body approach where continuumeffects, relevant in particular for the Hoyle state, are properly taken intoaccount.

aip conference proceedings

The algebraic molecular model in $^{12}$C and its application to the  $\alpha$+$^{12}$C scattering: from densities and transition densities to  optical potentials and nuclear formfactors