Momentum Transfer and Angle of Divergence of Pairs Produced by Photons

Abstract

The distribution of the momentum transferred to the pairs in pair production by photons has been derived from the Bethe-Heitler cross section. The effect of screening is evaluated using a shielded Coulomb potential for the nucleus. In the last part of the article the distribution of the angle of divergence of the pair is obtained, and the most probable angle of divergence is given by $\phi \left(\frac{E_{+}}{k}\right)·\frac{4m{c}^2}{k}$, where $k$ and $E_{+}$ are the energies of the photon and the positron and $\phi \left(\frac{E_{+}}{k}\right)\sim 1$ for $0.2<\mathrm{}\frac{E_{+}}{k}<0.5\mathrm{}$.