# Synopsis: Carbon-12 Caught in a Triangle

#### Evidence for Triangular D3h Symmetry in 12C

D. J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, Tz. Kokalova, D. J. Parker, and C. Wheldon

Published June 30, 2014

Carbon-12 (${}^{12}\text{C}$), like many nuclei, doesn’t conform to the simple picture of the nucleus as a homogenous distribution of protons and neutrons. Instead, its nucleons are thought to cluster into alpha particles (two protons and two neutrons) that arrange into an equilateral triangle, a configuration with ${\mathcal{D}}_{3h}$ symmetry. Several observed nuclear excitations support this picture. Now, Daniel Jose Marin-Labarri at the University of Birmingham, UK, and his colleagues report in Physical Review Letters the measurement of a new state that provides additional evidence for the triangular cluster model of ${}^{12}\text{C}$. The finding could point physicists to more accurate models of carbon’s structure, which are needed to better understand carbon nucleosynthesis.

Working at the Birmingham cyclotron facility, the researchers used a beam of high-energy helium-$4$ to excite and break apart the nuclei in a carbon target. By measuring the momenta of the emitted alpha particles they were able to reconstruct the energy levels of the carbon nuclei. Models of ${}^{12}\text{C}$ that assume it has ${\mathcal{D}}_{3h}$ symmetry predict a band of rotational states (think of a spinning top) having spin and parity, ${0}^{+},{2}^{+},{3}^{-},{4}^{±}$ and ${5}^{-}$; Marin-Lambarri and his colleagues observed the last of these, ${5}^{-}$, at an energy of $22.4$ mega-electron-volts.

The measurement could lead to a better understanding of the Hoyle state—an excited state of carbon-12, essential for nucleosynthesis. If, as Marin-Labarri’s data suggest, the ${\mathcal{D}}_{3h}$ cluster model is the right one, the Hoyle state is due to a breathing mode excitation of the triangular configuration. But this contradicts the findings of ab initio calculations (see 9 May 2011 Viewpoint), which suggest that the spatial structure of the Hoyle state is more like a linear chain of three alpha clusters. Future measurements of other states predicted by the two differing models are needed to decide which one best describes carbon. – Kevin Dusling