The Algebraic Cluster Model: Three-Body Clusters

Abstract

A new method is introduced to study three-body clusters. Triangular configurations with D 3h point-group symmetry are analyzed. The spectrum, transition form factors and B(Eλ) values of 12 C are investigated. It is concluded that the low-lying spectrum of 12 C can be described by three alphaparticles 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.

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

“…Algebraic models have been developed by Bijker and Iachello [18,19] with the aim to describe the discrete symmetries D 3h and T d associated with alpha-particles in a triangular or tetrahedral configuration. This approach has attracted renewed interest in view of novel experimental evidence recently found in 12 C and 16 O [20,21].…”

Evidence for Triangular D3h Symmetry in C12Marín-Lámbarri1, Bijker2, Freer3 et al. 2014Phys. Rev. Lett.Self Cite211142442View full textAdd to dashboardCite

“…atomic H + 3 molecule [4] where the predicted spectrum of a triangular oblate spinning top with a D 3h Symmetry was observed [1,2,4]. It was suggested [1,2] that the three alpha-particle system of 12 C should lead to similar "triatomic like" structure in nuclei.…”

The structure of the Hoyle state and its 2+partner state in12C

“…Both ab-initio no core shell model calculations [7] and EFT calculations [9] predict the Hoyle state to be of deformed prolate shape. In addition while the FMD model predicts an rms radius of the Hoyle state (3.48 fm) that is √ 2 larger than the ground state (2.39 fm) [4], calculations in the frame of the ab-initio EFT theory [9] predicts an rms radius (2.4 fm) equal (within the predicted error bar) to the rms radius of the ground state of 12 C and the ab-initio no core shell model calculations [7] predict an rms radius (2.93 fm) that is only 22% larger than the ground state of 12 C. The three alpha-particle structure of 12 C naturally leads to models that utilize triangular geometry [3,4,8,9]. Such triangular systems are ubiquitous in physics including the X 3 molecular system [10], and the three quark system [11,12] and their spectrum resemble the one predicted by the oblate spinning top with a D 3h symmetry [10,11].…”

“…Such triangular systems are ubiquitous in physics including the X 3 molecular system [10], and the three quark system [11,12] and their spectrum resemble the one predicted by the oblate spinning top with a D 3h symmetry [10,11]. The rotation-vibration spectrum predicted for the triangular three alpha-particle oblate spinning top appears to be a very useful phenomenological framework to discuss the (rotationvibration) spectrum of the three alpha-particle system of 12 C [3]. It is phenomenological schematic model (e.g.…”

“…A number of models have been proposed to describe the structure of 12 C including a group theoretical U(7) model with a D 3h symmetry [3], a microscopic Fermionic Molecular Dynamic (FMD) model [4] together with "BEC-like" cluster model [5], ab-initio no core shell model [6,7], and ab-initio lattice Effective Field Theory (EFT) [8,9]. It is shown by the ab-initio no core shell model calculations that the Hoyle state can only be described by a 10 ω shell model space [7], suggesting that it is an extended alphaclustering configuration.…”