This comprehensive study delves into the intricate interplay between protons and organic polymers, offering insights into proton therapy in cancer treatment. Focusing on the influence of the spatial electron density distribution on stopping power estimates, we employed real-time time-dependent density functional theory coupled with the Penn method. Surprisingly, the assumption of electron density homogeneity in polymers is fundamentally flawed, resulting in an overestimation of stopping power values at energies below 2 MeV. Moreover, the Bragg rule application in specific compounds exhibited significant deviations from experimental data around the stopping maximum, challenging established norms.

Normalized experimental differential and integral cross sections for vibrationally elastic scattering of low-energy electrons from isobutanol ${(\mathrm{C}}_4{\mathrm{H}}_9\mathrm{OH})$ are presented. The differential cross sections are measured at incident energies from 1 to 100 eV and scattering angles from $5^{\circ }$ to ${130}^{\circ }$. These cross sections are compared to earlier experimental and theoretical results for isobutanol and $n$-butanol, as well as to results for smaller alcohols and for alkanes. Further comparisons are made with calculated cross sections for isobutylamine ${(\mathrm{C}}_4{\mathrm{H}}_9{\mathrm{NH}}_2)$ and for smaller amines, including ethylamine ${(\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}_2),$ dimethylamine ${(\mathrm{CH}}_3{\mathrm{NHCH}}_3)$, the two ${\mathrm{C}}_3{\mathrm{H}}_7{\mathrm{NH}}_2$ isomers $n$-propylamine and isopropylamine, and ethylene diamine ${(\mathrm{NH}}_2{\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{NH}}_2).$ The calculated cross sections are obtained using the Schwinger multichannel method. The comparisons illuminate the role of molecular structure in determining the angular distribution of resonantly scattered electrons.

The self-consistent electron–ion potential V ( r ) is calculated for H ⁺ ions in an electron gas system as a function of the projectile energy to model the electronic stopping power for conduction-band electrons. The results show different self-consistent potentials at low projectile-energies, related to different degrees of excitation of the electron cloud surrounding the intruder ion. This behavior can explain the abrupt change of velocity dependent screening-length of the potential found by the use of the extended Friedel sum rule and the possible breakdown of the standard free electron gas model for the electronic stopping at low projectile energies. A dynamical interpolation of V ( r ) is proposed and used to calculate the stopping power for H ⁺ interacting with the valence electrons of Al. The results are in good agreement with the TDDFT benchmark calculations as well as with experimental data.

A nonlinear model for the stopping power of cluster ions based on partial-wave analysis is developed through the generalization of the induced density approach (IDA) model for the interaction of homo- and heteronuclear molecular ions with a free-electron gas (IDAMol). We apply IDAMol to the energy loss of ${{\mathrm{H}}_2}^{+}$ dimers in ${\mathrm{SiO}}_2$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$, where we find that the results are consistent with established linear (dielectric) models at higher speeds, as expected for small perturbations (small values of the projectile charge or high velocities). Specifically at low projectile energies, however, it is important that IDAMol goes beyond perturbation theory. This feature appears to be central for a good description of negative and positive vicinage effects, a measure of the deviation from the independent-atom model. The focus of this work, however, is the investigation of enhanced nonlinear effects. Here we present experimental results for a heteronuclear cluster ion namely ${\mathrm{HeH}}^{+}$ on ${\mathrm{Al}}_2{\mathrm{O}}_3$, in the energy range of few tens of keV/u using the medium energy ion scattering technique. The IDAMol results are corroborated by the experimental data and time-dependent density-functional calculations for this case. Strong nonlinearities are observed for the energy loss of the fragment ${\mathrm{H}}^{+}$ due to the higher charge of its He companion.

A recent experimental study of the energy losses of various ions in titanium nitride, in the low-energy range [M. A. Sortica et al., Sci. Rep. 9, 176 (2019)], showed a striking departure of the measured values from those predicted by density functional theory. They suggested electron promotion in atomic collisions between dressed atoms as an explanation. In this Rapid Communication, we investigate the process of energy loss of slow ions in TiN using theoretical formulations that are based, on one side, on self-consistent models of nonlinear screening and quantum scattering theory, and on the other, on ab initio computations of the electron-density profile of titanium nitride. Two theoretical approaches are considered to determine the average energy transfer: One is based on the local-density approximation for the inhomogeneous electron gas corresponding to the calculated density of TiN, and the other is based on the Penn model for the convolution of the inhomogeneous electron-gas response based on a measured electron-loss function. Both approaches produce very similar results and are in remarkable agreement with the experimental data, indicating that the observed enhancement in the energy-loss values is due to the contribution of a range of electron densities in the TiN compound.

This study provides accurate results for the electronic stopping cross sections of H, He, N, and Ne in silicon in low to intermediate energy ranges using various non-perturbative theoretical methods, including real-time time-dependent density functional theory, transport cross section, and induced-density approach. Recent experimental findings [Ntemou et al., Phys. Rev. B 107, 155145 (2023)] revealed discrepancies between the estimates of density functional theory and the observed values. We show that these discrepancies vanish by considering the nonuniform electron density of the deeper silicon bands for ion velocities approaching zero (v → 0). This indicates that mechanisms such as “elevator” and “promotion,” which can dynamically excite deeper-band electrons, are active, enabling a localized free-electron gas to emulate ion energy loss, as pointed out by Lim et al. [Phys. Rev. Lett. 116, 043201 (2016)]. The observation and the description of a velocity-proportionality breakdown in electronic stopping cross sections at very low velocities are considered to be a signature of the contributions of deeper-band electrons.