Toward highly accurate multigroup coupled photon-electron-positron cross-sections for the Boltzmann Fokker-Planck equation

Abstract

For many contemporary applications, ionizing radiation transport plays a pivotal role, requiring an accurate assessment of its impact on the exposed environment. While Monte Carlo simulations are widely considered the gold standard for accurate general-purpose coupled transport of photons, electrons and positrons in matter, discrete ordinates algorithms provide a viable alternative. This work consolidates cross-section models for coupled photon-electron-positron transport and provides the methodology to generate the data required by the multigroup Boltzmann Fokker-Planck transport equation and by energy and charge deposition formulas. It includes elastic, collisional and radiative inelastic interactions of leptons, annihilation of positrons, Compton scattering, Rayleigh scattering, photoelectric effect, pair production as well as fluorescence and Auger electron production from relaxation cascades following ionization. Comparative analyses of energy deposition in water, aluminum, and gold are conducted for incident beams of 1 MeV, 10 MeV, and 100 MeV electrons and photons, and juxtaposed against Monte Carlo reference calculations. While disparities of a few percent are typical, higher deviation can be observed due to discretization or physical model limitations. Energy spectrums per particle type at varying depths in the medium are also contrasted with Monte Carlo calculations to discern limitations in the current implementation and to propose potential avenues for enhancing the presented models. Energy and charge deposition calculations are also compared to experimental measurements. The cross-section production and transport algorithms are implemented in an open-source Julia package, Radiant.jl.