Forward Scattering of Light by a Coulomb Field

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Abstract
The complex scattering amplitude for the scattering of light by a Coulomb field (Delbrück scattering) in the forward direction is calculated exactly by two methods. First, the Feynman method is used and necessitates very tedious and complicated calculations. Then, the method of analytical continuation is applied to the pair production cross section and yields the same result much more easily. An exact analytical expression is obtained for the dispersive and absorptive parts of the amplitude. The result is plotted as a function of energy. The low energy limit agrees with previous calculations for this limit by Kemmer and Ludwig.