Relativistic corrections to the elastic electron scattering fromPb208

In the present work we have calculated the differential cross sections for the elastic electron scattering from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ using the charge distributions resulting from various corrections. The point proton and neutron mass distributions have been calculated from the spherical wave functions for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ obtained by Kolb et al. The relativistic correction to the nuclear charge distribution coming from the electromagnetic structure of the nucleon has been accomplished by assuming a linear superposition of Gaussian shapes for the proton and the neutron charge form factor. Results of this calculation are quite similar to an earlier calculation by Bertozzi et al., who have used a different wave function for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and have assumed exponential smearing for the proton corresponding to the dipole fit for the form factor. Also in the present work, reason for the small spin orbit contribution to the effective charge distribution is discussed in some detail. It is also shown that the use of a single Gaussian shape for the proton smearing usually underestimates the actual theoretical cross section.