Complex Scattering Amplitudes in Elastic Electron Scattering

The scattering amplitudes derived from the Moli\`ere approximation are compared with those derived from the first- and second-order Born approximations. A numerical analysis applying a Thomas-Fermi potential was performed. In certain ranges of $a=\frac{Z}{137\ensuremath{\beta}}$ and the scattering angle, the first-order Born approximation rendered amplitudes that can be applied for the more exact modulus of the Moli\`ere approximation, and the second-order Born approximation rendered phases of the scattering amplitudes that are comparable with those obtained by the Moli\`ere approximation.