Emergent geometry and duality in the carbon nucleus

Abstract

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, ${}^{12}$C, is similarly full of multifaceted complexity. Some nuclear states of ${}^{12}$C can be preferentially treated as a collection of independent particles held by the mean field of the nucleus, while other states behave more as a collection of three alpha-particle clusters. But these two pictures are not mutually exclusive, and some states can be described in either fashion${}^{1,2}$. In this work, we provide the first model-independent tomographic scan of the three-dimensional geometry of the nuclear states of ${}^{12}$C using the {\it ab initio} framework of nuclear lattice effective field theory. We find that the well-known but enigmatic Hoyle state is composed of a "bent-arm" or obtuse triangular arrangement of alpha clusters. We identify all of the low-lying nuclear states of ${}^{12}$C as having an intrinsic shape composed of three alpha clusters forming either an equilateral triangle or an obtuse triangle. From these basic structural formations, the various nuclear states correspond to different rotational and vibrational excitations as well as either distortions or large-amplitude displacements of the alpha clusters. The states with the equilateral triangle formation also have a dual description in terms of particle-hole excitations in the mean-field picture. We compare our theoretical calculations with experimental data for binding energies, quadrupole moments, electromagnetic transitions, charge densities, and form factors. The overall agreement is good, and further studies using higher-fidelity interactions are planned.

7+9 pages, 2+8 figures, discussion extended, references added. See final published version in Nature Communications for results that include ab initio N2LO chiral interactions

References in corpus (12)

• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Structure and rotations of the Hoyle state
• Evidence for Triangular D_3h Symmetry in 12C
• Shell-model study of boron, carbon, nitrogen and oxygen isotopes based on monopole-based-universal interaction
• Rod-shaped Nuclei at Extreme Spin and Isospin
• Pair decay width of the Hoyle state and carbon production in stars
• Density Functional Theory studies of cluster states in nuclei
• Breathing-like excited state of the Hoyle state in ${}^{12}\mathrm{C}$
• A stringent upper limit on the direct 3$\alpha$ decay of the Hoyle State in ${}^{12}$C
• Wigner SU(4) symmetry, clustering, and the spectrum of ${}^{12}$C
• Investigating the predicted breathing-mode excitation of the Hoyle state
• Precision measurement of the $E2$ transition strength to the 2${}_1^{+}$ state of ${}^{12}$C

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