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Three-Nucleon Bound States and the Wigner-SU(4) Limit

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Abstract

We examine the extent to which the properties of three-nucleon bound states are well-reproduced in the limit that nuclear forces satisfy Wigner’s SU(4) (spin–isospin) symmetry. To do this we compute the charge radii up to next-to-leading order (NLO) in an effective field theory that is an expansion in powers of R/a, with R the range of the nuclear force and a the nucleon–nucleon (\(N\!N\)) scattering lengths. In the Wigner-SU(4) limit, the triton and helium-3 point charge radii are equal. At NLO in the range expansion both are 1.66 fm. Adding the first-order corrections due to the breaking of Wigner symmetry in the \(N\!N\) scattering lengths gives a \({}^3\mathrm {H}\) point charge radius of 1.58 fm, which is remarkably close to the experimental number, \(1.5978\pm 0.040\) fm (Angeli and Marinova in At Data Nucl Data Tables 99:69–95, 2013). For the \({}^3\mathrm {He}\) point charge radius we find 1.70 fm, about 4% away from the experimental value of \(1.77527\pm 0.0054\) fm (Angeli and Marinova 2013). We also examine the Faddeev components that enter the tri-nucleon wave function and find that an expansion of them in powers of the symmetry-breaking parameter converges rapidly. Wigner’s SU(4) symmetry is thus a useful starting point for understanding tri-nucleon bound-state properties.

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  1. Department of Physics and Astronomy, Institute of Nuclear and Particle Physics, Ohio University, Athens, OH, 45701, USA

    Jared Vanasse & Daniel R. Phillips

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  1. Jared Vanasse
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This article belongs to the special issue “30th anniversary of Few-Body Systems”.

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Vanasse, J., Phillips, D.R. Three-Nucleon Bound States and the Wigner-SU(4) Limit. Few-Body Syst 58, 26 (2017). https://doi.org/10.1007/s00601-016-1173-2

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