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

Abstract

Abstract. The double and single differential cross-sections 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 integrands, 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-precission 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.

Neutrino production in electromagnetic cascades: An extra component of cosmogenic neutrino at ultrahigh energies

“…In terms of energy loss rate, it has been evaluated by some works (e.g., [29,31]). Here we adopt a recent evaluation on the basis of precise numerical calculations given by [32], While the energy loss rate is − dE dt tpp = 0.24αcσ T π 3 Λ 3 (kT ) 2 (ln 2E e kT ln 1.49E e kT − 1.04) , (B11) which gives us a threshold energy ω th,2 ∼ 2.3 × 10 7 when equal to the energy loss rate of CS in case 2. Such larger ω th,2 than ω th,1 implies the inelasticity of TPP is very small, i.e., one outgoing electron is leading extremely.…”

Constraints on the origin of ultra-high-energy cosmic rays from cosmogenic neutrinos and photons

“…The latter were calculated using a Monte Carlo code computing the most relevant interaction channels (i) for photons: the e + e − pair production (Peskin & Schroeder, 1995) and the double pair production (following Lee, 1998), (ii) for electrons and positrons: the inverse Compton scattering (Jones, 1968;Zdziarski & Svensson, 1989) and the triplet pair production (Haug, 1975;Mastichiadis, 1991;Anguelov et al, 1999). The competition between these processes was treated stochastically, whereas the synchrotron and adiabatic losses were treated as continuous processes.…”

Total cross sections of eγ → $$ eX\overline{X} $$ processes with X = μ, γ, e via multiloop methods

“…These processes have many astrophysical applications, see, e.g., refs. [5][6][7][8][9][10][11], and have been considered in a number of papers [6,9,[12][13][14][15][16][17][18]. Our approach is based on using the optical theorem and Cutcosky rules to express the total cross section via cut diagrams in forward kinematics.…”