Charge and magnetic properties of three-nucleon systems in pionless effective field theory

Abstract

A method to calculate the form factor for an external current with nonderivative coupling for the three-body system in an effective field theory (EFT) of short-range interactions is shown. Using this method, the point charge radius of $^{3}\mathrm{He}$ is calculated to next-to-next-to-leading order ($\mathrm{NNLO}$) in pionless EFT (EFT($\ensuremath{\pi}\phantom{\rule{-9pt}{0ex}}/$)), and the magnetic moment and magnetic radius of $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ are calculated to next-to-leading order (NLO). For the $^{3}\mathrm{He}$ charge and magnetic form factors Coulomb interactions are ignored. The $^{3}\mathrm{He}$ point charge radius is given by 1.74(4) fm at $\mathrm{NNLO}$. This agrees well with the experimental $^{3}\mathrm{He}$ point charge radius of 1.7753(54) fm [Angeli and Marinova, At. Data Nucl. Data Tables 99, 69 (2013)]. The $^{3}\mathrm{H}$ ($^{3}\mathrm{He}$) magnetic moment in units of nuclear magnetons is found to be 2.92(35) $(\ensuremath{-}2.08(25))$ at NLO in agreement with the experimental value of 2.979 ($\ensuremath{-}2.127$). For $^{3}\mathrm{H}$ ($^{3}\mathrm{He}$) the NLO magnetic radius is 1.78(11) fm (1.85(11) fm), which agrees with the experimental value of 1.840(182) fm (1.965(154) fm) [Sick, Prog. Part. Nucl. Phys. 47, 245 (2001)]. The fitting of the low-energy constant ${L}_{1}$ of the isovector two-body magnetic current and the consequences of Wigner-SU(4) symmetry for the three-nucleon magnetic moments are also discussed.