Scattering of High-Energy Electrons by Nuclei

Calculations of elastic scattering of electrons have been carried out for simple, spherically symmetric charge distributions. The atomic numbers considered are $Z=13, 29, 50, 74, \mathrm{and} 79$, and the electron energy varies from 15 to 90 Mev. The results for the homogeneous and shell distributions indicate that shape independence exists for energies such that $k{R}_h\lesssim 1.5$, where $R_h$ is the radius of the homogeneous model and $k$ is the electron wave number. This is a consequence of requiring that these two densities have the same mean square radius or second moment. The assumption that the scattering at higher energies depends on higher even moments has also been investigated. The scattering was calculated as a function of the fourth moment at an energy just above the shape independent region. Equating the second and fourth moments of two charge densities results in identical scattering for scattering angles up to 120°, but beyond this point the scattering differs by about 10 percent. An analysis of the existing experiments below 100 Mev indicates that the mean square radius of the nuclear charge density is given by a homogeneous distribution of radius $R_h=r_0{A}^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm., with $r_0=1.2\mathrm{}$ to within 10 percent.