Theory of Bremsstrahlung and Pair Production. II. Integral Cross Section for Pair Production

The differential cross section for bremsstrahlung and pair production at high energies obtained in the preceding paper by Bethe and Maximon has been integrated over all angles, and formulas are given for the integral cross section for all $Z$. For small $Z$, the correction to the Born approximation is proportional to $Z^2$, and the constant of proportionality is given. The correction for heavier elements is somewhat less than the $Z^2$ law would indicate. It is shown that the correction is associated only with large recoil momenta of the nucleus whereas screening is important only for small recoil momenta; and, therefore, the same correction is valid in the case of complete, incomplete, or no screening. Agreement of these new predictions with observations of pair-production cross section at 88 and 280 Mev is excellent and not unreasonable at 17.6 Mev.