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

Abstract

We 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.

Emergent geometry and duality in the carbon nucleus

“…For comparison we show the experimental data (black stars) 40 and results from our previous work with lattice spacing a = 1.64 fm (blue circles) and a = 1.97 fm (green pentagons), which were performed without three-nucleon forces. 38 Overall, the agreement with the empirical results is quite good. The triangular shapes surrounding the data points are explained later in Table 1.…”

“…The grey shaded regions indicate decay widths for cases where it has been measured. Previous results for lattice spacing a = 1.64 fm (blue circles) and a = 1.97 fm (green pentagons) are also shown 38. The triangular shapes indicate the intrinsic shape of each nuclear state, either equilateral or obtuse triangle arrangements of alpha clusters.…”

“…36 Perhaps most importantly, it reproduces the low-energy spectrum of 12 C well. 38 Lattice methods: For the lattice simulations presented here, we use a spatial lattice spacing a = 1.64 fm and a temporal lattice spacing of a t = 0.55 fm/c, where c is the speed of light. While the individual nucleons must reside on lattice sites, the center of mass (c.m.)…”

Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations

“…Numerous calculations of nuclear structure and many-body systems have been performed, in particular the structure of alpha cluster states such as the Hoyle state in 12 C [26,27,33,75] as well as states in 16 O [28]. As most other ab initio methods have difficulty computing such highly-correlated alpha cluster states, these works provide strong scientific justification for continuing efforts in lattice chiral effective field theory.…”

Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations

“…Numerous calculations of nuclear structure and many-body systems have been performed, in particular the structure of alpha cluster states such as the Hoyle state in 12 C [33,26,27,75] as well as states in 16 O [28]. As most other ab initio methods have difficulty computing such highly-correlated alpha cluster states, these works provide strong scientific justification for continuing efforts in lattice chiral effective field theory.…”