Delbrück scattering

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Abstract

We calculate the lowest-order Delbr\"uck scattering amplitude without approximations. We also show that this amplitude scales in the form of ${\ensuremath{\omega}}^{\ensuremath{-}1}f(\ensuremath{\theta})$ as $\frac{\ensuremath{\omega}}{m}\ensuremath{\rightarrow}\ensuremath{\infty}$ with $\ensuremath{\theta}$ fixed, where $\ensuremath{\omega}$ is the energy of the photon, $m$ is the electron mass, and $\ensuremath{\theta}$ is the scattering angle. In addition, we prove that this scaling behavior is obeyed by the Delbr\"uck amplitude even if the higher-order diagrams of multiphoton exchanges are taken into account. Existing experimental data appear to be in conflict with the scaling behavior, and we suggest that the data be reanalyzed or (and) additional experiments be performed.

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