In this paper we address the adequacy of various approximate methods of including Coulomb distortion effects in (e,eЈ) reactions by comparing to an exact treatment using Dirac-Coulomb distorted waves. In particular, we examine approximate methods and analyses of (e,eЈ) 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,eЈ) experiments including the newly published 208 Pb(e,eЈ) data from Saclay. We find that the assumptions used by Traini and others are not valid for typical (e,eЈ) 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,eЈ) 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,eЈ) reactions in the quasielastic region.

In this paper we apply a well-tested approximation of electron Coulomb distortion effects to the exclusive reaction (e, e ′ p) in the quasielastic region.We compare the approximate treatment of Coulomb distortion effects to the exact Distorted Wave Born Approximation evaluated by means of partial wave analysis to gauge the quality of our approximate treatment. We show that the approximate Møller potential has a plane-wave-like structure and hence permits the separation of the cross section into five terms which depend on bi-linear products of transforms of the transition four current elements.These transforms reduce to Fourier transforms when Coulomb distortion is not present, but become modified with the inclusion of Coulomb distortion.We investigate the application of the approximate formalism to a model of 208 P b(e, e ′ p) using Dirac-Hartree single particle wavefunctions for the ground state and relativistic optical model wavefunctions for the continuum proton.We show that it is still possible to extract, albeit with some approximation, the various structure functions from the experimentally measured data even for heavy nuclei.25.30.Fj 25.70.Bc.