Cross Sections For Ejection Of Electrons Research Articles

Differential cross sections for the single ionization of H2 by 75 keV proton impact

We have calculated the double and triple differential cross sections for electron ejection with energy of 14.6 eV in single ionization of H2 by 75 keV proton impact. A molecular version of the continuum distorted wave-eikonal initial state approach is applied, where the interaction between the projectile and the residual molecular ion is considered more properly than in previous applications of the method. For triple differential cross sections, the present results are in better agreement with the experimental data than those of other descriptions when large momentum transfer values are considered. For double differential cross sections the experimental data are reproduced quite well for both coherent and incoherent proton beams.

Fragmentation of positronium with excitation and ionization of the target

Calculations of positron and electron ejection cross sections are made for collisions of Ps $(1s)$ with the noble gases He, Ne, Ar, Kr, and Xe, allowing for target excitation (i.e., discrete excitation and ionization). Cross sections doubly differential and singly differential with respect to ejected energy and angle are reported, as well as total ionization cross sections. Our results show clearly that excitation of the target becomes very important at impact energies greater than about 2 times the ionization threshold of the atom. Comparison is made with absolute experimental measurements on He and Xe targets and, with one exception, good agreement is found at both total and single differential levels. Unfortunately, most of the measurements are at impact energies where target excitation is small or negligible. There is a need for experiments at higher impact energies to assess the predictions for target excitation.

Track formation and electron emission in swift ion collisions with condensed matter

Electron ejection from target atoms is one of the basic processes when ionizing radiation interacts with matter. The primary electrons and their subsequent secondary interactions lead to the deposition of energy around the ion trajectory. The detailed knowledge of the structure of these ion tracks is a key issue for our understanding of radiation effects in condensed matter, an important example being calculations of the RBE of heavy particles, where doubly differential electron ejection cross sections are a key input parameter. Usually, data obtained from single collisions, i.e. with gas targets, are used, but condensed matter effects may considerably alter the emission patterns. Therefore, we will focus on the primary ionization (binary encounter and soft electron emission), which is common to single atoms (gas targets) and condensed matter. Then, special emphasis will be given to discuss effects, which are only seen in condensed matter (electron transport and multiple scattering effects, jet-like structures, wake effects due to collective excitation of plasmons), but not in gaseous targets (single collisions).

Electron ejection by heavy particles as precursor of track formation in condensed matter

The detailed knowledge of the structure of ion tracks is a key issue for our understanding of radiation effects in condensed matter. Important examples are the radial energy deposition profile by electronic excitation for numerical simulations of track formation (via “Coulomb explosion” or “thermal spike”) in inert matter, and calculations of the RBE (relative biological effectiveness) of heavy particles in living matter (with important applications in dosimetry and hadrontherapy). In both cases, differential electron ejection cross sections are used as input parameter. The precursor of track formation is thus electron ejection from target atoms, or from the projectile itself. These primary electrons and their subsequent secondary interactions lead to the deposition of energy along and around the ion trajectory. We first briefly discuss “primary ionization” (binary encounter and soft electron emission, multiple collision sequences: “Fermi shuttle”) common to single atoms (gas targets) and condensed matter. Then, specific effects in condensed matter (electron transport, jet-like electron spikes, wake effects due to collective excitation of plasmons and emission of shock wave electrons) will be presented. Finally, we concentrate on effects connected to the high density of deposited energy and strong perturbation induced by heavy particles such as heavy ions and clusters (reduction effects due to screening, transport and “sweeping away”, multiple ionization, electronic temperatures from Auger spectroscopy).

Differential cross sections for ionization of atmospheric gases by electron impact

Absolute values of doubly differential cross sections for electron ejection in collisions of fast electrons with , , CO and molecules have been measured at the electron ejection angle of , in the incident electron energy range 100-1000 eV and in the ejected electron energy range 5-50 eV. Singly differential cross sections are also determined using a normalization procedure. The measured cross sections agree well with available data of other authors, except for those on at 1000 eV, where a disagreement of up to a factor of 3 is observed. However, a rather good agreement is found between experimental data of this work at high energies and calculations using the Born approximation.

Direct ionization in the quasimolecule H-He.

Doubly differential cross sections for electron ejection in H-He collisions have been measured in the incident atom energy range 2.3--10 keV. Analysis of the experimental data on the basis of the adiabatic theory of direct ionization has been made and parameters of the quasimolecule, namely, the energy of the initial 2p\ensuremath{\sigma} state coupled with the continuum, the effective charge, and the real and imaginary parts of the internuclear distance at which the ``superpromoted'' diabatic term crosses boundary of continuum, have been determined. The values of the initial-state energy and the effective charge agree well with the corresponding parameters of the Li united atom, whereas the dynamical characteristics ReR(E) and ImR(E) reveal considerable influence of electron correlations. The possibility for the development of an alternative method of quantitative spectroscopy of quasimolecules based on the analysis of experimental data on differential cross sections for direct ionization is discussed. \textcopyright{} 1996 The American Physical Society.

Projectile and electron spectra resulting from positron-argon collisions

A three-body classical trajectory Monte-Carlo calculation is used to evaluate the differential cross sections for the ejected electron, as well as the projectile scattering for 50, 100 and 150 eV e++Ar0 electron removal collisions. In the ionized electron spectra both the electron capture to the continuum (ECC) and binary peak structures are observed. The theoretical ECC peak is diffuse and shifted to lower energies than expected from simple arguments. The calculated double differential cross sections for electron ejection have been compared to experiment. When the experimental apparatus function of Moxom et al. (1992) is used to convolute the theoretical spectra, good agreement with their data is found that confirms a sharp ECC structure is not present in this system. Moreover, comparisons made at non-zero angles show substantial agreement between theory and experiment. The scattered positrons agree well with measurements made at 3 degrees by Kover et al. (1993), but differ at larger angles. In addition, the differential cross section for positronium formation is presented; no evidence of an observable Thomas peak is present.

Structures in differential cross sections for positron impact ionization of hydrogen

A singular structure in the differential cross section for electron ejection by positron impact occurs when the positron and the ionized electron have low relative momentum in the final channel. This is the analogue of the process of 'electron capture to the continuum', well known in positive-ion impact ionization. Near the singularity a dip, due to interference between two double-binary scattering processes, is predicted if the scattering angle of positron and electron equals the critical angle of 45'. Dip and singularity coincide in the high energy limit.

Relativistic theory forK-shell ionisation by fast electrons

The first-order Born approximation is applied for the calculation of the triply differential cross section for electron ejection from heavy target atoms. For the impinging electron, Coulomb waves as well as plane waves are used, and the exchange interaction is correctly accounted for. Two examples are considered,e−+Ag ande−+Ta. While for Ag, reasonable agreement with the experimental spectra is obtained with plane waves, the much heavier Ta target requires the use of Coulomb waves for the continuum electronic states.

Stopping powers calculated from empirical electron-ejection cross sections.

Ionization, and capture and loss contributions to the proton stopping power have been calculated in H/sub 2/, He, N/sub 2/, Ne, Ar, and Kr targets over the energy range 1--1000 keV. The model is based on the use of empirical analytical ionization, and electron-capture and electron-loss cross-section formulas. Except for energies less than 10 keV, the calculated stopping powers are in reasonable agreement with the data of Andersen and Ziegler.

Summing over excited states of the target in atomic collisions

A new approximation is introduced for summing the first Born cross section over the final excited states of the target in atomic collisions. The new approach attempts to model energy differences between target states while at the same time preserving completeness of the target state set. Tests of the approximation against accurate first Born calculations for electron loss from H(1s) and H(2s) and discrete excitation of H(1s) to the n=2 and n=3 levels, all in collision with a He target, prove very successful. Two particular applications of the method are made, the first to electron loss in H(1s)+Xe collisions, the second to the double differential cross section for electron ejection in He+(1s)+He encounters. In the latter case an existing discrepancy between theory and experiment for near forward electron ejection is resolved. The closure approximation is also discussed with particular emphasis on electron loss collisions.

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.

Double differential cross sections for electron ejection from helium by fast protons

The authors present measurements of the cross sections for the ejection of electrons from helium atoms by protons, differential in the electron ejection angle and energy. The proton energies range from 20 to 100 keV, while the electron energies range from 5 to 100 eV and the ejection angles from 0 to 100 degrees . The measurements are normalised by comparing the estimates of the total cross section, derived from double integration of the measured distributions, with published absolute values of the ionisation cross section. Although the energy distribution agrees with existing data, there is a substantial divergence in the angular behaviour. As the measurements include the zero-degree region, the electron capture into the continuum (ECC) peak is examined in detail and an estimate of the total cross section for this process is made over a range of proton energies.

Ionisation to the projectile continuum by positron and electron collisions with neutral atoms

It is pointed out that the singular structure in the differential cross section for electron ejection observed for heavy-ion impact ionisation should also be present for positron and electron impact ionisation. The structure occurs when the projectile and the ionised electron have low relative momentum in the final channel. For positrons the structure appears as a divergence, as for positive-ion impact. For electron impact a broad dip is predicted when both electrons emerge with nearly the same momentum.

Angular and energy dependence of cross sections for ejection of electrons from water vapor. II. 15-150-keV proton impact.

Absolute values of cross sections for electron ejection by protons of 15--150 keV energy have been measured as a function of the angle and energy of the electrons. The range of angles was 10\ifmmode^\circ\else\textdegree\fi{} to 160\ifmmode^\circ\else\textdegree\fi{} and the electron energy range was 1--300 eV. The doubly differential cross sections were also integrated over energy or angle to obtain singly differential and total cross sections and also average ejected electron energies. Good agreement is obtained with Senger's DDCS-MT (doubly differential cross section--mixed treatment) theoretical treatment using the Salin factor.

The importance of projectile ionisation in studies of forward electron ejection from solid targets

The velocity spectra of electrons ejected in the forward direction in ion-atom collisions with gas or solid targets are discussed in terms of charge exchange to the continuum (CEC) and of projectile ionisation. Measurements of the absolute cross sections for electron ejection during H 2 + (160–985 keV/amu) collisions with hydrogen gas show that projectile ionisation is the dominant source of ν e ≈ ν ion electrons over this energy range. The cusps observed show a width which is independent of projectile velocity unlike those for CEC. The significance of these results for collisions involving heavy ions and solid targets is discussed.

Doubly differential cross section for electron ejection in the plane-wave Born approximation: a hydrogenic case study

A study of the cross section for electron loss from He+ and H, which sums over all final states of the target atom (both bound and continuum), is presented. This study is used as a basis for the comparison of several closure approximations which effect an approximate sum over target final states. The qualitative structure of the doubly differential cross section depends strongly upon the specification of average energy of excitation of the target atom. Doubly differential cross sections due to electrons ejected from both the projectile and the target are presented and regions of velocity space where interference between these two processes may occur are identified.

Ionization by Low and Intermediate Energy Ion and Neutral Beams

One of the most important basic processes that take place in collisions of atomic systems is ionization resulting in the emission of electrons. A complete understanding of this process is complicated by the fact that electron emission can take place via a number of mechanisms, some of which are related. Simple measurements of the cross section for electron ejection as a function of projectile velocity does not usually provide enough information to unravel the various mechanisms. But cross sections which are differential in the angle and energy of the ejected electrons, which are now available for protons on a variety of target gases, can be used to elucidate these mechanisms. While most of the experiments of this type have been done at high energies (above, say, 100 keV) there is now data available at energies as low as 5 keV for protons on various gases and to 15 keV for neutral hydrogen atoms on helium gas. At these low energies the angular distributions tend to become less anisotropic than at higher energies and do not yield as much information, but from the energy distributions integrated over angle the authors have been able to construct a mechanism which describes the resultsmore » quite well. Also they have found a simple empirical equation for the cross sections differential in ejected electron energy which is of great potential usefulness to workers in various applied areas in which secondary electrons from collisions are involved.« less

A quantum theory of ionisation in fast collisions between ions and atomic systems

Ionisation of atomic systems by fast ions is considered. A second-order quantum theory is derived which correctly accounts for all distortions of the initial- and final-state wavefunctions arising from Coulomb interactions between three charged particles. The present transition amplitude is the rigorous first-order (or lowest order) approximation to the exact scattering amplitude for ionisation treated by the Faddeev equations in the distorted wave formalism. The problem is briefly studied by the impact parameter method as well, and its equivalence with the full quantal treatment is proved (for projectiles mainly scattered forward) in the limit of very large values of the reduced mass. Ionisation of atomic hydrogen by proton impact is examined in considerable detail at incident energies between 25 and 200 keV. Comprehensive comparisons of available experimental data with singly differential as well as total cross sections for electron ejection are made and the validity of the present method is assessed.

Energy and angular distributions of electrons ejected from water vapor by 0.3–1.5 MeV protons

Absolute cross sections, differential in electron energy and ejection angle, have been measured for ejection of electrons from water vapor by protons with energies from 0.3 to 1.5 MeV. These cross sections are compared with similar measurements for ionization of molecular hydrogen and oxygen and previously published results for hydrocarbon. The criteria for additivity and scalability of electron ejection cross sections are discussed.