A numerical approach to calculate cross sections for relativistic electrons and terrestrial gamma-ray flashes

Terrestrial gamma-ray flashes (TGFs) are bursts of energetic X- and gamma-rays which are emitted from thunderstorms as the Bremsstrahlung of relativistic electrons. While such relativistic particles propagate through the atmosphere, they interact with air molecules which can be studied with particle Monte Carlo models. Such models require cross sections as an input. Whilst there are well established data for elastic scattering, Bremsstrahlung and impact ionization through relativistic electrons as well as for photoionization, Compton scattering and pair production for energetic photons, we lack cross sections for photoexcitation, photodissociation or the excitation of air molecules through electrons which can contribute to the chemical activation of the atmosphere, potentially relevant for the study of greenhouse gas production from lightning in our atmosphere. In order to fill this cross section gap, we here present a novel numerical tool calculating cross sections directly from Feynman diagrams providing both differential and total cross sections. We provide an overview of the code structure and present benchmarking cases against well-known cross sections. Additionally, we will present a first application by calculating the cross section for photodissociation for a wide range of energies. The presented model is capable of calculating cross sections for more leptonic and photonic processes in the atmosphere than today. Subsequently, this will allow for more realistic simulations of energetic phenomena in our atmosphere. Program summary • Program title: Quantum Pathways: Feynman’s Numerical Solver (QP-FNS) • CPC Library link to program files: https://doi.org/10.17632/ggxh3wv2by.1 • Developer’s repository link: https://gitlab.gbar.dtu.dk/chrstk/cross-section-calculation • Licensing provisions: GNU General Public License 3 • Programming language: C++ • Nature of problem: This program calculates a numerical dataset for the total cross section and singly differentiated cross section (with respect to scattering angle), based on the Feynman diagrams for 2 → 2 particle processes. The cross sections can be calculated in either the laboratory or center of mass reference frame. • Solution method: The program uses quantum field theory to translate Feynman diagrams into quantifiable expressions, which it discretizes to calculate the scattering matrix. This is combined with expressions for the problem’s 4-momenta to solve for the differential cross section. Numerically integration is used to obtain the total cross section. • Additional comments: Energy input and output is in units of MeV. The Feynman diagram input is restricted to 2 → 2 tree level diagrams. Input expressions are in natural units, output expressions are in either natural or SI units, depending on which is requested in the input. See appendix A on how to compile the program, and appendix B on how to input diagrams.