Elastic and Inelastic Electron Scattering from Nuclear Multipole Moments in the First-Order Born Approximation

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Abstract
We consider elastic and inelastic scattering of electrons from deformed light nuclei in the Born approximation. For the elastic scattering case, we develop the most general expression for the cross section in terms of the electric and magnetic multipole moments of the nuclear ground state and the corresponding form factors, which are expressed by the (spectroscopic) moments of charge and magnetization distributions. For the inelastic scattering case, the transition form factors are similarly expressed by transition multipole densities of charge, current, and magnetization in the most general fashion. We also develop a model of collective vibrations of deformed ground-state charge and magnetization densities which, in the case of charge vibrations, explains present data and predicts the filling in of inelastic diffraction minima; in the case of vibration of magnetization, corresponding transitions are shown to appear at large momentum transfers only, where they may be identified as such by the action of selection rules. In the Appendices, we consider relations between spectroscopic and intrinsic quantities, consider static deformed and Helmtype models, and discuss charge and magnetic radii. In addition, the previously derived generalized Helm model is rederived in a simple fashion.