The carbon atom provides the backbone for the complex organic chemistry composing the building blocks of life. The physics of the carbon nucleus in its predominant isotope, carbon-12, is also full of complexity. Many experimental and theoretical investigations have been devoted to determining the spectrum and structure of the low-lying energy states of carbon-12. One example is the Hoyle state, a narrow resonance whose proximity to the energy threshold for three alpha particles greatly enhances the production of carbon in helium-burning stars.

In “Emergent geometry and duality in the carbon nucleus,” researchers from the University of Bonn (Germany), Forschungszentrum Jülich (Germany), Gaziantep Islamic Science and Technology University (Turkey), Graduate School of China Academy of Engineering Physics (China), Tbilisi State University (Georgia), and FRIB calculated the structure of the nuclear states of carbon-12 using the ab initio framework of nuclear lattice effective field theory. The Hoyle state is composed of a “bent arm” or obtuse triangular arrangement of alpha clusters. All the low-lying states of carbon-12 have an intrinsic shape composed of three alpha clusters forming either an equilateral triangle or an obtuse triangle. The states with the equilateral triangle shape also have a dual description in terms of particle-hole excitations in a mean-field picture.  The results are in good agreement with experimental data and provide the first model-independent density map of the nuclear states of carbon-12.

Dean Lee, professor of physics at FRIB and in Michigan State University’s Department of Physics and Astronomy and head of the Theoretical Nuclear Science department at FRIB, is one of the authors of the paper.

This material is based upon work supported by the U.S. Department of Energy, the German Research Foundation, the European Research Council, the Volkswagen Foundation, the Chinese Academy of Sciences President's International Fellowship Initiative, and the Nuclear Computational Low-Energy Initiative.

Michigan State University (MSU) operates the Facility for Rare Isotope Beams (FRIB) as a user facility for the U.S. Department of Energy Office of Science (DOE-SC), supporting the mission of the DOE-SC Office of Nuclear Physics. User facility operation is supported by the DOE-SC Office of Nuclear Physics as one of 28 DOE-SC user facilities.

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