Model-Independent Analysis of Inelastic Electron Scattering from Nuclei. II. Monopole Excitations at Arbitrary Momentum Transfer

A partial-wave calculation of inelastic electron scattering from nuclei is carried out analytically to second order in $\alpha Z$. The calculation is performed in a model-independent way, and it is therefore possible to display explicitly the connection between the differential cross section and the transition charge, as well as the ground-state charge distribution. Inelastic monopole cross sections are derived for both high and low energies and for arbitrary momentum transfers. The results are compared with the results of exact numerical calculations for given nuclear models. Good agreement is found for medium-heavy ($Z=38\mathrm{}$) and heavy ($Z=38\mathrm{}$) nuclei. It is also found that our results agree with the results of a WKB approximation, which has been obtained for a simple nuclear model and for high momentum transfer.