Theory of the Electromagnetic Form Factors ofH3andHe3

Abstract

A theoretical background is provided for recent experiments on the elastic scattering of high-energy electrons from ${\mathrm{H}}^{3}$ and ${\mathrm{He}}^{3}$. Formulas are derived on the basis of the isotopic spin formalism that relate the observed electric charge and magnetic moment form factors for the two nuclei to the charge and moment form factors of the proton and neutron, two form factors that describe the spatial distributions of the centers of the like pair of nucleons and the odd nucleon (body form factors), and an exchange magnetic moment form factor that is to be determined empirically. The body form factors are then calculated analytically for three assumptions as to the dependence of the wave function on the internucleon distances. Two parameters appear in the calculations with each wave function: a size parameter, and the amplitude of the mixed-symmetry $S$ state that, together with the dominant fully space-symmetric $S$ state, forms the nuclear ground state. The sign of this amplitude predicted on the basis of the known spin-dependent two-nucleon interaction is found to agree with the electron scattering experiments, and its magnitude is reasonable. The available experimental data show a definite preference for the Gaussian and Irving forms of wave function over a modified exponential form, and a slight preference for the Irving over the Gaussian form. The size parameters obtained for these two wave functions are in good agreement with those obtained from the Coulomb energy of ${\mathrm{He}}^{3}$, and the probability of the mixed-symmetry $S$ state is found to be about 4%.