Approximate treatment of electron Coulomb distortion in quasielastic (e,e') reactions

In this paper we address the adequacy of various approximate methods of including Coulomb distortion effects in (e,${\mathit{e}}^{\ensuremath{'}}$) reactions by comparing to an exact treatment using Dirac-Coulomb distorted waves. In particular, we examine approximate methods and analyses of (e,${\mathit{e}}^{\ensuremath{'}}$) reactions developed by Traini et al. using a high energy approximation of the distorted waves and phase shifts due to Lenz and Rosenfelder. This approximation has been used in the separation of longitudinal and transverse structure functions in a number of (e,${\mathit{e}}^{\ensuremath{'}}$) experiments including the newly published $^{208}\mathrm{Pb}$(e,${\mathit{e}}^{\ensuremath{'}}$) data from Saclay. We find that the assumptions used by Traini and others are not valid for typical (e,${\mathit{e}}^{\ensuremath{'}}$) experiments on medium and heavy nuclei, and hence the extracted structure functions based on this formalism are not reliable. We describe an improved approximation which is also based on the high energy approximation of Lenz and Rosenfelder and the analyses of Knoll and compare our results to the Saclay data. At each step of our analyses we compare our approximate results to the exact distorted wave results and can therefore quantify the errors made by our approximations. We find that for light nuclei, we can get an excellent treatment of Coulomb distortion effects on (e,${\mathit{e}}^{\ensuremath{'}}$) reactions just by using a good approximation to the distorted waves, but for medium and heavy nuclei simple additional ad hoc factors need to be included. We describe an explicit procedure for using our approximate analyses to extract so-called longitudinal and transverse structure functions from (e,${\mathit{e}}^{\ensuremath{'}}$) reactions in the quasielastic region. \textcopyright{} 1996 The American Physical Society.