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

Abstract

Densities and transition densities are computed in an equilateral triangular alpha-cluster model for ${}^{12}$C, 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 DWBA inelastic cross-sections for the ${}^{12}$C$(\alpha ,{\alpha }^{\prime })$ 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.

References in corpus (17)

• Alpha cluster condensation in 12C and 16O
• Properties of ${}^{12}$C in the {\it ab initio} nuclear shell-model
• Microscopic Clustering in Light Nuclei
• Structure and rotations of the Hoyle state
• Structure of ground and excited states of ${}^{12}$C
• Evidence for Triangular D_3h Symmetry in 12C
• Cluster structures within Fermionic Molecular Dynamics
• Evidence for tetrahedral symmetry in 16O
• The algebraic cluster model. Three-body clusters
• Hoyle state and rotational features in Carbon-12 within a no-core shell model framework
• Spectrum Generating Algebra for X${}_3$ Molecules
• The container picture with two-alpha correlation for the ground state of ${}^{12}$C
• Consistency between the monopole strength of the Hoyle state determined by structural calculation and that extracted from reaction observables
• $\alpha$ scattering cross sections on ${}^{12}$C with microscopic coupled-channel calculation
• Folding model analysis of the inelastic $\alpha {+}^{12}$C scattering at medium energies, and the isoscalar transition strengths of the cluster states of ${}^{12}$C
• Electromagnetic selection rules in the triangular alpha-cluster model of 12C
• Breaking and restoration of rotational symmetry in the low-energy spectrum of light alpha-conjugate nuclei on the lattice I: ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$

Cited by in corpus (7)

• Alpha-induced inelastic scattering and alpha-transfer reactions in ${}^{12}$C and ${}^{16}$O within the Algebraic Cluster Model
• Three-$\alpha$ configurations in the $0^{+}$ states of ${}^{12}\mathrm{C}$
• Drastic change in inelastic scattering depending on the development of dineutron correlation in ${}^{10}$Be
• Relation between transition density and proton inelastic scattering by ${}^{12}$C target at $E_p=$ 65 and 200 MeV
• Magnetic dipole moments as a strong signature for $\alpha$-clustering in even-even self-conjugate nuclei
• Three-$\alpha$ configurations of the second $J^{\pi }=2^{+}$ state in ${}^{12}$C
• Shape of 12C