https://doi.org/10.1140/epja/s10050-021-00586-6
Regular Article - Theoretical Physics
Wigner SU(4) symmetry, clustering, and the spectrum of 
C
1
Institut für Kernphysik, Institute for Advanced Simulation and Jülich Center for Hadron Physics, Forschungszentrum Jülich, 52425, Jülich, Germany
2
Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, 48824, East Lansing, MI, USA
3
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany
4
Tbilisi State University, 0186, Tbilisi, Georgia
Received:
14
June
2021
Accepted:
6
September
2021
Published online:
20
September
2021
We present lattice calculations of the low-lying spectrum of C using a simple nucleon–nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner’s SU(4) symmetry. We find strong signals for all excited states up to 
MeV above the ground state, and explore the structure of each state using a large variety of 
cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the clustering in the Hoyle state and the second 
state of C. The success of these calculations to describe the full low-lying energy spectrum using spin-independent interactions suggest that either the spin-orbit interactions are somewhat weak in the C system, or the effects of clustering are diminishing their influence. This is in agreement with previous findings from ab initio shell model calculations.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
