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

Shen, Shihang; Lähde, Timo A.; Lee, Dean; Meißner, Ulf-G.

doi:10.1140/epja/s10050-021-00586-6

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

Journal Article · Mon Sep 20 00:00:00 EDT 2021 · European Physical Journal. A

DOI:https://doi.org/10.1140/epja/s10050-021-00586-6· OSTI ID:1821034

; Lähde, Timo A.; Lee, Dean; Meißner, Ulf-G.

Abstract

We present lattice calculations of the low-lying spectrum of $$$$^{12}$$$$ $^{12}$ C using a simple nucleon–nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner’s SU(4) symmetry. We find strong signals for all excited states up to $$$$\sim 15$$$$ $\sim 15$ MeV above the ground state, and explore the structure of each state using a large variety of $$$$\alpha $$$$ $α$ cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the $$$$\alpha $$$$ $α$ clustering in the Hoyle state and the second $$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.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0013365

OSTI ID:: 1821034

Alternate ID(s):: OSTI ID: 1851786
OSTI ID: 23076435

Journal Information:: European Physical Journal. A, Journal Name: European Physical Journal. A Journal Issue: 9 Vol. 57; ISSN 1434-6001

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Germany

Language:: English

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