Electronic Stopping Power For Protons Research Articles

Electronic stopping power of protons in platinum: Direct valence and inner-shell-electron excitations from first-principles calculations

The electronic energy loss of proton in platinum (Pt) is studied through nonadiabatic electron-ion coupling dynamic simulations within time-dependent density functional formalism. We have clarified the counterintuitive deviation from velocity proportionality due to the existence of kink velocity of the $d$ electron excitation for a slow proton moving in metal Pt, whose valence $d$ band indeed extends up above the Fermi energy. We have also quantitatively investigated the involvement of the host core electron excitation in the ion-target interaction, through monitoring the evolution of the bound electron number on a specific orbital of the host atom during the close encounter with the flying incident ion. It is found that the low-lying $5p$, $5s$, and $4f$ configuration excitations play significant roles in determining the profile of the stopping curve around and above the stopping maximum.

Contribution of f -electron excitation to electronic stopping power of platinum for protons

The electronic stopping power of protons traveling along the channeling and off-channeling trajectories in platinum (Pt) is reported based on time-dependent density functional theory calculations for electrons combined with Ehrenfest molecular dynamics simulations for ions in real time and real space. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the excitation mechanism for the inner $4f$ electrons of Pt. The comparison of calculation results with experimental data showed that conduction electrons are sufficient to describe the electronic stopping power of Pt accurately in the low-energy range. The excitation of $4f$ electrons contributes substantially to the electronic stopping power of Pt as the proton velocity exceeds 1.0 a.u. Our calculated stopping power is in quantitative agreement with the experimental data up to the stopping maximum, and showed that the stopping power obtained from the off-channeling geometry is greatly improved in comparison with the channeling results. Finally, the velocity dependence of the mean steady-state charge of protons was quantified, and the results showed that the instantaneous charge state of protons exhibits periodic oscillations in the low-energy region, while the periodic oscillations disappears in the high-energy region due to more ionization of protons.

First-principles study of the electronic stopping power of Zn for protons

The electronic stopping power of Zn for energetic protons is studied by using a nonequilibrium approach based on real-time time-dependent density-functional theory combined with molecular dynamics simulations. We calculated the electronic stopping power of protons traveling along two channeling trajectories depending on the impact parameter and off-channeling trajectories, and revealed the mechanism for d-electron excitation. In the low-velocity range, we reproduced not only the velocity proportionality of the stopping power of Zn for protons, but also the smooth transition between two velocity proportionality regimes, which is ascribed to the gradually increasing efficiency for d-electron excitation. The off-channeling electronic stopping power is in a good agreement with experimental data in the low and middle-velocity regimes. Our results showed that the contribution of d-electron excitation to the electronic stopping is remarkable in the high-velocity regime.

AbInitio Prediction of a Negative Barkas Coefficient for Slow Protons and Antiprotons in LiF.

We report the abinitio prediction of a negative Barkas coefficient in lithium fluoride (LiF) insulator at low velocity (v<0.25 a.u., E_{kin}∼2 keV). The electronic stopping power of protons in LiF has been extensively studied both experimentally and theoretically because of a controversial threshold effect. While our time-dependent density-functional theory simulations confirm the presence of a velocity threshold below which the proton stopping power vanishes, our calculations demonstrate that the antiprotons do not experience such a threshold. The combination of those two contrasting behaviors gives rise to an unprecedented negative Barkas effect: the stopping power of antiprotons is larger than that of protons. We identify that the slow antiproton at close encounter destabilizes a p orbital of the F^{-} anion pointing toward the antiproton. This particular orbital becomes highly polarizable and hence contributes much to the stopping power.

First-principles study of the electronic stopping power of indium for protons and He ions

The electronic stopping power of protons and He ions traveling along the channeling and off-channeling trajectories in indium is reported based on time-dependent density functional theory combined with Ehrenfest molecular dynamics simulations. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the microcosmic excitation mechanism of the semicore $4d$ electrons of In. The velocity-proportional electronic stopping power and the kink velocity which is due to $4d$-electron excitation are reproduced in the low-energy regime. Because the $5s5p$ valence electrons are uniformly distributed in indium, the electronic excitation of valence electrons via Coulomb scattering is independent of the impact parameter in the investigated velocity range. On the contrary, due to the highly localized nature of semicore electrons, the excitation of $4d$ electrons increases significantly with decreasing of the impact parameter, which suggests that it is triggered by direct ion-electron collision. Our calculated stopping power is in quantitative agreement with the experimental data up to the stopping maximum, and showed that the stopping power obtained from the off-channeling geometry is greatly improved in comparison with the channeling results. Finally, we examined the extent to which the linear response theory is applicable to describe the electronic stopping power by quantifying the velocity dependence of the mean steady-state charge of protons and $\ensuremath{\alpha}$ particles and the effective charge state for $\ensuremath{\alpha}$ particles, and it is found that the linear response theory can be used to predict the stopping power in a wider energy range if the mean steady-state charge is used instead of assuming fully ionized charges.

Electronic stopping power of protons and alpha particles in nickel

The electronic stopping power of nickel for protons and alpha particles at velocities below and around the Fermi velocity has been obtained to high accuracy using time-dependent density functional theory. For the wide range of projectile velocities considered, we observed different regimes of electronic stopping due to the alternative participation of $s$- and $d$-band electrons. Despite the sharp discontinuity in the electronic density of states near the Fermi energy characteristic of the nickel band structure, we do not find an anomalous nonlinear electronic stopping power limit as a function of velocity. However, we find a crossover region above $v=0.15\phantom{\rule{0.28em}{0ex}}\mathrm{a}.\mathrm{u}.$ both for protons and alpha particles, related to the increase in participating host electrons and, in the case of alpha particles, to an increase of the charge state. We compare our calculated results with widely available experimental data and analyze the low velocity limits in the context of Lindhard's linear response theory and previous nonlinear density functional calculations. The comparison shows good accord with the lowest velocity experiments available. This may indicate that the adiabatic local density approximation is already a good theory to calculate electronic stopping power in materials at low velocity.

Ab initioelectronic stopping power and threshold effect of channeled slow light ions inHfO2

We present an ab initio study of the electronic stopping power of protons and helium ions in an insulating material, ${\mathrm{HfO}}_{2}$. The calculations are carried out in channeling conditions with different impact parameters by employing Ehrenfest dynamics and real-time, time-dependent density functional theory. The satisfactory comparison with available experiments demonstrates that this approach provides an accurate description of electronic stopping power. The velocity-proportional stopping power is predicted for protons and helium ions in the low-energy region, which conforms to the linear response theory. Due to the existence of a wide band gap, a threshold effect in the extremely low velocity regime below excitation is expected. For protons, the threshold velocity is observable, while it does not appear in the case of helium ions. This indicates the existence of extra energy-loss channels beyond the electron-hole pair excitation when helium ions are moving through the crystal. To analyze it, we checked the charge state of the moving projectiles and an explicit charge exchange behavior between the ions and host atoms was found. The missing threshold effect for helium ions is attributed to the charge transfer, which also contributes to energy loss of the ion.

Electronic band structure effects in the stopping of protons in copper

We present an ab initio study of the electronic stopping power of protons in copper over a wide range of proton velocities $v = 0.02-10~\mathrm{a.u.}$ where we take into account non-linear effects. Time-dependent density functional theory coupled with molecular dynamics is used to study electronic excitations produced by energetic protons. A plane-wave pseudopotential scheme is employed to solve the time-dependent Kohn-Sham equations for a moving ion in a periodic crystal. The electronic excitations and the band structure determine the stopping power of the material and alter the interatomic forces for both channeling and off-channeling trajectories. Our off-channeling results are in quantitative agreement with experiments, and at low velocity they unveil a crossover region of superlinear velocity dependence (with a power of $\sim 1.5$) in the velocity range $v = 0.07-0.3~\mathrm{a.u.}$, which we associate to the copper crystalline electronic band structure. The results are rationalized by simple band models connecting two separate regimes. We find that the limit of electronic stopping $v\to 0$ is not as simple as phenomenological models suggest and it plagued by band-structure effects.

Electronic stopping for protons andαparticles from first-principles electron dynamics: The case of silicon carbide

We present the first-principles determination of electronic stopping power for protons and $\ensuremath{\alpha}$ particles in a semiconductor material of great technological interest: silicon carbide. The calculations are based on nonequilibrium simulations of the electronic response to swift ions using real-time, time-dependent density functional theory (RT-TDDFT). We compare the results from this first-principles approach to those of the widely used linear response formalism and determine the ion velocity regime within which linear response treatments are appropriate. We also use the nonequilibrium electron densities in our simulations to quantitatively address the longstanding question of the velocity-dependent effective charge state of projectile ions in a material, due to its importance in linear response theory. We further examine the validity of the recently proposed centroid path approximation for reducing the computational cost of acquiring stopping power curves from RT-TDDFT simulations.

Electronic stopping power for proton in amino acids and protein in 0.05–10 MeV range

The stopping powers for 0.05–10MeV protons in a group of 15 amino acids and a protein have been systematically calculated. The calculations are based on Ashley’s dielectric model. An approach of evaluating the optical energy loss function is incorporated into the Ashley’s model because no experimental optical data are available for these bioorganic compounds. The Barkas-effect correction and Bloch correction are included and an empirical minimum impact parameter a is used for the Barkas-effect correction. The proton stopping powers for the 15 amino acids and the protein in the energy range from 0.05 to 10MeV are presented here for the first time and might be useful for studies of various radiation effects in these materials.

Electronic stopping power of liquid water for protons down to the Bragg peak

An improved dielectric response model that accurately represents the recent experimental data for liquid water over the whole Bethe surface is used to calculate the electronic stopping power of protons (of fixed-charge) in liquid water from several MeV down to the Bragg peak region. The results are by approximately 20% lower than the ICRU values and earlier studies. A shell-correction term with a contribution of 15-20% to Bethe's high-energy stopping number is obtained. The present work offers a first-principle approach for stopping power calculations that overcomes the well-known limitations of Bethe's stopping theory, namely, the need for separate determination of the mean excitation energy (the I-value) and the shell-corrections. In particular, all type of inner-shell effects are built into the model through the kinematically restricted integrals over the Bethe surface. The net contribution of higher-order corrections is found to be minimal over most of the present range. Thus, within the uncertainty of the dielectric model (few %) the present calculations are 'exact' down to approximately 100 keV.

Modifications to a universal electronic stopping power equation for ions

Modifications to a universal electronic stopping power equation for nonrelativistic heavy ions in solids have been made. Some calculations of electronic stopping power for protons are performed using the new equation for a variety of targets with different atomic numbers. The results are close to that of the TRIM program.

Experimental and theoretical study of the ratio between the electron emission yield and the electronic stopping power for protons incident on thin carbon foils

It is often assumed that the kinetic electron emission yield γ is proportional to the electronic stopping power d E/d x for ions incident on solid targets. Though these two phenomena are based on the same physical process in which the incident ions lose their energy in the target in electron excitations, there is no reason why the ratio Λ= γ/(d E/d x) should be constant. We present in this paper a comparison between experimental and theoretical results for protons incident on thin carbon foils in a wide energy range (200 keV–9.2 MeV). The ratios Λ B= γ B/(d E/d x) and Λ F= γ F/(d E/d x) for both the backward (B) and forward (F) emission yields are studied as a function of the incident proton energy as well as the target thickness.

Electronic stopping power of protons and He ions in a dilute electron gas of a metal

Electronic stopping power of protons and He ions in a dilute electron gas of a metal

Electronic stopping power for protons in an LiF monolayer

In our previous work, the stopping properties of metallic and covalent films were investigated. Here we consider an ionically bound film. The energy loss of a proton in an LiF monolayer (LiF-1L) is calculated in orbital fashion, based on kinetic theory. The required momentum density and mean excitation energy are obtained from the local density approximation and local plasma approximation respectively. For comparison, the LiF molecule is treated by use of a large intermolecular distance in the film. We find the stopping cross section of the LiF molecule to be only slightly larger than that for the LiF-1L. The Bragg rule (additivity of stopping for the corresponding atoms) is not valid for the ionically bound molecule nor the corresponding extended system, but may be valid if additivity of stopping of atomic ions is assumed. © 1993 John Wiley & Sons, Inc.

A fitted expression for the electronic stopping power of protons in solids

The energy losses of protons in solids are calculated using local-field correction (LFC) dielectric function and the local-density approximation for a wide variety of projectile energies ranging from 1 to 10 4 keV. We fit the electronic stopping power dependent on eight parameters based on our numerical results, and compare our calculations with the experimental data and the results of other theories.

Chemical bond effects on the low-energy electronic stopping power of protons: use of molecular fragments

We propose the use of molecular fragments in a recently derived modified version of the Firsow model to account for the low-energy electronic stopping cross section due to molecular targets. The method is free of adjustable parameters and is based on the floating spherical Gaussian (FSGO) representation of molecular orbitals, being particularly useful for the treatment of large molecular targets. The results of this work indicate fair agreement with other calculations for protons incident on a wide variety of systems. Support is given to both, the use of characteristic molecular groups as well as the core and bond (CAB) partition scheme for the stopping power analysis of compound materials.

Stopping power of proton in monocrystalline, polycrystalline and amorphous silicon

The allotropic effect on the electronic stopping power of protons in solids was systematically determined by the nuclear resonance reaction 27Al(p, γ) 28Si at Ep = 774 and 992keV in an silicon on sapphire (SOS) sample of epitaxial Si on sapphire. Details of the experimental technique are described. The experimental error is less than 3%.

Local-field corrections in the calculation of electronic stopping power for protons

The energy loss of slow protons in a degenerate electron gas is calculated on the basis of the dielectric theory. The influence of various longitudinal dielectric functions is examined. Comparison with the results of the kinetic theory is made. The effect of the local-field correction on the straggling parameter is also discussed.