Higher-Order Effects in Electron-Nucleus Scattering

Higher-order effects are calculated in the framework of the eigenchannel theory for elastic and inelastic electron-nucleus scattering in the energy region $100\le E\le 250$ MeV. A dispersion effect of about 12% is found for the elastic scattering on ${\mathrm{Ni}}^{58}$ at a momentum transfer $q\approx 500$ MeV/c. For inelastic scattering, the reorientation effect is discussed, in addition to the dispersion effect. The total higher-order effect changes the form factor for a hindered first-order transition by 50% at its minima. Furthermore, the dependence of the higher-order effects on the transition potentials of the virtual excitations, the model dependence, and the dependence on the energy $E$ of the electron and the momentum transfer $q$ are discussed. A closed formula for the $S$ matrix is developed by calculating the eigenchannels in stationary perturbation theory.