AbstractWe present lattice calculations of the low-lying spectrum of $$^{12}$$
12
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 $$\sim 15$$
∼
15
MeV above the ground state, and explore the structure of each state using a large variety of $$\alpha $$
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 $$\alpha $$
α
clustering in the Hoyle state and the second $$2^+$$
2
+
state of $$^{12}$$
12
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 $$^{12}$$
12
C system, or the effects of $$\alpha $$
α
clustering are diminishing their influence. This is in agreement with previous findings from ab initio shell model calculations.
The structure of the Hoyle state and its 2+partner state in12C