Electromagnetic Form Factors of ${\mathrm{H}}^3$ and ${\mathrm{He}}^3$ with Realistic Potentials

The charge and magnetic form factors of ${\mathrm{H}}^3$ and ${\mathrm{He}}^3$ have been calculated on the lines of Schiff's analysis for the problem. The three-body wave functions used for this purpose are the ones which had earlier been derived in an exact fashion by the authors, using separable potentials involving central as well as tensor forces. These wave functions are all characterized by a small $S^{\prime }$-state probability (∼1%). The calculations of the form factors and their corresponding radii have been carried out (a) for pure $s$-wave forces, and (b) for tensor forces, using the potential parameters of both Yamaguchi and Naqvi. It has been found that, whereas the agreement with experiment for pure $s$-wave forces is poor, the inclusion of tensor forces improves the results considerably, so that they fall short of experimental values by not more than about 10%, which is fully within the scope of hard-core effects. To account for the appreciable difference (∼0.17 F) between the charge radii of ${\mathrm{He}}^3$ and ${\mathrm{H}}^3$, we require a positive value for the slope of neutron charge distribution, which is in agreement with the recent analysis from inelastic electron-deuteron scattering. A reasonable value for this slope, deduced from deuteron-scattering data, however, accounts for only about 0.1 F of this difference in the two radii. The remaining difference of about 0.07 F could probably be ascribed to hard-core effects, electromagnetic violations of charge independence, and effects of exchange moments.