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We describe a calculation for the electron Coulomb distortion efFects in (e,e p ) in the quasielastic region from medium and heavy nuclei. The bound nucleons are described by single-particle Dirac wave functions in the presence of scalar and vector potentials which are parametrized fits to relativistic Hartree potentials, while the wave function of the knocked-out nucleon is a solution to the Dirac equation with the relativistic optical potential. The electron wave functions are solutions to the Dirac equation in the presence of the Coulomb potential of the nucleus and the interaction with the selected nucleon is treated to first order. We examine the Ca(e, e'p) reaction in both parallel and co-q constant kinematics.We find that electron Coulomb distortion has a smaller efFect in co-q constant kinematics than in parallel kinematics. The principal efFect in parallel kinematics is to shift the maximum and minimum of the reduced cross section which is consistent with the experimental data. Occupation numbers of about 70% to 80% are needed to normalize the distorted-wave Born approximation calculation to the~Ca(e, e'p) experimental data. We also calculate the reduced cross section for the 3s&zz state in Pb and compare our results to experimental data and previous calculations. We find no significant difFerence in using relativistic, as compared with nonrelativistic, nuclear wave functions. We do find significant corrections to earlier methods of treating Coulomb distortion which, in turn, afFect the occupation number extracted from experiment. We find an occupation number for this state of 71.4%%uo. PACS number{s): 25.30.c, 24.90.+d

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.

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Optical potentials obtained &om elastic proton scattering have been successfully used to describe the final state interaction in (e, e'p) reactions. However, spectroscopic factors extracted from experimental data are often quite different depending on whether relativistic calculations or nonrelativistic calculations are used. Since the calculation of the (e, e p) cross section requires the wave functions of the outgoing proton in the nuclear interior, different optical potential models could cause the differences in these calculations. We use a model which can take either nonrelativistic or relativistic optical potentials while keeping all other aspects of the calculation the same, and 6nd that a relativistic optical potential compared with a nonrelativistic optical potential can cause a difference as much as 14%. We examined several optical models as well as the use of the Percy factor in nonrelativistic calculations.PACS number(s): 25.30.Bf, 24.10.Ht, 27.40.+z Exclusive (e, e'p) experiments in the quasielastic region have been proven to be a good tool for studying single-particle properties of the nucleus, and have provided a testing ground for difFerent nuclear models [1,2].During the past few years, several high-resolution experiments have been carried out on medium/heavy nuclei at NIKHEF-K [2 -6), Amsterdam. The analysis of these experimental data yields information on the single-particle wave functions and spectroscopic factors of the target nuclei. Generally, the analysis is carried out within the framework of either a relativistic distorted wave Born approximation (RDWBA) [7,8] or a nonrelativistic distorted wave Born approximation (DWBA) or Impulse approximation (DWIA) [9,10]. Both models can provide good descriptions of the data. However the extracted spectroscopic factors based on these two models are often quite different: for example, for Ca and Pb target nuclei, the relativistic model generally requires a spectroscopic factor which is about 10 -20%%up larger than the nonrelativistic model. The models require a bound-state wave function (@s) and an optical potential (usually Rom elastic proton scattering) for the outgoing proton wave function (gy), to calculate the single particle nucleon transition current where J" is the &ee nucleon current operator. Since the various components that go into these two model calculations are from different origins, any of the components (for example, the bound-state wave function, the optical potential for the final-state interaction, the form of the current operator, the use of a Percy nonlocal factor, or the electron Coulomb distortion, etc. ) could be the reason for the difFerence. In this paper we compare the use of difFerent outgoing proton wave functions generated by difFerent optical potentials which are or could be used in these calculations.In the relativistic DWBA calculations, a global phenoxnenological optical potential developed by Clark and co-workers is usually used [ll). There are several new versions of these global optical potentials [12] which...