The algebraic cluster model. Three-body clusters

Abstract

A new method is introduced to study three-body clusters. Triangular configurations with ${\mathcal{D}}_{3h}$ point-group symmetry are analyzed. The spectrum, transition form factors and $B(E\lambda )$ values of ${}^{12}$C are investigated. It is concluded that the low-lying spectrum of ${}^{12}$C can be described by three alpha-particles at the vertices of an equilateral triangle, but not as a rigid structure. Large rotation-vibration interactions, Coriolis forces and vibration-vibration interactions are needed. Other interpretations, such as the harmonic oscillator and a soft deformed oscillator with SO(6) hyperspherical symmetry, appear to be excluded by electron scattering data.

31 pages, 10 figures, 5 tables. Annals of Physics (N.Y.), in press

References in corpus (4)

• Algebraic models of hadron structure: I. Nonstrange baryons
• Cluster states in nuclei as representations of a U(n+1) group
• Spectrum Generating Algebra for X${}_3$ Molecules
• Algebraic treatment of three-body problems

Cited by in corpus (47)

• Microscopic Clustering in Light Nuclei
• Evidence for Triangular D_3h Symmetry in 12C
• Unambiguous Identification of the Second 2+ State in 12C and the Structure of the Hoyle State
• Evidence for tetrahedral symmetry in 16O
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• The Algebraic Cluster Model: Structure of 16O
• Alpha cluster structures and monopole excitations in ${}^{13}$C
• Cluster structure of light nuclei
• The long and winding road from chiral effective Lagrangians to nuclear structure
• Nonlocalized Clustering and Evolution of Cluster Structure in Nuclei
• Evidence for Triangular D'(3h) Symmetry in 13C
• A stringent upper limit on the direct 3$\alpha$ decay of the Hoyle State in ${}^{12}$C
• Angular momentum and parity projected multidimensionally constrained relativistic Hartree-Bogoliubov model
• Multi-cluster dynamics in ${}_{\Lambda }^{13}\mathrm{C}$ and analogy to clustering in ${}^{12}\mathrm{C}$
• Cluster structure of 20Ne: Evidence for D(3h) symmetry
• 12C within the Semimicroscopic Algebraic Cluster Model
• Influence of nuclear structure in relativistic heavy-ion collisions
• Electromagnetic selection rules in the triangular alpha-cluster model of 12C
• Investigating the predicted breathing-mode excitation of the Hoyle state
• Nonlocalized motion in two-dimensional container of $\alpha$ particles in $3^{-}$ and $4^{-}$ states of ${}^{12}$C
• Transition densities and form factors in the triangular $\alpha$-cluster model of ${}^{12}$C with application to ${}^{12}$C+$\alpha$ scattering
• Geometrical symmetries of nuclear systems: D(3h) and T(d) symmetries in light nuclei
• Alpha-induced inelastic scattering and alpha-transfer reactions in ${}^{12}$C and ${}^{16}$O within the Algebraic Cluster Model
• Three-body bremsstrahlung and the rotational character of the 12C-spectrum
• Phenomenological and microscopic cluster models II. Phase transitions
• 16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle
• The Hoyle Family: The search for alpha-condensate states in light nuclei
• Higher-rank discrete symmetries in the IBM. I Octahedral shapes: general Hamiltonian
• Cluster structure of 21Ne and 21Na
• Electromagnetic transition rates of Carbon-12 and Oxygen-16 in rotational-vibrational models
• 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
• Discrete symmetries in the cluster shell model
• First order Coriolis-coupling for rotational spectrum of a tetrahedrally-deformed core plus one-particle system
• Signatures of $\alpha$-clustering in ${}^{12}$C and ${}^{13}$C
• New Procedure for Evaluation of U(3) Coupling and Recoupling Coefficients
• Symmetries and order in cluster nuclei
• Three-$\alpha$ configurations of the second $J^{\pi }=2^{+}$ state in ${}^{12}$C
• Magnetic dipole moments as a strong signature for $\alpha$-clustering in even-even self-conjugate nuclei
• Electromagnetic transitions in the algebraic cluster model
• Odd-mass nuclei in the cluster shell model
• Exploring the Diversity of Nuclear Density through Information Entropy
• States of the ${}^{12}$C Nucleus in the Toroidal Configuration
• Splitting of single-particle levels in clusters potentials
• Quantum Phase Transitions within a nuclear cluster model and an effective model of QCD
• Triangular symmetry in cluster nuclei
• Algebraic cluster models calculations for shape phase transitions of boson-fermion systems
• Geometric symmetries in light nuclei