Form Factors in Electron-Trinucleon Scattering

We analyze the four form factors in electron-trinucleon ($e$-${\mathrm{H}}^{3}$ or $e$-${\mathrm{He}}^{3}$) elastic scattering using two alternative sets of four unknowns: (i) the neutron electric form factor, the form factor ${F}_{1}$ for the dominant $S$ state, and the isovector- and isoscalar-exchange magnetic form factors---here we neglect the mixed symmetry ${S}^{\ensuremath{'}}$ state; (ii) the form factors ${F}_{O}$ and ${F}_{L}$ for odd and like nucleons, and the isovector- and isoscalar-exchange magnetic form factors---here we assume knowledge of the neutron electric form factor, essentially 0.02 ${q}^{2}$ in our region. The first alternative gives positive neutron electric form factors that seem somewhat high; the second alternative gives a plausible value of 1% for the probability of the mixed-symmetry ${S}^{\ensuremath{'}}$ state, and also gives a reasonable shape for the isovector-exchange form factor. The isoscalar-exchange form factor stays less than 0.06 nm. We find good agreement between our results for ${F}_{1}$ and calculations based on three different wave functions adjusted to give the experimental Coulomb energy.