Electromagnetic structure of the helium isotopes

Abstract

The elastic-electron scattering cross sections from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ have been measured at incident electron energies between 170 and 750 MeV. Cross sections were separated into their longitudinal (charge) and transverse (magnetic) contributions using the Rosenbluth formula. Values of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ charge form factor have been extracted to $q^2=20\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$ and for the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ magnetic form factor to $q^2=16\mathrm{}$ ${\mathrm{fm}}^{-2\mathrm{}}$. The ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ form factor has been determined up to 6.2 ${\mathrm{fm}}^{-2\mathrm{}}$. Densities for the charge and magnetization have been deduced from phenomenological models used in a phase-shift solution of the Dirac equation. A model-independent determination of the nuclear densities has been performed in order to obtain realistic errors on the extracted distributions. After unfolding the nucleon size from the distributions the point density is shown to have a significant central depression for a radius <0.8 fm for both ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. Comparison of the form factors is made with Faddeev and variational three-body calculations that use realistic two-body $\mathrm{NN}$ interactions. The influence of off-shell effects, three-body forces, meson-exchange corrections, and short-range correlations are discussed. At present no theoretical calculation that uses input derived entirely from nucleon-nucleon scattering is able to reproduce the experimental data.