Small Angle Scattering of Light by a Coulomb Field

The angular distribution for small angles and the total cross section for Delbrück scattering (the elastic scattering of $\gamma$-rays by the Coulomb field of heavy nuclei) are calculated approximately. The method is a combination of an impact parameter and an analytic continuation method. It is valid for energies $\hslash \omega$ large compared to the electron rest energy $m{c}^2$. Curves are given for the shapes of the dispersive and absorptive parts of the differential cross section, valid for angles of order $\frac{m{c}^2}{\hslash \omega }$ or less.