High energy approximations for the total Born cross section for pair production in a screened Coulomb field.

Abstract

We derive the high energy limit of the momentum distribution associated with the total Born approximation cross section for pair production in a static screened Coulomb field. This high energy distribution is free of the ``large'' terms which appear in the exact momentum distribution and cancel leaving a remainder of relative order (m/k${)}^{2}$, the cancellation having been performed analytically. (k is the incident photon energy, m the electron rest mass.) The high energy distribution is used to derive the total pair production cross section both for an unscreened Coulomb field and in the limit of complete screening, and the results are compared with expressions given in the literature. It is shown that the largest corrections to the high energy limit of the total cross section [of relative orders (2m/k${)}^{2}$${\mathrm{ln}}^{3}$(2k/m) and (2m/k${)}^{2}$${\mathrm{ln}}^{2}$(2k/m)] are independent of screening, and these are given analytically.