Effects of Coulomb distortion and final state interaction on the fourth and fifth structure functions

We examine the question of whether the fourth and fifth structure functions (called ${\mathrm{W}}_{\mathrm{LT}}$ and ${\mathrm{W}}_{\mathrm{LT}\prime }$) defined by the plane wave Born approximation (PWBA) for the reaction (e,e′p) are still meaningful quantities in the presence of electron Coulomb distortion. For a heavy target (${\mathrm{Pb}}^{208}$), the apparent structure functions obtained in the presence of the electron Coulomb distortion have shapes (in terms of the number of maxima or minima) similar to those defined in PWBA; however, the magnitudes are changed greatly. For the fourth structure function, the distortion can change the magnitude, even for ${\mathrm{O}}^{16}$, by more than 15%. For proton knockout from (l±12) spin-orbit doublet states, the changes caused by electron distortion have opposite effects, increasing the magnitude of the one while decreasing the other. The Coulomb effects on the fifth structure function depend on the out of plane angle used in the extraction. For a small angle (e.g., 10°), the electron distortion can be more than 15% in ${\mathrm{O}}^{16}$. However, for certain kinematic choices, the Coulomb distortion effects on the fifth structure function can largely be removed. For proton knockout from spin-orbit doublet states the ratio of the fifth structure functions is of interest. We find that this ratio is nearly independent of the central part of the proton final state interaction and has the power of investigating the spin-orbit interaction of optical potentials.