Simple Analytic Expressions for the Total Cross Section for γ-e Pair Production

Abstract

The total cross section for pair production by photons in the field of free electrons is fitted to simple analytic expressions in four intervals of the incident photon energy which cover the whole range between threshold and infinity.The knowledge of accurate cross sections for pair production in the field of electrons or positrons (triplet production) is required in evaluations of total photon absorption cross sections [1,2], for calculations of the cross section for pair production in the field of atoms [3], and in astrophysical prob lems [4][5][6]. Compared to the familiar BetheHeitler formulae [7] for pair production in the Coulomb field of a nucleus, the cross section for triplet production, though obtained by straight forward application of quantum electrodynamics, is extremely complicated due to recoil and exchange effects [8]. Haug [9] has succeeded in deriving an expression for the doubly differential cross section for pair production in the field of free electrons in lowest-order perturbation theory (Born approxi mation) without neglecting the Feynman diagrams which describe exchange and the interaction of the incident photon with the initial electron. This lengthy formula has to be integrated numerically for obtaining the total cross section at ■ In order to facilitate the calculation of ot, the total cross sec tion for triplet production has been fitted to simple analytical expressions in four intervals of the photon energy, the fractional error of the approximation being less than 0.3% everywhere, mostly less than 0.1%.The total cross section at is a relativistic in variant ; it is a function of the invariant product of the energy-momentum four-vectors of the incident photon and electron which in the rest system of the target electron reduces to the photon energy k. If

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“…According to the results given in table 1 the values of σ toti (s ⊥ ) at s ⊥ > 10 4 are described correctly by the Haug formula [8]:…”

Supernova explosions of massive stars and cosmic rays

“…The newest AMS data confirm this dependence with a slope of can be expected to throw light on these questions. (Haug 1975(Haug , 1981(Haug , 1985(Haug , 2004. So three leptons result from this process, hence the name.…”

Electron–positron pair production by photons: A historical overview

“…in which k e BG is the Borsellino (1947a, b)-Ghizzetti (1947 unscreened triplet cross section including retardation, the ratio k e H /k e BG uses the Haug (1975Haug ( , 1981Haug ( , 1985 results to include the g-e interaction and exchange effects, and the Dk e BH (scr) screening and electron-binding effects were computed according to the Bethe-Heitler (Wheeler-Lamb) expression, using the non-relativistic incoherent scattering functions S(x,Z) compiled by Hubbell et al (1975) from various available sources, and the triplet radiative correction factor 1.01, as advised by Mork (1967), is taken as this constant value over the entire energy range.…”