Pair Production by Photons on Electrons

Abstract

The cross section for production of electron pairs by unpolarized photons in the field of an electron is calculated. The total cross section is obtained by numerical integration. The contributions to the total cross section from different diagrams (exchange and $\gamma -e$ terms) are calculated separately, and it is shown that Borsellino's result for the cross section is valid for photon energies above about 8 MeV, the deviation from the correct cross section being of order 1% at this energy. Votruba's results for the total cross section are confirmed for energies very close to threshold (within about 10 keV of threshold). The results of Kopylov et al. appear to be in error by a factor of 2. Dividing their results by this factor, we find agreement with ours within limits of error. The recoil momentum distribution is computed numerically for some energies and it is found to agree with the results of Borsellino. At high energies it is also in agreement with the results of Suh and Bethe. The momentum distribution for pair production in the field of a very heavy particle is also calculated for some energies from the formulas of Borsellino and Jost et al. From a comparison of the recoil distributions for pair production on electrons with that on very heavy particles, an estimate of the error in the Wheeler-Lamb results can be made. Comparison with some experiments is given.