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On the Numerical Analysis of Triplet Pair Production Cross-Sections and the Mean Energy of Produced Particles for Modelling Electron-Photon Cascade in a Soft Photon Field
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The double and single differential cross-section with respect to positron and electron energies as well as the total cross-section of triplet production in the laboratory frame are calculated numerically in order to develop a Monte Carlo code for modelling electron-photon cascades in a soft photon field. To avoid numerical integration irregularities of the integrals, which are inherent to problems of this type, we have used suitable substitutions in combination with a modern powerful program code (Mathematica) allowing one to achieve reliable higher-precision results. The results obtained for the total cross-section closely agree with others estimated analytically or by a different numerical approach. the results for the double and single differential cross-sections turn out to be somewhat different from some reported recently. The mean energy of the produced particles, as a function of the characteristic collisional parameter (the electron rest frame photon energy), is calculated and approximated by an analytical expression that revises other known approximations over a wide range of values of the argument. The primary-electron energy loss rate due to triplet pair production is shown to prevail over the inverse Compton scattering loss rate at several (~2) orders of magnitude higher interaction energy than that predicted formerly.
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