Analytic Distorted-Wave Approximation for High-Energy Electron Scattering Calculations

A three-dimensional WKB approximation for high-energy electron scattering on nuclei is derived and approximated analytically in the vicinity of the nucleus. This approximation contains five parameters which can be calculated from the charge distribution and are not adjustable. It is applied here to calculations of elastic scattering and monopole and quadrupole excitation; the method employed involves an asymptotic expansion in inverse powers of $\mathrm{qR}$, where $q$ is the momentum transfer and $R$ is the nuclear radius. In spite of the several approximations, the calculations reproduce qualitatively all the features of the exact results, such as position and filling in of diffraction minima, and they are quantitatively very good as well. Although the charge and excitation distributions treated here are somewhat idealized, it should be straightforward to extend the results to more realistic situations.