Triangulating Carbon-12

College best publication award

Evidence for triangular D3h symmetry in 12C was awarded College of Engineering and Physical Sciences Best Publication Award June 2014.

Summary by Carl Wheldon and Tzany Kokalova

Investigations performed by members of the nuclear physics group at the MC40 cyclotron in Birmingham have uncovered a resonance at high-energy, the properties of which suggest that the protons and neutrons are clustered into three alpha particles arranged at the vertices of an equilateral triangle. This is the first time such a symmetry has been observed in nuclei and also a significant step into finally revealing the long sought after structure of the Hoyle state – the nuclear gateway for the synthesis of all heavier elements in the stars.

Carbon-12's pivotal role.
Carbon-12 (6-protons and 6-neutrons) plays a key role in nucleosynthesis and the forging of the elements in stars. The Hoyle state is an excited state of carbon-12 and was discovered experimentally in 1954. Since then scientists all over the world have been trying to establish its underlying structure. It is known that the state is built from three alpha particles, but the precise arrangement of those (e.g. the deformation) is still unknown. Since the experimental discovery of the state there have been many theoretical predictions from a variety of models, both for the ground state and the Hoyle state of carbon-12. In the early 60's it was suggested that the Hoyle state may posses a structure in which the alpha particles are situated in a linear chain whereas recently, ab inito calculations described its structure as more like a bent arm.

Contemporary experimental challenge.
The group at Birmingham used an energetic beam of helium-4 from the MC40 cyclotron to bombard a carbon target. The carbon-nuclei were excited to high energies before disintegrating; ultimately into three alpha-particles. Detecting the energy and direction of the emitted alpha particles enabled the originating excited state in carbon-12 to be reconstructed. The data available indicate a characteristic sequence of states with spins and parities built on the lowest energy level of carbon-12, namely: 0+, 2+, 3–, 4± and 5–. It is the latter of these predicted states, the 5– resonance, that was observed in the Birmingham experiment and provides the compelling evidence for the triangular structure [Physical Review Letters: http://dx.doi.org/10.1103/PhysRevLett.113.012502]. The group have since confirmed the experimental data, in a second measurement using a different reaction [Phys. Rev. C: http://dx.doi.org/10.1103/PhysRevC.90.014319].

Expanding triangles.
The properties of this band of states has been predicted by only one theoretical model developed by Iachello and Bijker that assumes a D3h symmetry, i.e. an equilateral triangular spinning top. The new results confirm a triangular arrangement of the alpha-particles in carbon-12, the first time such a symmetry has been observed in nuclear physics.
Herein lies an important clue to understanding the precise nature of the Hoyle state. The model that predicts the triangular symmetry of the ground-state sequence of levels also predicts the structure of the excited Hoyle resonance to be a stretching mode in which the alpha-particle triangle expands.

The current work and future experiments planned by the group here in Birmingham, may finally uncover the exotic behaviour of one of nature's most unusual isotopes.

Experiment performed by Carl Wheldon, Tzany Kokalova, Martin Freer, Daniel Marín-Lámbarri and David Parker.

Figure created by Martin Freer.