Electron Coulomb effects in quasielastic (e,e’p) reactions

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 ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(e,e’p) reaction in both parallel and ω-q constant kinematics. We find that electron Coulomb distortion has a smaller effect in ω-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 ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(e,e’p) experimental data. We also calculate the reduced cross section for the 3${\mathit{s}}_{1/2}$ state in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ 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%.