Three-nucleon bound states and the Wigner-SU(4) limit

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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 (EFT) that is an expansion in powers of R/a, with R the range of the nuclear force and a the nucleon-nucleon (NN) 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 NN scattering lengths gives a ³H point charge radius of 1.58 fm, which is remarkably close to the experimental number, 1.5978±0.040 fm (Angeli and Marinova in At Data Nucl Data Tables 99:69-95, 2013). For the ³He point charge radius we find 1.70 fm, about 4% away from the experimental value of 1.77527±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.