Energy deposition of H and He ion beams in hydroxyapatite films: a study with implications for ion-beam cancer therapy

The contribution of inner electron excitation to the electronic stopping power of palladium for protons

The electronic stopping power of palladium (Pd) for protons is investigated based on time-dependent density functional theory combined with Ehrenfest molecular dynamics simulations. The electronic stopping power of Pd with explicitly considering inner electrons for protons is calculated and the excitation mechanism for the inner electrons of Pd is revealed. The velocity proportionality of the low-energy stopping power of Pd is reproduced. Our study verified that the inner electron excitation contributes significantly to the electronic stopping power of Pd in the high energy range, which is strongly dependent on the impact parameter. The electronic stopping power obtained from the off-channeling geometry is in quantitative agreement with the experimental data in a wide velocity range, and the discrepancy around the stopping maximum is further reduced by considering the relativistic correction on the binding energy of inner electrons. The velocity dependence of the mean steady-state charge of protons is quantified, and the results showed that the participation of 4p-electrons reduces the mean steady-state charge of protons, and consequently decreases the electronic stopping power of Pd in the low energy range.

On the Z1-dependence of electronic stopping in TiN

We present a thorough experimental study of electronic stopping of H, He, B, N, Ne and Al ions in TiN with the aim to learn about the energy loss mechanisms of slow ions. The energy loss was measured by means of time-of-flight medium-energy ion scattering. Thin films of TiN on silicon with a δ-layer of W at the TiN/Si interface were used as targets. We compare our results to non-linear density functional theory calculations, examining electron-hole pair excitations by screened ions in a free electron gas in the static limit, with a density equivalent to the expected value for TiN. These calculations predict oscillations in the electronic stopping power for increasing atomic number Z1 of the projectile. An increasing discrepancy between our experimental results and predictions by theory for increasing Z1 was observed. This observation can be attributed to contributions from energy loss channels different from electron-hole pair excitation in binary Coulomb collisions.

Energy Spectra of Protons and Generated Secondary Electrons around the Bragg Peak in Materials of Interest in Proton Therapy

The number and energy of secondary electrons generated around the trajectories of swift protons interacting with biological materials are highly relevant in proton therapy, due to the prominent role of low-energy electrons in the production of biodamage. For a given material, electron energy distributions are determined by the proton energy; and it is imperative that the distribution of proton energy at depths around the Bragg peak region be described as accurately as possible. With this objective, we simulated the energy distributions of proton beams of clinically relevant energies (50-300 MeV) at depths around the Bragg peak in liquid water and the water-equivalent polymer poly(methyl methacrylate) (PMMA). By using a simple model, this simulation has been conveniently extended to account for nuclear fragmentation reactions, providing depth-dose curves in excellent agreement with available experimental data. Special care has been taken to describe the electronic excitation spectrum of the target, taking into account its condensed phase nature. A predictive formula has been obtained for the mean value and the width of the proton energy distribution at the Bragg peak depth, quantities which are found to grow linearly with the initial energy of the beam, in good agreement with available data. To accurately characterize (in number and energy) the electrons generated around the proton paths, the energy distributions of the latter at each depth have been convoluted with the energy-dependent ionization inverse mean free paths. This results in a number of low-energy electrons around the Bragg peak larger than when only the proton beam average energy at the given depths is considered. The convoluted ionization inverse mean free path closely resembles the Bragg curve shape. The average energy of the secondary electrons is nearly constant (∼55 eV for liquid water and ∼43 eV for PMMA) in the plateau of the Bragg curve, independent of the proton incident energy and suddenly decaying once the Bragg peak is reached. These findings highlight the importance of a precise calculation of the proton beam energy distribution as a function of the target depth to reliably characterize the secondary electrons generated around the Bragg peak region.