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

TL;DR

This paper investigates how well three-nucleon bound states are described by Wigner's SU(4) symmetry using effective field theory, finding close agreement with experimental charge radii after symmetry-breaking corrections.

Contribution

It demonstrates that Wigner-SU(4) symmetry provides a good approximation for tri-nucleon properties, with effective field theory calculations closely matching experimental data.

Findings

Charge radii are nearly equal in the SU(4) limit.

First-order symmetry-breaking corrections improve agreement with experiment.

Rapid convergence of wave function components in symmetry-breaking expansion.

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 (EFT) 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, $1.5978\pm0.040$ 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 $1.77527\pm0.0054$ 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.