Screening Effects in Atomic Pair Production below 5 MeV

Abstract

Quantitative predictions for atomic-electron screening effects in low-energy pair production follow from the knowledge that the small-distance shape of screened-electron and positron continuum wave functions is close to that of point-Coulomb wave functions of shifted energy. These predictions are verified by making exact numerical calculations in representative cases. The energy-shift normalization theory is then used in conjunction with the point-Coulomb results of @verb/ to obtain predictions for atomic-pair-production energy distributions and total cross sections for photon energies from threshold to 5 MeV. Atomicelectron screening effects cause appreciable modifications of the total cross sections for photon energies below 1.5 MeV and continue to have a major effect on some portions of the energy distribution at higher photon energies. Results are also compared with Bethe-Heitler predictions and with experiments.With the continuing improvements in computers it is becoming feasible to make fairly accurate theoretical calculations of atomic-pair-production cross sections in the low-energy region where the Bethe-Maximon~high-energy results and Born approximation (the well-known Bethe -Heitler formula) need not be valid. Relativistic calculations of pair production in a point-Coulomb-potential model have now been reported by Qhrerbg Mork, and Olsen (QlMO); more extensive results have been given by (|)verbg'. This use of a point-Coulomb model relies on the expectation, based on form-factor estimates, 4 that the effects of atomic-electron screening would be unimportant in this energy region. Such an estimate is obtained because the maximum impact parameter r~discussed by Heitler, 5 equal to q~, with q &, = k' -P, p, is of the order of the electron Compton wavelength and is quite small compared to the radius of the atom. However, we subsequently performed the lengthy relativistic calculations~of pair-production cross sections in screened potentials and found that, near threshold, atomic-electron screening effects are important. At electron-Comptonwavelength distances an electron sees a point-Coulomb potential corresponding to the nuclear charge Z. The electron wave function has a hydrogenlike shape; the only effect of atomic-electron screening, as described by a central potential V deviating from the point-Coulomb form, is to modify the normalization.For a very-low-energy continuum wave function (but not for higher energies) this normalization is indeed sensitive to the screening. We showed in fact that we could roughly obtain screened pair-production cross sections from point-Coulomb cross sections simply by using a multiplicative normalization factor.We have recently examined~in greater detail the

Atomic Photoelectric Effect Above 10 keV

“…6Z "/I x I E (Mev)'"j for E (MeV) &0.95 MeV, which has been estimated by Tseng (1970) to be valid for the point-Coulomb potential. It may be used for kinetic energies of the electron down to 1 keV for low-Z elements and to 20 keV for heavy elements.…”

“…te have shown that the arguments are valid in internal conversion. Pratt (1971, 1972) have demonstrated these effects in pair production near threshold.…”

High-energy electron-positron photoproduction cross section close to the end of the spectrum

“…Namely, the spectrum of slow electron in the screened Coulomb field can be obtain from that in unscreened field by means of the shift ǫ − → ǫ − + ∆ and values of the energy shift ∆ for various atoms are presented in Refs. [23][24][25]. Analogously, for slow positron the corresponding shift is ǫ + → ǫ + − ∆.…”

“…Therefore, one can account for the screening by employing the prescription formulated in Refs. [23][24][25]. Namely, the spectrum of slow electron in the screened Coulomb field can be obtain from that in unscreened field by means of the shift ǫ − → ǫ − + ∆ and values of the energy shift ∆ for various atoms are presented in Refs.…”

Mesure absolue de la section efficace totale de création de paires, près du seuil, au moyen d'une source d'énergie variable

“…Ces diff6rentes predictions theoriques utilisent, pour 1'electron et le positon crees, -soit, en premiere approximation, des ondes planes [20] (section efficace totale : 0'8)' -soit, un developpement en fonctions d'onde coulombiennes, et ce, en tenant compte [21,22] (section efficace totale : O'T.P., voir Fig. 1) ou pas [23,24] (section efficace totale : O'Ø.M.O" voir Fig.…”