Cluster states in nuclei as representations of a U(n+1) group

Abstract

We propose a description of cluster states in nuclei in terms of representations of unitary algebras U(n+1), where n is the number of space degrees of freedom. Within this framework, a variety of situations including both vibrational and rotational spectra, soft and rigid configurations, identical and non-identical constituents can be described. As an example, we show how the method can be used to study alpha-clustering configurations in 12C with point group symmetry D(3h).

5 pages, 2 figures, Phys. Rev. C, in press

References in corpus (2)

• Algebraic models of hadron structure: I. Nonstrange baryons
• Spectrum Generating Algebra for X${}_3$ Molecules

Cited by in corpus (37)

• Evidence for Triangular D_3h Symmetry in 12C
• Evidence for tetrahedral symmetry in 16O
• The algebraic cluster model. Three-body clusters
• Status of Alpha-Particle Condensate Structure of the Hoyle State
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• Alpha particle clusters and their condensation in nuclear systems
• The Algebraic Cluster Model: Structure of 16O
• Structure of low-lying 12C-resonances
• Alpha cluster structures and monopole excitations in ${}^{13}$C
• Cluster structure of light nuclei
• Origin of Low-Lying Enhanced E1 Strength in Rare-Earth Nuclei
• Nonlocalized Clustering and Evolution of Cluster Structure in Nuclei
• Evidence for Triangular D'(3h) Symmetry in 13C
• 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
• Electromagnetic selection rules in the triangular alpha-cluster model of 12C
• Investigating the predicted breathing-mode excitation of the Hoyle state
• Geometrical symmetries of nuclear systems: D(3h) and T(d) symmetries in light nuclei
• Shape of 13C studied by the real-time evolution method
• Cluster structure of 21Ne and 21Na
• Higher-rank discrete symmetries in the IBM. I Octahedral shapes: general Hamiltonian
• Unbound states in ${}^{12}$C populated by $\gamma$-decay of the $(J^{\pi },T)=(2^{+},1)$ 16.11 MeV state
• Consistent alpha-cluster description of the 12C (0^+_2) resonance
• Discrete symmetries in the cluster shell model
• Symmetries and order in cluster nuclei
• Magnetic dipole moments as a strong signature for $\alpha$-clustering in even-even self-conjugate nuclei
• First order Coriolis-coupling for rotational spectrum of a tetrahedrally-deformed core plus one-particle system
• Shape of 12C
• Signatures of $\alpha$-clustering in ${}^{12}$C and ${}^{13}$C
• Electromagnetic transitions in the algebraic cluster model
• Odd-mass nuclei in the cluster shell model
• Splitting of single-particle levels in clusters potentials
• States of the ${}^{12}$C Nucleus in the Toroidal Configuration
• Nuclear lattice simulations: Status and perspectives
• Geometric symmetries in light nuclei
• Triangular symmetry in cluster nuclei
• Algebraic cluster models calculations for shape phase transitions of boson-fermion systems