Evidence for Triangular D3h Symmetry in C12

Abstract

We report a measurement of a new high spin J π = 5 − state at 22.4(0.2) MeV in 12 C which fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D 3h symmetry characterized by the sequence 0 + , 2 + , 3 − , 4 ± , 5 − with almost degenerate 4 + and 4 − (parity doublet) states. Such a D 3h symmetry was observed in triatomic molecules and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in 12 C such as the (0 + ) Hoyle band and the (1 − ) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12 C and light nuclei. In particular the observation (or non-observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha-particle composing the Hoyle state at 7.654 MeV in 12 C.

From the Stable to the Exotic: Clustering in Light Nuclei

“…This 2 + 2 state that appears at around 10 MeV is considered to be the 2 + excitation of the "Hoyle" state (in agreement with the previous experimental investigation of Itoh et al [25]) according to the α cluster [30] and α condensation models [22]. On the other hand, the experiment 12 C(α,α) 12 C * carried out at the Birmingham cyclotron [29], UK, populates a new state compatible with an equilateral triangle configuration of three α particles. Still, the structure of the "Hoyle" state remains controversial as experimental results of its direct decay into three α particles are found to be in disagreement [31,32,33,34,35,36].…”

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]. Discrete symmetries associated with alpha-particle clustering, while an important and attractive field of activity, differ from those considered here where they arise in the context of the collective model of the nucleus.…”

“…With reference to Eqs. (20) and (21), the inequalities (40) express the condition that (i) the s-g mixing is strong enough as compared to the energy difference g − s to develop a hexadecapole deformed minimum and (ii) the s-d and d-g mixing is sufficiently weak as compared to the energy differences s − d and g − d , respectively, so as the minimum to remain at β 2 = 0.…”

Alpha particle clusters and their condensation in nuclear systems

“…Other forerunners of α cluster physics with this kind of models were Kameny [21] and Glassgold and Galonsky [22]. The latter discussed energy levels of 12 C calculating the rotations and vibrations of an equilateral triangle arrangement of the three α's, see also a recent application of this idea in [23] discussed below. Several works also tried to solve, e.g., the 3α system in considering the 3-body Schrödinger equation with an effective α-α potential reproducing the α-α phase shifts, see two recent publications [24,25].…”