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Production of Electron-Positron Pairs


THE production of a pair of positive and negative electrons by two photons was one of the consequences of his theory of the electron first considered by Dirac. This effect is essentially at the basis of all pair production phenomena, and it may be of interest to point out that from the formula for it, recently given by Breit and Wheeler1, we may readily deduce, to a certain approximation, the probabilities for the production of pairs by high-energy photons and electrons in the field of an atomic nucleus. The correlation of these effects depends on the fact that for an observer moving relative to a nucleus with a velocity approaching that of light, the field of the nucleus is approximately equivalent to a radiation field. In the region effective for producing pairs—at distances from the nucleus of the order of and greater than /mc—the nuclear field corresponds, for an observer travelling with velocity v, to a distribution of photons the number of which in the frequency interval dv is given by The cross-section,, for pair-production by a photon, hv, of energy mc2, 1, is now obtained by considering its interaction with the photons, which, according to (1), represent the nuclear field. For a system S, moving with the incident photon with a velocity such that the energy of the photon is reduced from mc2 to mc2, the expression for thus obtained is (v) is the cross-section for pair-production by a photon of energy hv and a photon of energy mc2, travelling in opposite directions. The second factor is the number of virtual photons in the nuclear field with frequency in the range dv. On substituting for (v) the expression given by Breit and Wheeler and integrating, this gives which agrees with the result obtained by Heitler and Sauter by direct application of Dirac's theory. In this formula, and also the other formulæ given in this note, g is used to denote a numerical factor of the order of unity. Its exact value in the different cases cannot be derived by the present method and this represents the degree of approximation involved.


  1. Phys. Rev., 45, 766; 1934. The value given must be divided by 4 for use in the present connexion, according to a communication from the authors.

  2. Proc. Roy. Soc., A., 146, 83; 1934.

  3. Compare v. Weiszäcker, Z. Phys., 88, 612; 1934; and E. J. Williams, Phys. Rev., 45, 729; 1934.

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WILLIAMS, E. Production of Electron-Positron Pairs. Nature 135, 66 (1935).

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