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

Abstract

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.

9 pages, 9 figures, discussion extended, references added

References in corpus (9)

• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Structure and rotations of the Hoyle state
• Dynamics of the linear-chain alpha cluster in microscopic time-dependent relativistic density functional theory
• Spin-orbit decomposition of ab initio wavefunctions
• A stringent upper limit on the direct 3$\alpha$ decay of the Hoyle State in ${}^{12}$C
• Breaking and restoration of rotational symmetry on the lattice for bound state multiplets
• Impurity Lattice Monte Carlo for Hypernuclei
• Effective interactions between nuclear clusters
• Uncertainties of Euclidean Time Extrapolation in Lattice Effective Field Theory

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• A Vision for the Science of Rare Isotopes
• Magnetic dipole moments as a strong signature for $\alpha$-clustering in even-even self-conjugate nuclei
• Searching for the Tetraneutron Resonance on the Lattice
• Controlled Gate Networks: Theory and Application to Eigenvalue Estimation
• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations
• Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation