Stopping Cross Sections Research Articles

Revisiting the stopping powers of Si and SiO 2 for 4He ions: 0.5–2.0 MeV

Stopping cross-sections for 4He ions in both amorphous Si and SiO 2 have been investigated over the energy region 0.5–2.0 MeV using Rutherford backscattering spectrometry (RBS), with special emphasis on the experimental determination of Q×Ω – the charge × solid angle product. The solid angle has been determined via the use of Harwell Series II Bi-implanted Si specimens. We find no significant disagreement with experimental stopping powers reported for amorphous Si. For SiO 2, our results are ∼3% smaller than recent measurements. Using Bragg’s rule, a functional oxygen stopping cross-section useful for RBS analyses of condensed media targets has been extracted. The reasons for simulating measured pulse height spectra, as distinct from energy spectra, are delineated.

Computer-simulation calculations of the electronic stopping of fast heavy charges by a classical harmonic oscillator

The accuracy of Bohr’s and more recent analytical calculations of the electronic stopping of heavy charges by a classical harmonic oscillator is analyzed. According to results in this paper, for [Formula Presented] (ξ being the Bohr stopping parameter) the present simulations agree with previous theoretical calculations, whereas for smaller |ξ| values, discrepancies are evident. In fact, for [Formula Presented] the stopping cross section seems to be sensitive to the sign of the ion charge. The so-called Barkas effect is unambiguously observed and positively charged projectiles appear to have a larger stopping compared to that of negative ones at the same ξ. Bohr’s calculations, however, seem to reproduce the stopping of negative charges relatively well, but those of positive ions are consequently underestimated. By giving the electron an initial velocity, the so-called inner-shell effect on the stopping can be readily studied. The present simulations show that previous analytical predictions of this effect do not account for the present results. © 2003 The American Physical Society.

A simple model for latent track formation due to cluster ion stopping and fragmentation in solids

An estimate of the electronic stopping of a swift cluster ion during different stages of penetration in a given material is presented. We take a simplified approach to the stopping process by neglecting vicinage effects on the stopping cross section as well as spatial distortion due to Coulomb forces among ions. The different stages of penetration and energy loss are based on the hypothesis of formation of a transient plasma (the plasma stopping regime)—due to the release of energetic electrons from the target material—within and around the spatial region defined by the correlated positions of each cluster constituent ion (atom). The density of the transient plasma is treated as a function of the rate of energy deposition and depth up to a point where the rate of energy deposition yields a threshold value where the ejected target electrons immediately recombine so that stopping in a cold target begins (conventional stopping regime) and where the cluster constituent ions start being neutralized according to a charge equilibration scheme as depicted by the effective charge relation of Betz. The model is applied to the stopping of 40.2 Mev C 60 3+ projectiles penetrating an Yttrium–Iron Garnet (YIG) target. Also, in this case, a possible explanation for the experimentally observed cluster-fragmentation events at a certain depth is presented.

Energy loss studies of protons colliding with ethane: preliminary results

This paper reports theoretical calculations for projectile kinetic energy loss and stopping power of protons colliding with C 2H 6, for projectile energies of a few eV up to 25 keV. The many body character of the system and the strong coupling of the electronic and nuclear degrees of freedom make this system suitable for study using electron–nuclear dynamics. We report the stopping cross section as well as the electron capture cross section as a function of the projectile kinetic energy. We find that chemical dissociation plays an important role in charge exchange due to the bond breaking during the collision. We also obtain the stopping cross section using Bragg’s rule in order to analyze chemical effects (bond contributions). Finally, comparison to the available experimental data is provided.

Material dependence of electronic stopping

The dependence of the electronic stopping cross-section on the atomic number of the target material has been studied on the basis of binary stopping theory over a wide range of beam energies. A distinct dependence on ion type and energy is found for the predicted Z 2-structure which becomes significantly less pronounced for screened heavy ions than for protons and antiprotons. This behavior is caused primarily by the interplay between projectile screening and closing of inner target shells as a function of the beam velocity and introduces a pronounced Z 2-structure in the effective-charge ratio. Related effects are found for stopping in three different phases of carbon and in lithium fluoride.

Numerical calculations of neutral beam injection in spheromaks

A numerical study of neutral beam injection into spheromaks ispresented. The beam evolution is calculated through a Monte-Carlosimulation and the plasma MHD equilibrium is determinedself-consistently with the current produced by the beam. The exactequations of motion are used for the beam particles instead of the usualguiding-centre approximation. The guiding-centre trajectories areclearly different from the actual particle trajectories and thisdifference produces discrepancies in the total driven current and in thecurrent profiles. A reduction of the plasma effective charge, Zeff,does not result in an improvement in the current drive efficiencybecause the reduction of the stopping cross section is compensated by anincrease in the electron cancelling current. The safety factor profile ofthe self-consistent equilibria shows a clear sensitivity to the drivencurrent profile. The value at the magnetic axis (q0) diminishes whenthe beam is injected at the magnetic axis and increases for injectionabove the axis. Power deposition profiles for simple injectionconfigurations are also shown.

Electronic stopping powers of molybdenum metal for 19F ions at low velocity

Electronic stopping powers for 80–350 keV 19F ions in molybdenum were obtained by range measurement. Depth profiles of 19F in molybdenum were measured by using the 19F(p,αγ) 16O resonant nuclear reaction at E R=872.1 keV. A proper convolution calculation method was used to extract the true distribution of fluorine from the experimental excitation yield curves. The electronic stopping powers were derived through fitting the projected range distributions, simulated by using the TRIM/XLL code, to the experimentally measured range distributions. The electronic stopping cross sections were compared with those obtained from Monte Carlo simulation codes.

Stopping power calculation of rubidium and strontium for protons

We have evaluated the stopping cross-section (SCS) and the energy-loss straggling of rubidium and strontium targets, for a wide range of proton energies. The calculations are done in the framework of the dielectric formalism, using a combination of Mermin-type energy-loss functions to describe the behaviour of the outer electrons of the target, while the inner-shell electrons are described through their generalized oscillator strengths. Our calculated SCSs agree with the experimental data better than other theoretical and interpolated results, in a wide range of proton energies.

Differential scattering cross-sections, inelastic energy losses and ion fractions in backscattering of keV He + ions from monolayer metal adsorbates on solid surfaces measured by means of CAICISS

Energy spectra of He atoms and He + ions backscattered at an angle of ∼180° by monolayer metal adsorbates (Ag, Sn, Sb, Pb and Bi) on the Si(1 1 1)- 3 × 3 surfaces and monolayer Si atoms on the graphite surface have been measured by means of the coaxial impact collision ion scattering spectroscopy technique combined with low energy electron diffraction, Auger electron spectroscopy and Rutherford backscattering spectrometry techniques in the energy range from 0.5 to 3.0 keV. It is found from their data analysis that the ratios of the experimental scattering cross-section to the magic formula of the Thomas–Fermi cross-section for different adsorbates deviate from unity: for instance 1.2 for Si, 0.8 for Ag, 1.5 for Sn, 1.2 for Sb, 1.2 for Pb and 1.6 for Bi. It is also found that the average inelastic energy loss for Si increases monotonically with increasing the incident energy, while those for the other adsorbates increase stepwisely at around 1.0 keV and thereafter gradually. Moreover, it is found that the stopping cross-sections at 2 keV and at zero impact parameter obtained in the present study are by an order of magnitude smaller than, but, in their functional dependence on Z 2, very similar to the empirical data of electronic stopping cross-sections by Ziegler. Finally, it is found that the ion fractions for Sn, Sb, Pb and Bi show oscillatory variations with the inverse velocity of primary ions which are explained in terms of the quasi-resonant charge exchange between the He 1s state and the 4d states or 5d states of the adsorbate atoms. On the other hand, it is also found that the ion fraction for Ag decreases very gradually from 1/3 and those for Si are less than 0.05 in the energy range below 3 keV. The latter two results on the inelastic energy losses and the ion fractions are discussed in terms of promotion of the quasi-molecular orbitals and charge exchange between the quasi-molecular orbitals formed during the close collisions of He and adsorbates.

Quantum and classical stopping cross-sections of swift heavy ions derived from the evolution with time of the Wigner function

The charge dependent stopping cross-section of partially ionized heavy ions in a carbon target is determined in the energy range of a few MeV/n. It is done by calculating during an ion–atom collision the classical evolution of the Wigner function of the target electrons. A special emphasis in our calculations is put on the contribution of the 1s electrons for which we analyze the influence of the overlapping domain, concerning the impact parameter, of the charge transfer and energy loss processes. We give a detail comparison with the experimental results provided by Blazevic of 2 MeV/n neon ions interacting with a thin carbon foil target.

Trajectory and molecular binding effects in stopping cross section for hydrogen beams on H2

The complex interaction of an atomic projectile with a molecular target is studied by considering the time-dependent electron-nuclear dynamics of the collision. We calculate the energy loss, charge exchange, and differential cross section for a hydrogen beam colliding with molecular hydrogen targets for projectiles energies from 10 eV/amu up to 25 keV/amu. We obtain the total, electronic, nuclear, and rovibrational contribution for the orientationally averaged stopping cross section of the molecular target when scattering over all the angles is considered. We emphasize the violation of Bragg’s rule (additivity of the atomic energy loss for the compound target) and the acceptance angle dependence of the experimental stopping cross section.

Electronic energy loss of swift protons in the oxides Al 2O 3, SiO 2 and ZrO 2

We have evaluated the energy loss of protons when moving through several oxides (Al 2O 3, SiO 2, and ZrO 2). The calculations were done in the framework of the dielectric formalism, using a combination of Mermin-type energy-loss functions to describe the outer electrons, together with generalized oscillator strengths to take into account electrons from the inner shells. This method provides a realistic description of the electronic properties of each target. The calculated stopping cross-sections compare fairly well with the available experimental data in a wide range of proton energies.

Molecular target and projectile angular scattering effects in stopping power and charge exchange at low-to-intermediate projectile energies

We analyze the implications of the molecular structure of a target and the angular scattering effects on projectile-target collisions within the Electron-Nuclear Dynamics (END) approach. We show the suitability of the END method for the analysis of molecular scattering processes such as differential cross sections, charge exchange, and energy loss as required for the study of the stopping cross section. As a consequence of these effects, we show that the rovibronic energy loss becomes of greatest importance at low projectile energies. Furthermore, we find that the Bragg additivity rule and the linear-velocity dependence of the stopping cross section are not fulfilled at low projectile energies. Finally, we analyze the differences in the scattering processes for molecular and atomic targets, and show that in a transmission experiment with small exit window, the acceptance angle corresponds to different impact parameter selection for molecular targets than for atomic ones. Thus, the measured stopping cross section becomes a function of the acceptance angle of the experimental setup. We present results for hydrogen beams on ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ gas targets.

Electronic stopping powers for fluorine ions in 19F +-implanted tin-oxide films prepared by APCVD

Electronic stopping powers for 50–180 keV 19F ions in tin-oxide films were obtained by range measurement. Depth profiles of 19F in tin-oxide films were measured by using the 19F(p,αγ) 16O resonant nuclear reaction at E R=872.1 keV. A proper convolution calculation method was used to extract the true distribution of fluorine from the experimental excitation yield curves. The electronic stopping powers were derived through fitting the projected range distributions, simulated by using the TRIM/XLL code, to the experimentally measured range distributions. It is shown that the electronic stopping cross-sections obtained in this work agree well with those calculated by using TRIM90 and can be well described by the four-parameter formulae. But they are systematically larger than the results obtained from the TRIM98 code.

Stopping cross sections for 0.3–2.5 MeV protons in GaN and InP

The stopping cross sections of the III–V semiconductor materials GaN and InP for 0.3–2.5 MeV H1 have been studied by the Rutherford backscattering technique. The data are given with an estimated uncertainty better than 2% and the agreement with earlier data existing for InP below 500 keV is good. A commonly used model ZBL-85 predicts the data correctly at the high energy end of our energy interval, but overestimates the stopping values by 7% and 4% for GaN and InP, respectively, at the lower energies.

Experimental analysis of the stopping cross sections and of the charge changing processes for Cl q+ projectiles at the maximum of the stopping power

Chlorine 7+ ions interacting with different states of matter are compared in the framework of an accurate experimental measurement of energy loss as a function of the exiting charge state.

Modeling of swift heavy ions interaction with dense matter

Theoretical study of swift heavy ions interacting with dense targets made of low z material is the subject of the present work. An improved CKLT stopping formula is presented in its classical and quantum forms and a simple procedure is derived for calculating the CKLT stopping cross-section with non-coulombic interaction potentials. This method is applied to Cl q+ ions interacting with a hydrogen gas target.

ENERGY LOSS AND ENERGY STRAGGLING OF LIGHT IONS IN FULLERITE

To determinate the stopping cross section in fullerite a feasible approach, taking into account the high radiation sensitivity and mechanical fragility of fullerite films, should be employed. In this work, the stopping cross sections of 1H, 3H, 4He and 7Li ions for several selected energies were measured by Rutherford backscattering, neutron depth profiling and alpha spectroscopy using sandwich structures of samples composed of fullerite deposited on a firm substrate (Si, steel) with an intermediate marker (Au, N, Li, B, Pu). In addition, ion transmission through a thin C film supporting a fullerite layer was also utilized. The measured stopping cross sections follow the theoretical predictions calculated for carbon, but are systematically (10–35%) higher than the theoretical ones (with the exception of 5 — 5.5 MeV 4He). The observed deviation of the experimental data can partly be explained by the chemical state effects in fullerite, which accounts for about 20–50% of the difference. The measured energy straggling exceeds Bohr's value by a factor of about 2 for alpha spectroscopy and ion transmission, and 2.5 or 9.5 for Rutherford backscattering and neutron depth profiling, respectively. The discrepancy can be explained by a thickness variation, such as surface roughness of the fullerite films.

Effective charge and related/unrelated quantities in heavy-ion stopping

Stopping cross sections for swift heavy ions are commonly parameterized in terms of a velocity-dependent effective charge defined with reference to proton or helium stopping. This assumes projectile screening by core electrons to be a dominating factor governing the velocity dependence of the stopping cross section. In this note we demonstrate, on the basis of improved theoretical estimates of stopping cross sections, that projectile screening only affects the quantitative details of the velocity dependence of the effective charge while the general behavior reflects the transition from the Born to the classical regime. This is consistent with the experience that effective charges derived from measured stopping cross sections show dependencies on projectile and target atomic number which differ distinctly from those of the equilibrium projectile charge. It follows that there is no theoretical basis for the effective-charge concept as it is commonly used in heavy-ion stopping.

Range distribution and electronic stopping powers for fluorine ions in [formula omitted]-implanted potassium titanyl phosphate and LiNbO 3

Range distributions and electronic stopping cross-sections for fluorine ions in 19 F + -implanted potassium titanyl phosphate (KTP) and LiNbO 3 in an energy range of 50–330 keV were measured by using the 19 F(p,αγ) 16O resonant nuclear reaction at E R=872.1 keV. A proper convolution calculation method was used to extract the true distribution of fluorine from the experimental excitation yield curves. The electronic stopping powers were derived by fitting the projected range distributions simulated by using TRIM/XLL code to the experimentally measured range distributions. The experimental range distribution parameters, R p and ΔR p, and the electronic stopping cross-sections were compared with those obtained from different Monte Carlo simulation computer codes.