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We examine the extent to which the properties of three-nucleon bound statesare 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 tonext-to-leading order (NLO) in an effective field theory (EFT) that is anexpansion 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, thetriton and Helium-3 point charge radii are equal. At NLO in the range expansionboth are $1.66$ fm. Adding the first-order corrections due to the breaking ofWigner symmetry in the $N\!N$ scattering lengths gives a ${}^3\mathrm{H}$ pointcharge radius of $1.58$ fm, which is remarkably close to the experimentalnumber, $1.5978\pm0.040$ fm (Angeli and Marinova in At Data Nucl Data Tables99:69-95, 2013). For the ${}^3\mathrm{He}$ point charge radius we find $1.70$fm, about 4% away from the experimental value of $1.77527\pm0.0054$ fm (Angeliand Marinova 2013). We also examine the Faddeev components that enter thetri-nucleon wave function and find that an expansion of them in powers of thesymmetry-breaking parameter converges rapidly. Wigner's SU(4) symmetry is thusa useful starting point for understanding tri-nucleon bound-state properties.

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