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

The double and single differential cross-sections with respect to positron and electron energies as well as the total cross-section of tripler product ion 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 integrands, whi ch are inherent to problems of this type, we have used suitable substitutio ns in combination with a modem 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 o r by a different numerical approach. The results for the double and single differential cross-sections turn out to be somewhat different from some rep orted recently. The mean energy of the produced particles, as a function of the characteristic collisional parameter (the electron rest frame photon e nergy), is calculated and approximated by an analytical expression that rev ises other known approximations over a wide range of values of the argument . The primary-electron energy loss rate due to triplet pair production is s hown to prevail over the inverse Compton scattering loss rate at several (s imilar to 2) orders of magnitude higher interaction energy than that predic ted formerly.