Measurement of Linear Photon Polarization by Pair Production

The cross section for production of electron positron pairs by linearly polarized high energy photons is calculated for the case in which the pair particles and the photon are nearly coplanar. The cross section is integrated over the polar angles ${\theta }_1$ and ${\theta }_2$ between the momenta of the positron and the photon, and the momenta of the electron and the photon, respectively, and over a small range $2\Delta \phi$ of the azimuthal angle $\varphi ={\varphi }_1-{\varphi }_2$ between the pair particles about $\varphi =\pi$. The asymmetry ratio, defined as the ratio of the number of pairs emitted parallel to the photon polarization plane to the number of pairs emitted perpendicular to this plane, is plotted as a function of $\Delta \phi$ for the cases of no screening and complete screening. It is shown that for very small $\Delta \phi$ the cross section is a very rapidly varying function of $\Delta \phi$, such that the pairs emitted within the angular region $2\Delta \phi$ are predominantly perpendicular to the polarization plane for $\Delta \phi <\Delta {\phi }_0$ [$\Delta {\phi }_0=1.23\left(\frac{Z^{\frac{1}{3}}}{111}\right)$ for complete screening, for example] and predominantly parallel to this plane for $\Delta \phi >\Delta {\phi }_0$.