APPROXIMATE TREATMENT OF ELECTRON COULOMB DISTORTION IN QUASI-ELASTIC(E,E') REACTIONS

In this paper we address the adequacy of various approximate methods o f including Coulomb distortion effects in (e,e') reactions by comparin g to an exact treatment using Dirac-Coulomb distorted waves. In partic ular, we examine approximate methods and analyses of (e,e') reactions developed by Traini et al. using a high energy approximation of the di storted waves and phase shifts due to Lent and Rosenfelder. This appro ximation has been used in the separation of longitudinal and transvers e structure functions in a number of (e,e') experiments including the newly published Pb-208 (e,e') data from Saclay. We find that the assum ptions used by Traini and others are not valid for typical (e,e') expe riments on medium and heavy nuclei, and hence the extracted structure functions based on this formalism are not reliable. We describe an imp roved approximation which is also based on the high energy approximati on of Lent and Rosenfelder and the analyses of Knell and compare our r esults to the Saclay data. At each step of our analyses we compare our approximate results to the exact distorted wave results and can there fore 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 quasielast ic region.