The electric multipole strength distributions for transitions from the ${}^{12}\mathrm{C}\left(0_1^{+}\right)$ ground state to $3\alpha$ ($0^{+}$, $1^{-}$, $2^{+}$, and $3^{-}$) continuum states are studied in terms of $3\alpha$ model. Several sets of the $3\alpha$ Hamiltonian are introduced phenomenologically with conventional $\alpha \text{−}\alpha$ interaction potentials and $3\alpha$ potentials with different range parameters. The transition strength distributions are obtained from wave functions of $3\alpha$ bound and continuum states calculated by the Faddeev three-body formalism. From these strength distributions, the resonance parameters (energy, $3\alpha$-decay width, and transition strength) of $3\alpha$ resonance states are extracted. Dependencies of these observables on interaction potential models are studied to examine the introduced interaction models. Using the transition strength distributions, excitation-energy spectra in the ${}^{12}\mathrm{C}(\alpha ,{\alpha }^{\prime })3\alpha$ reaction are calculated to compare with experimental data.

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• Inelastic scattering reactions
• Nuclear reactions
• 6 ≤ A ≤ 19
• Multipole matrix elements
• Few-body systems