Elastic electron scattering formalism for relativistic nuclear models

The classical static equation of motion for a relativistic vector field interacting through direct and derivative coupling with a spinor source term is presented in spherical coordinates. The equation is generalized to include the effects of form factors at the vector-spinor vertices. Using appropriate nucleon electromagnetic form factors and nuclear single-particle wave functions resulting from relativistic self-consistent model calculations of spherical nuclei, the contributions of the various components of the nucleon electromagnetic form factors to the effective nuclear charge distributions and the elastic electron scattering cross sections for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ are analyzed.