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

Abstract

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 firstprinciples, non-equilibrium 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 but 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 its 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 comprises K-shell holes even at the high proton velocity of 8.0 a.u.. The excitation behavior revealed here is distinctly different from that of photonbased ionizing radiation such as X/γ-rays.When a highly energetic ion travels through and interacts with matter, its kinetic energy is transferred into the target material's electronic and nuclear subsystems. This energy loss of the projectile ion can arise from both elastic collisions with nuclei (nuclear stopping) and inelastic scattering events (electronic stopping). When the particle's kinetic energy is sufficiently large (on the order of ~10 keV per nucleon), the major contribution to the energy transfer comprises electronic stopping wherein the projectile ion induces massive electronic excitations in the target matter 1-2 . This electronic stopping phenomenon is at the heart of emerging ion bean cancer therapies. The use of proton beam radiation over more conventional radiation based on X/γ-ray photons is often considered more effective because of the ion's distinct spatial energy deposition profile with a very sharp peak. [3][4] By calibrating the initial kinetic energy of the protons, this energy deposition peak can be tuned to coincide with the location of the tumour. This energy deposition profile is largely determined by electronic stopping power, which measures the rate of energy transfer from the charged particle to electrons in matter per unit distance of the energetic particle's movement. 1,[5][6][7] The stopping power is a continuous function of the particle velocity, and the velocities near the...

Efficient ab initio calculation of electronic stopping in disordered systems via geometry pre-sampling: Application to liquid water

“…Yao et al demonstrated that, for protons in water, the ensemble average of S e (v p = 8.0 a.u.) based on 64 regularly distributed trajectories in a 16 Å-long water box converges very well to SRIM's data 23 . This value v p = 8 a.u.…”

“…Local-orbital implementations, either numerical as in SIESTA 74 , or Gaussian basis functions as in CP2K and other codes 52,75 , are significantly more efficient provided a smart choice of basis set is made that captures the possibility of electrons being excited to high energy states or even ejected. Moreover, it has recently been shown that both valence and core electrons can contribute significantly to electronic stopping 23,30,51 .…”

“…Since S e (v p ) is sensitive to the local electronic structure of the target along the ion trajectory, an accurate comparison of rt-TDDFT calculations with observations requires a statistical reconstruction of the long experimental trajectory using a large number of nanometer-scale rt-TDDFT simulations. 16,23,49,55 . Yao et al demonstrated that, for protons in water, the ensemble average of S e (v p = 8.0 a.u.)…”

“…Despite the fact that proton beams have been widely used for cancer therapy, the stopping curve for protons in liquid water has not been determined experimentally in the region of the Bragg peak and below (E k < 100 keV). This is significant, because liquid water is overwhelmingly used to model the average biological medium 23 . Experimental data are available only at proton energies above 0.3 MeV 20, 23 .…”

“…This is significant, because liquid water is overwhelmingly used to model the average biological medium 23 . Experimental data are available only at proton energies above 0.3 MeV 20, 23 . Therefore, any information below this energy is based on extrapolation from higher-energy experimental data, using theoretical models and Bragg's rule with empirical scaling (see below).…”