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