We calculated numerically in a relativistic partial-wave formulation the positron energy spectra of pair-production sigma(E+) in the field of atoms with atomic number Z = 1, 6, 13, and 82 for photons of energies near threshold, k = 2.001, 2.01, and 2.10 m(e)C2, where E+ is the positron energy. Our results indicate that in this low-photon-energy region, the atomic-electron screening effect increases as Z increases, k decreases, and E+ decreases. The ratio of screened to point-Coulomb cross sections sigma(E+) varies from 0.985 to 1.69 X 10(4). When the screening effect is important, it increases the cross section sigma(E+). Our results also indicate that the approximate treatment of screening through energy-shift screening theory becomes inadequate when the screening effect is very important. The approximate treatment of screening through the corrected-effective normalization screening theory works fine in this low-photon-energy region, except for the case with Z = 6, k = 2.001 m(e)c2, and E+ = 1.0001 m(e)c2, where the screening effect is not a normalization effect.
