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

Journal Article · Wed Sep 01 04:00:00 EDT 2021 · European Physical Journal. A

DOI:https://doi.org/10.1140/epja/s10050-021-00586-6· OSTI ID:1851786

Shen, Shihang ^[1]; Lähde, Timo A.; Lee, Dean; Meißner, Ulf-G.

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1. OSTI

We present lattice calculations of the low-lying spectrum of$$$$^{12}$$$$ ${}^{12}$ C using a simple nucleon–nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner’s SU(4) symmetry. We find strong signals for all excited states up to$$$$\sim 15$$$$ $~15$  MeV above the ground state, and explore the structure of each state using a large variety of$$$$\alpha $$$$ $\alpha$ cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the$$$$\alpha $$$$ $\alpha$ clustering in the Hoyle state and the second$$2^+$$ $2^{+}$ state of$$$$^{12}$$$$ ${}^{12}$ C. The success of these calculations to describe the full low-lying energy spectrum using spin-independent interactions suggest that either the spin-orbit interactions are somewhat weak in the$$$$^{12}$$$$ ${}^{12}$ C system, or the effects of$$$$\alpha $$$$ $\alpha$ clustering are diminishing their influence. This is in agreement with previous findings fromab initioshell model calculations.

• Research Organization: Michigan State Univ., East Lansing, MI (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: SC0013365
• OSTI ID: 1851786
• Journal Information: European Physical Journal. A, Journal Name: European Physical Journal. A Journal Issue: 9 Vol. 57; ISSN 1434-6001
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

Physics