Describing Compton scattering and two-quanta positron annihilation based on Compton profiles: Two models suited for the Monte Carlo method

An accurate description of the basic physics processes of Compton scattering and positron annihilation in matter requires the consideration of atomic shell structure effects and, in specific, the momentum distributions of the atomic electrons. Two algorithms which model Compton scattering and two-quanta positron annihilation at rest accounting for shell structure effects are proposed. Two-quanta positron annihilation is a physics process which is of particular importance for applications such as positron emission tomography (PET). Both models use a detailed description of the processes which incorporate consistently Doppler broadening and binding effects. This together with the relatively low level of complexity of the models makes them particularly suited to be employed by fast sampling methods for Monte Carlo particle transport. Momentum distributions of shell electrons are obtained from parametrized one-electron Compton profiles. For conduction electrons, momentum distributions are derived in the framework of a Fermi gas. The Compton scattering model uses an approach which does not employ any free parameter. In contrast, a few semi-empirical approximations are included for the description of the complex physics of electron-positron annihilation resulting in acollinear photons. Comparisons of the Compton scattering model with simpler approaches illustrate the detailed accounting for shell structure effects. A satisfactory agreement is found for comparisons of both newly-developed models with experimental data.