An Extended Model for Positron-Electron Annihilation Incorporating Atomic Binding and Momentum Distribution Effects

This work presents a comprehensive theoretical-computational investigation of the positron-electron annihilation process, focusing on critical evaluation of the standard approximation that treats atomic electrons as free and at rest. We develop and validate corrections accounting for atomic binding effects, initial electron momentum, and electron density distribution in materials with different atomic numbers (Z) and electronic structures. Using a hybrid approach combining quantum scattering analytical methods with high-performance Fortran simulations, we quantify systematic deviations introduced by the simplified approximation, particularly for low-energy incident positrons (E+ < 1 MeV) and high-electron-density materials. Our implementation provides more accurate cross-sections, contributing to refined electromagnetic shower simulations with potential impacts on medical imaging (PET) and materials spectroscopy.