QuasielasticCa40(e,e’p) cross sections in a many-particle self-consistent Hartree model

A fully distorted partial-wave calculation is presented for the reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(e,e’p${)}^{39}$K which uses relativistic self-consistent Hartree wave functions for both the target nucleus and the residual nucleus. The final state interaction of the knocked-out nucleon is described by an optical potential and the Coulomb distortion of the electron wave functions is also included. We assume standard values for meson coupling constants and masses in the Hartree calculations and the optical potential used comes from global fits to elastic proton scattering; hence, this calculation is a description of (e,e’p) reactions with no free parameters. We examine the proton knocked-out from the ${\mathit{d}}_{3/2}$ state of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ which leaves the residual nucleus ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ in its ground state. Agreement with the experimental data of NIKHEF is good and the calculated spectroscopic factor agrees very well with the one extracted from experiment. There seems to be no need to make the assumption that the ${\mathit{d}}_{3/2}$ state is appreciably depleted. We also calculate the (e,e’p) cross section from the 2${\mathit{s}}_{1/2}$ and 1${\mathit{f}}_{7/2}$ orbitals. For the 2${\mathit{s}}_{1/2}$ orbital the shape does not agree so well with the experimental data. The ${\mathit{f}}_{7/2}$ orbital leads to approximately the correct shape and we extract a spectroscopic factor of 3.7%.