Wigner SU(4) symmetry, clustering, and the spectrum of ¹² C

We present lattice calculations of the low-lying spectrum of ¹²C 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 ∼ 15 MeV above the ground state, and explore the structure of each state using a large variety of α cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the α clustering in the Hoyle state and the second 2 ⁺ state of ¹²C. 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 ¹²C system, or the effects of α clustering are diminishing their influence. This is in agreement with previous findings from ab initio shell model calculations.