Coulomb Effects and Wigner-SU(4) Symmetry in He-3 Charge and Magnetic Properties

This work studies the non-perturbative Coulomb corrections to the He-3 binding energy, magnetic moment, and charge and magnetic radii in leading-order (LO) Pionless Effective Field Theory (Pionless EFT). The splitting between He-3 and H-3 binding energy is found to be 0.85(3) MeV. The Coulomb corrections to the He-3 point charge radius and full magnetic radius are found to be 0.043(2) fm and 0.036(2) fm, respectively. These corrections are 4% of the LO predictions without Coulomb and should be taken into account at next-to-next-to-leading order or beyond in Pionless EFT to achieve the desired EFT accuracy. The Coulomb correction to the He-3 magnetic moment is found to be -0.0041(1)$\mu_N$, only 0.2% of the LO prediction without Coulomb. The impact of Wigner-SU(4) symmetry in the presence of the non-perturbative Coulomb interaction is also discussed and used to help explain the hierarchy of Coulomb effects in He-3 observables.