Binary Encounter Approximation Research Articles

Absolute Electron Impact Cross Sections for Single Ionization of Metastable Atoms of H, He, Ne, Ar, Kr, Xe and Rn

AbstractCross sections for single ionization of metastable atoms of H, He, Ne, Ar, Kr, Xe and Rn by electrons with impact energy E (threshold < E < 200 eV) are determined using a recently developed semiclassical formula. The formula consists of an energy dependent term (classical binary encounter approximation) and a term containing the weighted sum of the squared radii of maximum charge density of the outer electron subshells (Born Bethe approximation). Although this formula was originally devised and applied for ground state atoms, a comparison of the present calculations with previous calculations and measurements indicates that this formula can also be used successfully in case of metastable atoms.

Double K-shell vacancy production in Ca, Ti, V and Cr bombarded by protons

High-resolution proton-induced X-ray spectra in thick Ca, Ti, V and Cr targets were measured using a Bragg spectrometer combined with a proportional position-sensitive detector. The corresponding double K-shell ionisation cross sections were obtained from the hypersatellite line yields in the proton energy range from 1.3 to 1.7 MeV. They were also calculated within the semiclassical and binary encounter approximations using the independent double ionisation model. The agreement between calculated cross sections and experimental ones was improved when the change of the ionisation energy for the second ionised electron was taken into account. The results of the semiclassical approximation were found to be better than those of the binary encounter approximation.

Differential cross sections for secondary electron production by proton impact.

The differential cross section for ionization of atoms and molecules by proton impact is modeled over a wide range of incident-proton and ejected-electron energies by an analytical equation. This equation is based on the molecular promotion model at low energies and on the classical binary-encounter approximation, modified to agree with the Bethe theory of ionization, at high energies. Three adjustable parameters are sufficient to fit the experimental electron energy distribution at any given impact energy. Equations are given which fit two of these parameters as a function of proton energy over the range of 5 keV to 5 MeV. The third parameter is found to be a constant, independent of proton energy, but its value varies somewhat from target to target. The relation of one of these parameters to the optical oscillator strength is discussed as is the extension of the model to multishell targets. As examples, the model is applied to fit data on molecular hydrogen, helium, and argon. Quantities such as the stopping cross section, the average ejection energy, and the fraction of electrons ejected with energies greater than a given value are easily calculated using this model.

Transport of low- and medium-energy electron and ion beams in seawater and its vapors.

A general theory of stopping power for electrons and ions in a target medium (gas, liquid, or thin solid foil) containing neutral as well as positive and negative ions is developed. The approach is quite accurate in the low- and medium-energy range (less than 1 MeV), where the Bethe stopping-power cross section is inaccurate. The energy transfer during individual collisions is treated by the binary-encounter approximation. The theory is applied to determine the stopping power of seawater, whose major components are H2O molecules and Na(+) and Cl(-) ions. The stopping-power cross sections for low- and medium-energy protons in water show excellent agreement with existing measurements.

Model for the capture of secondary electrons by a fast ion

A capture process is discussed which is strongly assisted by the relaxation of energetic secondary electrons inside a solid target. The following processes are incorporated into the model (in a simplified form): — the production of secondary electrons by a fast projectile inside the target (in binary encounter approximation of the projectile with free target electrons), — the dynamics of the secondary electrons (in continuously slowing down approximation without elastic scattering), — the reduction of the screening of the projectile charge at the exit surface (in sudden approximation and neglecting the image charge). The capture efficiently populates Rydberg states with high angular momenta and gives high coherences between Rydberg states. The application to convoy electrons gives contributions only to the innermost part of the cusp shaped velocity spectra which is possibly caused by the neglect of elastic scattering of the secondary electrons.

Singly Differential Cross-Sections for Producing Secondary Electrons from Hydrogen Gas by keV to MeV Proton Collisions

An analytical equation is presented which yields singly differential cross-sections for electron ejection by proton collisions. The expression is a combination of a modification of the classical binary encounter approximation for small electron energies and an exponential equation for high energies which was derived from a promotion model. The equation is consistent with the Bethe theory of inelastic scattering. The equation is fitted to experimental energy distributions of electrons over the range of proton energies from 5 keV to 1.5 MeV. Related quantities such as the average electron energy and stopping cross-section are easily calculated from the model.

Differential cross sections for ionization of water vapor by high-velocity bare ions and electrons

A semiempirical model of single differential cross sections (SDCS) for ionization of water vapor by fast electrons and bare ions is presented. At low secondary-electron energy, the model is based on an asymptotic expansion of the first Born approximation with coefficients, that are independent of projectile properties, evaluated from experimental photoabsorption and proton-impact ionization data. As the secondary-electron energy increases, the model converges to a binary-encounter approximation. Comparisons with measured differential, total, and dissociative cross sections for ionization of water by fast electrons are used to test the model. For primary electrons with energy greater than about 500 eV, agreement with these data is generally within experimental uncertainty; however, some discrepancies of uncertain origin exist.

L-subshell ionisation of Z approximately 50 targets by4He ion bombardment

L X-ray production cross section for 4He ion bombardment of Ag, Cd, In, Sn, Sb, Te and I have been measured in the energy range 0.6-5.0 MeV. Subshell ionisation cross sections have been extracted and compared with the predictions of the binary encounter approximation with corrections accounting for binding and Coulomb retardation effects (BEABC), the semiclassical approximation with binding, energy loss, Coulomb deflection and relativistic corrections included (SCACBR) and the perturbed stationary state theory including energy loss. Coulomb deflection and relativistic corrections (ECPSSR). For the L2 and L3 subshells a good agreement is obtained with the ECPSSR predictions and, for the higher incident energies, with the BEABC ones, while the SCACBR theory overestimates the experimental data. For the L1 subshell the agreement is worse; especially for the lower incident energies (E(4He)<2 MeV) the present way of calculating theoretical corrections turns out to be inadequate to reproduce the experimental findings.

Semiclassical impact-parameter expansion of delta-electron spectrum

The impact-parameter dependence of the secondary electron production in collisions of heavy charged particles with atoms and the energy distribution of delta-electrons are studied using a statistical model of an atom and the binary encounter approximation. As a result of this model the analytical expressions, describing inelastic scattering of heavy charged particles by a statistical atom have been derived.

Alpha particle and deuteron impactL-shell ionization of Ar, Cu, Ge, Br, Zr and Ag

Alpha particle and deuteron impactL-subshell ionization cross-sections of Ar, Cu, Ge, Br, Zr and Ag have been computed using Vriens’ expressions for ionization cross-section of atoms due to impact of heavy charged particles. The effects of Coulomb deflection of the projectile and increase in binding of the target electron in the presence of projectile have been incorporated. Hartree-Fock velocity distributions for the target electrons have been used in the present calculations. The simple binary encounter approximation model is found to give results which are in satisfactory agreement with those obtained from experiments and from other theories.

Electron loss from Na Rydberg atoms by ion impact.

The absolute cross section for removal of Rydberg electrons from Na Rydberg atoms by impact of singly charged ions was measured. ${\mathrm{Ne}}^{+}$, ${\mathrm{Ar}}^{+}$, and ${\mathrm{Xe}}^{+}$, accelerated to energies 1--5 keV, bombarded a Na atomic-beam target that was laser excited to nd states, n=30--45. Electron loss, the sum of ionization and charge transfer, was detected by collecting impact-produced ${\mathrm{Na}}^{+}$ from the target after 1--3 \ensuremath{\mu}s exposure to the projectile beam. The velocity dependence of the cross section was measured for n=40 with projectile velocities v\ifmmode \tilde{}\else \~{}\fi{}=0.8--3.7 times the Bohr orbital velocity of the target atoms. The n dependence was measured at reduced velocity v\ifmmode \tilde{}\else \~{}\fi{}=2.0 for n=30--45. A study of field ionization of higher collisionally excited states was made, and important corresponding corrections were applied to the data. The effects of collisional l change in the target and of l mixing due to applied, pulsed electric fields were noted. The absolute unnormalized cross section for n=40 agreed with classical-trajectory calculations and with the classical binary-encounter approximation. The classically predicted n scaling of the cross section at fixed reduced velocity was directly demonstrated, and a scaling exponent 4.08\ifmmode\pm\else\textpm\fi{}0.07 between n=1 and 45 was found. The results may be compared with ${\mathrm{H}}^{+}$+H(1s) collisions at projectile energies 16--340 keV.

Collisional ionisation and the atomic model

A consistent classical theory of atomic ionisation by charged particles is presented. The theory is consistent in the sense that not only individual collisions between the charged projectile and the atomic electron are described in a classical way (the theory is based on the binary-encounter approximation corrected for the collective field of the atom) but the entire atomic system considered as a classical structure with well defined electron orbits. The developed theory is applied to the analysis of atomic ionisation by heavy charged particles. The theoretical results appear to be sensitive to the atomic model used; in the case of the free-fall atomic model, they are found to be in good agreement with the experimental data.

A wide bandpass low energy electron spectrometer

We have developed a high efficiency, wide bandpass solenoid spectrometer for the detection of electrons between 1 and 20 keV. The apparatus utilizes baffles to impose minimum and maximum constraints ofthe radii of electron trajectories, and therefore on the component of their momentum perpendicular to the magnetic field. Electric fields parallel to the magnetic field and time-of-flight information are used to contrain the electron's momentum component along the magnetic axis. A microchannel plate detects the electrons with high efficiency and provides fast timing. The performance of the apparatus was studied through a comparison between binary encounter approximation (BEA) calculations and measurements of δ-electron emmission in 5 MeV proton collisions with thin solid carbon targets.

L-subshell ionisation for 4He ion bombardment of tellurium

L-subshell ionisation cross sections for 4He ion bombardment of Te in the energy range 0.6−5.0 MeV, obtained by means of X-ray production measurements, have been compared with the predictions of different theories (binary encounter approximation, plane-wave Born approximation, semiclassical approximation). The effects of various corrections taking into account binding modifications, polarisation and relativistic motion of the atomic electrons and Coulomb retardation and energy loss of the projectile have been considered. The binding modification turns out to be the most relevant correction, but it is still inadequate to describe the low energy part of the cross sections.

α-particle and deuteron impact K-shell ionisation of atoms in binary encounter approximation

K-shell ionisation cross sections for atoms due to the impact of α-particles and deuterons 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 separately. Hartree-Fock velocity distributions for the target electrons have been used in the present work. The calculated cross-sections and the ratio R = σ α /4 σ d have been compared with experimental results and other available calculations. The present calculations are found to give a good account of experimental results.

Absolute partial and total electron impact ionization cross sections for CF4 from threshold up to 180 eV

Electron impact ionization of carbon tetrafluoride was studied as a function of electron energy from threshold up to 180 eV. A double focusing mass spectrometer system with an improved electron impact ion source was used, alleviating the problems of ion extraction from the source and the transmission of the extracted ions through the mass spectrometer system. Absolute partial ionization cross section functions for the production of CF+3, CF+2, CF+, C+, F+, CF2+3, and CF2+2 in CF4 have been determined. In addition, the total (and the counting) ionization cross section function of CF4 has been determined (summation method) and is compared with calculations based on classical and semiclassical binary encounter approximations. Using nth root extrapolation ionization energies of the following doubly charged fragment ions have been derived: AE (CF2+3) =41.8±0.3 eV, AE (CF2+2) =42.9±0.3 eV, and AE (CF2+)=52.1±0.5 eV. In accordance with previous results no stable CF+4 parent ion has been detected, however, a metastable dissociation process CF+*4→ CF+3+F has been observed.

Comparison of calculations of effective charges in ion-atom collisions

The effect of the static screening of the projectile on the differential and total cross section of the direct Coulomb ionizations, calculated by different methods in the Born and binary encounter approximations, are examined together with the effective ionizing projectile charges defined in these calculation procedures. Comparison is made with the effective charges determined in ion-atom collisions.

Electron stripping cross section from multiply charged ions by neutral atoms

Electron stripping cross sections for energetic highly charged C and Ne ions are calculated using the method based on the binary encounter approximation. Electrons of the ion are considered to be stripped by collision with the target nucleus, i.e. the electron screening is ignored. The cross section is written in terms of relative velocity between each electron and the target nucleus. The velocity distribution of electrons of the ions is obtained by the Thomas-Fermi statistical model for the purpose of obtaining the general behavior of projectile and target atomic number dependences. The effect of shell-structure on the cross section is taken into account by considering the average binding energies of electrons that are supposed to exist in each shell.

Inelastic scattering of charged particles by a statistical atom

The angular and energy distribution of secondary electrons ejected in collisions of heavy charged particles has been calculated in the binary encounter approximation using the statistical Thomas-Fermi method. Comparisons are made with reported experimental results.

He + impact ionization of K

The integral ionization cross sections of the potassium (K) atomic system by He + ion impact have been calculated in the binary encounter approximation (BEA) using the configuration interaction (CI) wavefunction. Comparison is made with the available experimental observation and theoretical prediction. Agreement between our present calculated results and experimental data is reasonably good.