On the production of electron pairs

Abstract

The production of positive-negative electron pairs by a beam of γ-rays traversing matter has been examined by various authors, the most comprehensive treatment being that of Bethe and Heitler. These authors employ the usual "Born Approximation" method, and justify its use for such elements as lead by pointing out that for γ-rays in the region hv / mc 2 = 3 to 11, the results obtained are in fairly good agreement with experiments. We reproduce some of their results below, namely, the ratio of the absorption due to combined Compton and photo-electric effects to that due to production of electron pairs. The theoretical ratios are calculated for energies hv / mc 2 = 3, 5·2, and 11. The values in brackets refer to measurements made in rather thick plates of lead, whereas the value for the 5·2 mc 2 γ-radiation is reduced to infinitely thin plates. Even so, the calculation of the absorption in a thin plate from experiment in thick plates involves a good deal of uncertainty, The agreement in the first column is not of any great significance, owing to the further uncertainty of the distribution of the energy in the γ-rays used. The results for aluminium are somewhat disturbing, as one would expect the Born Approximation to be more accurate here.