K-Shell Core-Electron Excitations in Electronic Stopping of Protons in Water from First Principles

Understanding the role of core-electron excitation in liquid water under proton irradiation has become important due to the growing use of proton beams in radiation oncology. Using a first-principles, nonequilibrium simulation approach based on real-time, time-dependent density functional theory, we determine the electronic stopping power, the velocity-dependent energy transfer rate from irradiating ions to electrons. The electronic stopping power curve agrees quantitatively with experimental data over the velocity range available. At the same time, significant differences are observed between our first-principles result and commonly used perturbation theoretic models. Excitations of the water molecules' oxygen core electrons are a crucial factor in determining the electronic stopping power curve beyond its maximum. The core-electron contribution is responsible for as much as one third of the stopping power at the high proton velocity of 8.0 a.u. (1.6 MeV). K-shell core-electron excitations not only provide an additional channel for the energy transfer-they also significantly influence the valence electron excitations. In the excitation process, generated holes remain highly localized within a few angstroms around the irradiating proton path, whereas electrons are excited away from the path. In spite of their great contribution to the stopping power, K-shell electrons play a rather minor role in terms of the excitation density; only 1% of the hole population composes K-shell holes, even at the high proton velocity of 8.0 a.u. The excitation behavior revealed is distinctly different from that of photon-based ionizing radiation such as x or γ rays.