Binary Encounter Approximation Research Articles

Reflection coefficients of light ions/atoms from solids: comparison of analytical results with simulation codes using the binary encounter approximation

Medium energy ion and atom backscattering from solids has been studied by means of transport theory. The analytical results have been compared with computer simulations using the binary encounter approximation (TRIM and MARLOWE). In the analytical and the computer simulation approaches identical realistic potentials were employed to describe elastic collisions of light projectiles with target atoms. Electronic energy losses were accounted for by the formula of Lindhard and Scharff. The analytical approach is based on the solution of the transport equation with appropriate boundary conditions. A simple analytical expression for the total reflection coefficient has been derived under the assumption that the majority of backscattered particles leave the target without losing a considerable amount of their kinetic energy. The backscattering coefficient is shown to be a universal function of the angle of incidence and the ratio of the linear range and the transport mean free path of a projectile.

Calculation of heavy-ion track structure

A Monte Carlo model is presented to study details of the energy deposition inside tracks of heavy charged particles in water vapor. The input data for most of the calculations are double differential cross sections for electron emission after heavy ion impact based on the binary encounter approximation. The paths of the liberated electrons are simulated, taking into account elastic scattering, ionization, and excitation. Each basic interaction of an electron or heavy ion is treated individually. Radial dose distributions and specific energy deposition are calculated for projectiles from protons to uranium for beam energies of several MeV/u. Good agreement with measurements in tissue-equivalent gas and propane is obtained for light and medium-heavy projectiles, whereas for heavy projectiles such as uranium, deviations around a factor of 2–3 are observed.

Effects of multiple ionization on the Kα spectrum of aluminum in intense lithium beam experiments

The effect of multiple ionization on Kα spectra is investigated for aluminum targets irradiated by intense lithium beams. Multiple ionization cross sections have been calculated using a formulation incorporating single-electron ionization probability in the binomial distribution. In contrast to conventional binary-encounter approximation (BEA) theory, the single-electron ionization probabilities for each atomic shell have been calculated using a combination of modified plane-wave Born approximation (MPWBA) and an empirical effective interaction radius which is dependent on both the target ion and the projectile. Our calculations show that the effect of multiple inner-shell ionization on aluminum Kα spectra observed in intense lithium beam experiments is important. Multiple ionization effects become less important as the target ionization state increases. Nevertheless, even for highly ionized species up through Be-like Al multiple ionization effects can be significant and must be considered in the analysis of spectra obtained in intense Li beam-plasma interaction experiments.

Electron impact ionization of Ba, Ba+ and Ba2+

The binary encounter approximation has been used to investigate the effect of charge state of the target atom (ion) on the electron impact excitation autoionization cross-sections. Roothan-Hartree-Fock (RHF) velocity distribution for the bound electrons has been used through-out the calculations. The present results give a good account of the experimental observations.

Dynamic charge states and energy deposition of swift helium ions in neon

We report pilot calculations using the method of electron nuclear dynamics for study of charge changing and energy deposition characteristics of low energy He ions in Ne. In the spirit of the binary encounter approximation, trajectories, charge changing cross sections and energy deposition are calculated for single encounters.

A quasielastic scattering approximation for target ionisation by heavy structured projectiles

A modification of the impulse approximation for capture to continuum is used to describe the ejection of loosely bound target electrons by heavy ions. In contrast to the currently applied elastic scattering models based on the binary encounter approximation, the present model treats only the short-range part of the ionic field within the elastic scattering theory, but uses the more sophisticated impulse approximation for the Coulomb tail of the interaction potential. Calculations have been performed for Bq+, Feq+, Auq+ and Uq+ colliding with helium at energies between 0.5 and 6 MeV/amu. The comparison with absolute experimental spectra shows that theory works well for light projectiles, being able to describe the intensity and its variations with ionic chargeqion in the binary encounter peak region. For very heavy low-energy projectile ions the intensity is, however, seriously under-predicted at small emission angles, indicating a breakdown of perturbative treatments.

PIXE and RBS analysis of sediments from El-Kansera barrage on Oued Beht river in Morocco

Elemental analyses of sediments from the barrage El-Kansera on the river Oued Beht in Morocco, are reported. These analyses were performed by means of proton induced X-ray emission (PIXE), and Rutherford backscattering spectroscopy (RBS). The RBS analysis allowed the determination of the sediments matrix composition, which was used for the PIXE analysis. The quantitative analyses of the PIXE spectra were performed by using the binary encounter approximation (BEA) for the inner shell ionization cross section. Preliminary results are presented, and a comparison with literature data is discussed.

Track structure and DNA damage

Heavy particles like protons or heavier ions are different in their biological efficiency when compared to sparsely ionizing radiation. These differences have been attributed to the different pattern of energy deposition in the track of the particles. In radiobiological models two different approaches are used for the characterization of the radiation quality: the continuous dose distribution of the various track structure models and the separation in small compartments inside the track which are used in microdosimetry. In a recent Monte Carlo calculation using the binary encounter approximation as input for the electron emission process, the radial distribution of the dose is calculated for heavy ions. The result of this calculation is compared to other models and used for a qualitative interpretation of the induction of DNA damage by particles.

Electron impact double ionization of Ba and Ba+

Electron impact double ionization cross-sections for Ba and Ba+ have been calculated in the binary encounter approximation. Hartree-Fock velocity distribution has been used for the first ejected electron and a hydrogenic velocity distribution for the second. For Ba+ the focusing effects of the target ion on the incident electron have been incorporated in the calculations. Contributions from ionization-autoionization to the ionization cross-sections, as observed in experiments, have been included in the present work. The calculated results show structures as observed in recent experiments.

Electron impact double ionization of singly charged ions C+, N+, O+, F+ and Ne+

The first absolute cross section measurements For double ionization of C+, N+, O+ and Ne+ ions by electron impact are reported. The animated crossed beams method has been employed in the energy range from below ionization thresholds to approximately 2500 eV. The classical binary encounter approximation overestimates measured cross sections by almost two orders of magnitude. Along the sequence, the cross section maximum does not follow classical scaling laws. A simple scaling law based on an electron pair ejection model is proposed for the prediction of direct double ionization. Inner-shell ionization followed by autoionization is seen to play a dominant role for C+ only.

Calculations of heavy-ion track structure.

A Monte Carlo model is presented to study details of the energy deposition inside tracks of heavy charged particles in water vapor. The input data for most of the calculations based on the binary encounter approximation are double-differential cross sections for electron emission after heavy-ion impact. The paths of the liberated electrons are simulated, taking into account elastic scattering, ionization, and excitation. Each basic interaction of an electron or heavy ion is treated individually. Radial dose distributions and specific energy deposition are calculated for projectiles from protons to uranium in the energy range from one to several hundred mega-electron volts per unified atomic mass unit. Good agreement with measurements in tissue-equivalent gas and propane is obtained for light and medium-heavy projectiles, whereas for heavy projectiles such as uranium, deviations around a factor of 2-3 are observed.

Electron impact ionization of Zn+ and Ga+

We have investigated the contribution of excitation-autoionization to the electron impact ionization of Zn+ and Ga+ using the binary encounter approximation. Hartree-Fock velocity distributions for the bound electrons have been used throughout the calculations of direct and indirect ionization cross-sections. The calculated cross-sections are in good agreement with recent experiments. We have also compared our results with other theoretical calculations.

On the momentum representation of hydrogenic wave functions: Some properties and an application

The wave functions in momentum space for discrete states of hydrogenlike atoms are discussed in terms of both the early contributions to the subject and their present usefulness in atomic physics. The derivation of some of their important properties is outlined, in particular the expectation values of various powers of momentum and kinetic energy, and the kinetic energy distribution. As an application, the cross section for ionization of hydrogen in the metastable 2S state by electron impact is calculated with the aid of the binary-encounter approximation, which requires the use of momentum-space wave functions.

K-shell x-ray production cross sections for low-Z elements (11

K-shell x-ray production cross sections for Na, Mg, Al, Si, Cl, K, Ca, and Ti bombarded by $^{4}\mathrm{He}^{+}$ ions in the energy range 1.0--2.5 MeV have been measured using thin targets. The ionization cross sections deduced are compared with various Coulomb-ionization theories based on the plane-wave Born approximation, the binary-encounter approximation, and the simplified semiclassical approximation according to the Andersen, L/gsgaard, and Lund [Nucl. Instrum. Methods 192, 79 (1982)] and 1s\ensuremath{\sigma} molecular-orbital ionization theory. The calculations based on a perturbed-stationary-state approach including all the corrections such as the Coulomb deflection, the increased binding energy, and the relativistic effects, describe the data best although there are deviations in the case of Na at lower energies.

K-shell-ionization cross sections for low-Z elements (11

K-shell-ionization cross sections for Na, Mg, Al, Si, Cl, K, Ca, and Ti by protons in the energy range 0.5--2.5 MeV have been measured using thin targets. Measurements have also been performed for thin targets of Fe, Ni, and Cu at a few energies. The energy range of protons for these targets corresponds to the reduced velocity (${\mathit{v}}_{1}$/${\mathit{v}}_{2\mathit{K}}$) range 0.2--1.1, in which the cross sections are very sensitive to the increased binding energy and the Coulomb-deflection effects. The measured ionization cross sections are compared with the predictions of the theory based on the perturbed-stationary-state approach including the Coulomb-deflection, energy-loss, and relativistic corrections. The data have been scaled according to various scaling laws to test the validity of the universal nature of the various Coulomb ionization theories based on the plane-wave Born approximation, the binary-encounter approximation, and the simplified semiclassical approximation model as given by L\ae{}gsgaard, Andersen, and Lund [in Proceedings of the Tenth International Conference on the Physics of Electronic and Atomic Collisions, edited by G. Watel (North-Holland, Amsterdam, 1978), p. 353]. The measured data have also been compared with the calculations of Montenegro and Siguad [J. Phys. B 18, 299 (1985)] based on the theory of 1s\ensuremath{\sigma} molecular-orbital ionization.

Theoretical description of the anomalous q-dependence of the zero degree binary peak in F q+ + H 2 collisions

The anomalous q-dependence of the zero degree binary peak recently observed by Richard et al. [J. Phys. B23 (1990) L213] is explained in terms of the differences between the scattering of target electrons by either a bare or a clothed projectile. Calculations have been performed using the impulse or binary encounter approximation. That is, the convolution of the quantum mechanical elastic cross section and the target momentum distribution is calculated. The non-Coulomb phase-shifts due to the screened projectile-electron interaction were obtained by direct integration of the radial Schrödinger equation using Hartree-Fock model potentials. Very good agreement is obtained between theory and experiment and, furthermore, this model is used to illuminate the underlying dynamics which leads to the anomalous behavior.

Electron impact single and double ionization of halogens

The binary encounter approximation has been used for calculations of electron impact single ionization cross-sections for F, Cl, Br and I and double ionization cross-sections for Br and I. Contributions of ionization from inner shells have also been included in the calculations. Hartree-Fock momentum distribution has been used for the bound electron as far as possible. The results have been found to be in satisfactory agreement with experimental observations.

Proton and α-particle impactM-shell ionization of atoms in binary encounter approximation

M-shell ionization cross sections for atoms due to the impact of proton and α-particles have been calculated in the binary encounter approximation. The effects of Coulomb deflection of the incident projectile and increase in binding of the target electron have been investigated. Roothan-Hartree-Fock velocity distribution for the target electrons has been used in the present work. The calculated cross-sections have been compared with experimental results and other theoretical calculations wherever available. The present calculations give a good account of experimental observations.

Electron impact ionization cross sections of molecules: Part II. Theoretical determination of total (counting) ionization cross sections of molecules: a new approach

Cross sections for single ionization of molecules by electrons (threshold ⩽ E ⩽ 200 eV) have been calculated using a newly developed semiclassical formula. The formula is a combination of the classical binary encounter approximation, the Born-Bethe approximation and the additivity rule. This formula has been applied to H 2, N 2, O 2, H 2O, CO 2, C 2H 2, NH 3, CH 4, CF 4, C 2H 4, CH 3OH, SF 6, UF 6, C 2H 6 and C 6H 6 and the cross sections obtained have been compared with results from the classical binary encounter approximation (Gryzinski formula), the semiclassical Jain-Khare approach, and reliable experimental data. The main advantage of the present treatment is that ionization cross sections can be described by a simple analytical formula (depending only on basic atomic properties), which yields results in better agreement with experimental data than the classical formulae.

The effect of the relativistic Hartree-Fock-Roothaan momentum distribution in the binary encounter approximation for inner shell ionization

K- and L-shell ionization cross sections of gold due to impact of proton and alpha particles have been calculated in the binary encounter approximation incorporating the effects of Coulomb deflection of the projectile, of increase in binding of the target electron, and of polarization and relativity. Relativistic Hartree-Fock-Roothaan (RHFR) momentum distributions for the target electron along with an approximate relativistic correction to the collision dynamics have been used in the present calculations. A comparison with the corresponding calculations using non-relativistic Hartree-Fock-Roothaan wave functions, experimental results and other available calculations is presented.