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Form factors for $\alpha+{^{12}}$C inelastic scattering are obtained withintwo theoretical ($\alpha+\alpha+\alpha$) approaches: The hypersphericalframework for three identical bosons, and the algebraic cluster model assumingthe $D_{3h}$ symmetry of an equilateral triangle subject to rotations andvibrations. Results show a good agreement, with form factors involving theHoyle state having a slightly larger extension within the hypersphericalapproach. Coupled-channel calculations using these form factors are ongoing.

epj web of conferences

Three-body description of $\boldsymbol{^{12}}$C: From the hyperspherical  formulation to the algebraic cluster model and its application to  $\boldsymbol{\alpha}+\boldsymbol{^{12}}$C inelastic scattering