Opening Angles of Electron-Positron Pairs

The cross section for production of a high-energy electron-positron pair of opening angle θ and electron energy ε₁, d²σ(θ, ε₁)dθdε₁ is calculated. Comparison with available experimental data shows good agreement with the present theory. The cross section d²σ(θ, ε₁)dθdε₁ is shown to be closely related to the cross section for an angle θ₁ between the photon and the electron, d²σ(θ₁, ε₁)dθ₁dε₁. At high photon energies the functional dependence of d²σ(θ, ε₁)dθdε₁ on the variable w=(ε₁ε₂k)θ is very nearly the same as the functional dependence of d²σ(θ₁, ε₁)dθdε₁ on the variable u=ε₁θ₁. The experimental method of estimating the energy of a photon creating a pair from the opening angle of the pair is discussed. Formulas for the most probable photon energy for a measured opening angle, including the effect of multiple scattering, are given.