A Proposal to Measure Photon-Photon Scattering

Abstract

We discuss a possibility to measure the photon-photon scattering cross section at low energy in a theoretical standpoint. The cross section of photon-photon scattering at low energy can be written as $\frac{d\sigma }{d\Omega }\simeq \frac{{\alpha }^4}{(12\pi {)}^2{\omega }^2}(3+2{\cos }^2\theta +{\cos }^4\theta )$ with $\omega$ the energy of photon. The magnitude of the cross section at $\omega \simeq 1$ eV should be $10^{37}$ times larger than the prediction of Heisenberg and Euler who calculated the photon scattering by the classical picture of field theory. Due to a difficulty of the initial condition of photon-photon reaction process, we propose to first measure $\gamma +\gamma \to e^{+}+e^{-}$ reaction at a few MeV before measuring $\gamma +\gamma \to \gamma +\gamma$ elastic scattering.

7 pages, no figure