Thursday·June 10, 2021

[Submitted on 9 Jun 2021]

Wigner SU(4) symmetry, clustering, and the spectrum of ${}^{12}$C

Shihang Shen🇩🇪 · Timo A. Lähde🇩🇪 · Dean Lee🇺🇸 · Ulf-G. Meißner🇩🇪

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