Sum Rules for Inelastic Electron Scattering

Sum rules are constructed for the analysis of inelastic electron scattering at high energy (∼150 Mev) from light nuclei. Effects taken into account are: nucleon charge, recoil, and magnetic-moment currents; exchange currents; finite nucleon size; nuclear center-of-mass motion; and the kinematical factors describing the correct relation between initial and final electron energies, the scattering angle, and the nuclear excitation energy. It appears that a sensitive test of the role of exchange currents in the nuclear ground state is provided by a sum rule for the energy-weighted cross section for fixed-momentum transfer: ${\sigma }_E=\int \stackrel{}{\left|\mathrm{q}\right|=\mathrm{const}}\epsilon \sigma (\epsilon , q)d\epsilon .$