Exact Screened Calculations of Atomic-Field Pair Production and Low-Energy Screening

A discussion of relativistic-pair-production cross sections is given for incident-photon energies in the range 1.073-2.615 MeV. Cross sections are obtained numerically for a screened potential, using an exact partial-wave formulation. Comparisons are made with previous authors' results. For low photon energies the effect of atomic-electron screening on pari-production cross sections is significant. The screening increases the cross section, since the atomic electrons decrease the nuclear Coulomb repulsion of the positron. Comparisons of screened with unscreened results show that angular distributions are essentially unaffected in shape by the screening; cross sections are simply renormalized by replacing ${\left|N_{+}{N}_{-}\right|}^2$ in the point-Coulomb field by ${\left|N_{+}{N}_{-}\right|}^2$ in the screened field, where $N_{\pm }$ are the normalizations of the positron and electron wave functions at the origin.