Cross Sections For Ionization Of Atoms Research Articles

Modified Kolbensvedt model for the electron impact K-shell ionization cross-sections of atoms and ions

A modification of the Kolbensvedt model, MKLV, in terms of ionic, correlation (between the incident and target electrons) and relativistic corrections, is proposed to calculate the K-shell electron impact ionization cross-sections of neutral and ionic targets. The modified model, with a single set of parameters, is found to reproduce satisfactorily the experimental data for the neutral H, Al, Ar, Mn, Ge, Mo, Ag, Sn, Au, Bi and U and ionic Li+, B4+ and O7+ targets better than the existing empirical models from threshold energies to as high as 104 MeV. For the Ag target, the calculations from MKLV follow closely the results of Scofield, and for Au, those of Scofield, and Ndefru and Malik, both done in the relativistic Born approximation with the Moller interaction, at energies higher than the peak region.

An overview of the BEB method for electron‐impact ionization of atoms and molecules

AbstractAn accurate and simple method for the calculation of electron‐impact ionization cross sections of atoms and molecules was developed by Kim and Rudd in 1994. Since then, many articles by Kim and coworkers have demonstrated the validity of the technique and have applied it to various atomic and molecular systems. The method is particularly useful for computational modeling, where numerous cross sections are needed. This paper presents the basic formulas and method of calculation, shows applications to some neutral atoms, and describes the NIST website where results of recent calculations are available. The limitations of the method as well as the advantages are outlined. Published in 2005 John Wiley & Sons, Ltd.

A detailed comparison of calculated and measured electron-impact ionization cross sections of atoms using the Deutsch–Märk (DM) formalism

We present a comprehensive comparison between the results of the recently revised DM formula, which now exhibits the quantum mechanically correct high-energy behavior, and measured atomic ionization cross sections for selected atoms covering a wide range of targets of different electronic structure as well as elements along columns of the periodic table. Specifically, we selected the following elements (listed in order of increasing atomic number Z): Na, Si, S, Cl, K, Ca, Fe, Ga, Br, In, Cs, Hg, Bi, and U. The main objective of this study is to compare the results of the revised DM formula for these elements in both the low- and high-energy regime with available experimental data and to extend the formalism to targets with higher atomic number Z, where contributions to the ionization cross section from f-electrons have to be considered. In cases, where several, sometimes conflicting experimental data sets have been reported, an attempt is made to provide guidance as to the reliability of various measured cross sections. In addition, we also calculated ionization cross sections for the technically important species Cr, Mn, and W, for which no experimental data are available.

High-temperature mass spectrometry: Instrumental techniques, ionization cross-sections, pressure measurements, and thermodynamic data (IUPAC Technical Report)

Abstract An assessment of high-temperature mass spectrometry and of sources of inaccuracy is made. Experimental, calculated, and estimated cross-sections for ionization of atoms and inorganic molecules typically present in high-temperature vapors are summarized. Experimental cross-sections determined for some 56 atoms are generally close to theoretically calculated values, especially when excitation–autoionization is taken into account. Absolute or relative cross-sections for formation of parent ions were measured for ca. 100 molecules. These include homonuclear diatomic and polyatomic molecules, oxides, chalcogenides, halides, and hydroxides. Additivity of atomic cross-sections supplemented by empirical corrections provides fair estimates of molecular cross-sections. Causes of uncertainty are differences in interatomic distances and in shapes of potential energy curves (surfaces) of neutral molecules and of molecular ions and tendency toward dissociative ionization in certain types of molecules. Various mass spectrometric procedures are described that render the accuracy of measured thermodynamic properties of materials largely independent of ionization cross-sections. This accuracy is comparable with that of other techniques applicable under the conditions of interest, but often only the mass spectrometric procedure is appropriate at high temperatures.

Electron spectra in the ionization of atoms by neutrinos

For neutrinos of O(10keV) energies, their oscillation lengths are less than a few hundred meters, thereby suggesting the fascinating idea of oscillation experiments of small geometrical size. To help evaluating this idea we calculate the ionization cross sections of H, He, Ne and Xe, using any neutrino flavor, in the few keV energy range. We find that the atomic ionization cross sections per electron are always smaller than the neutrino cross sections off free electrons, approaching it from below as the energy increases to the 100 keV region. At the 10-20 keV range though, atomic binding effects are very important, particularly for the heavier atoms, inducing a factor of two reduction of the Xe ionization cross section, compared to the free electron one.

Revised high energy behavior of the Deutsch-Märk (DM) formula for the calculation of electron impact ionization cross sections of atoms

We modified the Deutsch-Märk (DM) formula for the calculation of single atomic ionization cross sections by replacing the previously used Gryzinsky-type energy dependence by a “scaled” ln(E)/E energy dependence. This modified energy dependence yields, in the limit of high impact energies, the well-established Born–Bethe ln(E)/E energy dependence, while reproducing, at lower impact energies, the DM cross section function. The revised DM formula, whose energy dependence has been determined from a fitting procedure using reliable, measured ionization cross sections for the atoms H, He, C, Ne, Mg, Al, and Ag, was subsequently used to calculate as an example ionization cross sections for the atoms O, F, P, Ar, Ge, Kr, and Xe and excellent to very good agreement was found between the calculated and the measured cross sections for these atoms over a wide range of impact energies.

Two Components of the Total Ionization Cross Sections of Atoms and Molecules by Electron Impact: Resonant Excitation and Decay of the Fermi Electron-Hole System and the Dipole Electron Transition from a Bound to a Free State at a Binary Collision

Large volume of the experimental data on the ionization cross sections of atoms and molecules by electron impact obtained by various authors using different methods is analyzed. The dependence of the ionization cross section Q on the energy of the incident electron E is described by a curve with a maximum. For E ≤ I, where I is the ionization potential, the cross section naturally vanishes. For E > I, it first increases fast, passes through a high maximum, and then monotonically decreases with increasing E. For comparatively large energies E > 100 I, the Bethe formula describes the experimental data almost exactly, but in the region of maximum I < E < 10 I, it deviates significantly from the measurement data. In the present paper it has been established that the experimental dependence Q(E) in the region of maximum is well described by a resonant curve similar to Lorentz distribution. It is assumed that the main contribution to the atomic ionization by a slow electron comes from the resonant excitation and the decay of the Fermi electron-hole system. An empirical formula for the cross section of atom ionization by electron impact Q(E) is suggested which takes into account resonance for incident electrons of small energies and is transformed into the Bethe formula for large E. The parameters of the formula for the ionization cross section are calculated by the least-squares method for H, He, Ne, Ar, C, N, O, Li, Na, H2, N2, O2, K-shells of C, N, Ne, Ar, K, Ca, Rb, and Sr atoms and molecules. A comparison of the experimental dependences of the ionization cross section on the energy of the incident electron with the Bethe theoretical formula and empirical formulas suggested by Lotz, Alkhazov, Kim and Rudd, and Povyshev et al. demonstrates that the formula suggested in the present paper describes the available experimental data better than others.

Some recent progress on the measurement of K-shell ionization cross-sections of atoms by electron impact: Application to Ti and Cr elements

In this paper, we have taken some measures to improve the accuracy of our experimental data for K-shell ionization cross-sections by electron impact. These measures include (1) measurement of the thin target thickness with Rutherford backscattering spectroscopy and (2) detection efficiency calibration in the lower energy region using thick carbon target bremsstrahlung by electron impact and (3) electron reflection correction and electron mean track length correction based upon Monte Carlo method. These measures are applied to the measurement of K-shell ionization cross-sections of Ti and Cr elements from the threshold energies up to 26 keV. From the comparison with some theoretical models, empirical formulae and some previous experimental data, it is concluded that these measures taken in this paper are effective in the improvement of accuracy of experimental data. The present experimental data for Ti and Cr elements also clarify the discrepancies among some experimental data sets. In addition, these measures will also be very helpful in the measurement of K-shell ionization cross-sections for lower Z elements and in the measurement of L, M-shell ionization cross-sections for medium and higher Z elements.

Single and double ionization cross sections of atoms colliding with relativistic structural heavy ions

The single and double ionization cross sections of hydrogen and helium atoms colliding with relativistic structural heavy ions are calculated within the framework of the eikonal approximation. By structural ions are implied those containing partly occupied electron shells. It is shown that an allowance for the finite size of charged ions leads to significant changes in the ionization cross sections as compared to those determined for the point ions possessing the same charges and energies.

The ionization of H, He or Ne atoms using neutrinos or antineutrinos at keV energies

We calculate the ionization cross sections for H, He or Ne atoms using ν e and ν ̄ e scattering at keV energies. Such cross sections are useful for e.g., ν ̄ e -oscillation experiments using a tritium source. Using realistic atomic wave functions, we find that for E ν ≲10 keV the atomic ionization cross sections, normalized to one electron per unit volume, are smaller than the corresponding free electron ones, and that they approach it from below as energies of 20 keV are reached.

Absolute and total electron-capture cross sections in slowArq+−C60collisions

We present experimental absolute and total electron-capture cross sections for ${\mathrm{Ar}}^{q+}\ensuremath{-}{\mathrm{C}}_{60}$ $(q=4,$ 6, and 8--18) collisions at $3.3q \mathrm{keV}.$ The absolute scale is based on the ${\mathrm{C}}_{60}$ vapor pressure by Abrefah et al. [Appl. Phys. Lett. 60, 1313 (1992)], which together with the results of Mathews et al. [J. Phys. Chem. 96, 3566, (1992)] are the only possible choices among the many, widely dispersed, vapor pressures reported in the literature. In order to support this statement, we calculate total electron-capture cross sections modeling ${\mathrm{C}}_{60}$ as a pointlike object and as an infinitely conducting sphere (ICS). These model results are shown to differ little, since polarization and finite-size effects are relatively unimportant for the distant collisions at which the outermost (first) electrons are transferred. We are thus able to use the semiempirical formula for absolute ion-atom cross sections by Selberg et al. [Phys. Rev. A 54, 4127 (1996)], treating ${\mathrm{C}}_{60}$ as a hypothetical atom with ionization potential ${I}_{1}=7.6 \mathrm{eV},$ and the ICS model to define lower and upper bounds for the absolute cross-section scale. We find significant oscillations in the total electron-capture cross sections as functions of q.

High-order perturbation expansion of non-Hermitian Floquet theory for multiphoton and above-threshold ionization processes

A high-order perturbation theory is presented for efficient and accurate computation of multiphoton and above-threshold ionization cross sections of atoms and molecules in weak to medium strength laser fields. The procedure is based on a Raleigh-Schrodinger perturbative expansion of the time-independent non-Hermitian Floquet Hamiltonian. The reduced Green function and generalized pseudospectral discretization techniques are extended to facilitate the calculation of complex quasienergy resonance states without the need of diagonaliz- ing the full Floquet Hamiltonian. Explicit expressions are presented for the determination of intensity- dependent total and partial rates and electron angular distributions. The theory is applied to a case study of multiphoton detachment of H 2 for a range of laser frequencies ~corresponding to the absorption of a minimum of two photons! and laser intensities from 10 7 to 10 12 W/cm 2 . It is found that a 16th-order perturbative Floquet procedure provides an excellent description of the two-photon-dominant detachment processes for laser inten- sity up to 2310 11 W/cm 2 . The predicted electron angular distributions are in good agreement with recent experimental data.

On the application of relaxed-orbital Hartree-Fock approximation for the ionization cross sections of atoms

For the ionization of atoms the possibility of using radial orbitals of the initial and final states calculated for different Hamiltonians is demonstrated. For a limited number of final states, the additional orthogonality constraints should be imposed on the continuum radial wavefunction taking into account the orthogonality between the final state of the ion + electron and initial excited states of the atom. Within the framework of the relaxed-orbital Hartree-Fock approximation agreement between the length and velocity forms can be achieved if the orthogonality constraints of the wavefunctions of excited states with those of all lower-lying states of the same symmetry are correctly fulfilled.

ANALYSIS ON ENERGY ABSORPTION EDGE AND ELECTRON POPULATIONS OF Al

A theoretical explanation for L core-shell absorption edge of electron energy loss spectrum of Al, an analysis of the electronic populations and a comparison between different partial cross sections are given. The edge was first normalized to the same atomic ionization cross section (per atom per electronvolt). The contributions for the cross section come from three respects:the first one is the electronic transitions from the core-shell to valence-shell calculated by extended Hückel band model, the second one is the final ionization state obtained by electron gas model, the third comes from the elastic backscatting of outgoing waves by the atoms that neighbor the excited atom. The agreement between the calculation result and the experimental result is good.

Electron-impact ionization of atoms and ions from hydrogenic nl states

The dipole Bethe logarithmic constants for high-energy ionization cross sections of atoms and ions by electron impact have been calculated using the relation between and the bound-free Gaunt factor . By this method the values of are expanded to n = 50 and the constants calculated previously for the states 1s have been improved.

Systematics of subshell electron ionization cross sections

The excellent agreement between recent converged close-coupling calculations of electron ionization cross sections of atoms and ions and plane-wave Born approximation (PWBA) calculations leads to the hypothesis that PWBA calculations are accurate to 10% at high energy, and therefore can be used to renormalize experimental data to produce cross sections of 10% accuracy near threshold. Comparisons are made of various calculations of 2s and 3s electron ionization cross sections in low-Z atoms and ions, of PWBA calculations and experiments for atoms and ions up to , and of scaled peak cross sections to interrelate experiments and calculations on isoelectronic sequences.

Analytical parametrization for the shape of atomic ionization cross sections

The behavior of the ionization cross section of atoms is known classically in the limits of threshold energy and at high energies. These two limits are used to construct a simple analytical formula for the ionization cross section that depends upon two parameters: the magnitude of the maximum of the cross section and its position in energy. The parametrization has been tested for electron- and positron-impact ionization as well as for proton- and antiproton-impact ionization. It reproduces in all cases the shape of the cross section and offers a unified treatment for ionization by bare projectiles irrespectively of their charge and mass.

Semiempirical formula for multiple ionization cross sections of atoms by electron impact

On the basis of experimental data on multiple-ionization cross sections σn of neutral atoms by electron impact a semiempirical formula for σn, n ⩾ 3, has been deduced where n is the number of ejected electrons. It has been shown that the cross section σn depends on three atomic parameters: the minimal ionization energy required to remove n electrons from the target, the total number of target electrons and the number of ejected electrons. The electron-impact energy dependence of the cross sections σn with different n is described by one universal function. As the number of ejected electrons n increases the cross section σn falls off approximately as σn ~ n−6.A comparison of σn calculated by the proposed semiempirical formula with available experimental data for the atomic targets from Ne to U and the number of the ejected electrons from n = 3 to n = 13 has been performed.For the first time, the formula suggested can be used for estimation of multiple-ionization cross sections σn, n ⩾ 3, from threshold up to high electron energies E ≈ 105 eV for an arbitrary atomic target.

Systematic ion-atom interaction cross sections and stopping powers in the plane wave Born approximation

In Chapter 14 of Atomic and Molecular Processes, Bates (1962) outlines a procedure for calculating ion-atom cross sections in the plane-wave Born approximation (pwBa). The procedure involves integration over the product of elastic scattering factors or generalized oscillator strengths for excitation or ionization from both projectile and target. We have programmed this procedure to use our large database of excitation and ionization generalized oscillator strengths (GOS). The program calculates both cross sections (CS) and stopping power (SP) on a subshell basis. The calculations are done in the center of mass system where the distinction between projectile and target is lost. Thus, the SP in the laboratory frames of both target and projectile are symmetrical in nuclear and net charges. The traditional simple modeling of SP, using scaled proton SP and an effective projectile charge, is unsymmetrical, and therefore dubious as a guide for extrapolating to ion-ion SP. At high projectile energy, the SP curves, as a function of increasing projectile charge, approach the scaled protonic result from above, indicating that lowering the average charge raises the SP, in contradiction to the traditional picture that the projectile SP increases with increasing effective charge (assuming there is an underlying physical reality relating the effective and average charge). Comparison with experimental SP data (mostly from 30 years ago) shows generally poor agreement for Li ion projectiles in the 1–10 MeV range.

Absolute electron impact ionization cross sections for highly charged ions: Scaling law for hydrogen-like ions

Scaling laws are of great importance in the description of elementary processes in plasma physics and plasma chemistry. This is particularly true for electron impact induced ionization of atoms, molecules and their respective ions. The recently proposed semi-classical DM (Deutsch-Märk) approach for the calculation of the single ionization cross section of atoms is applied here to the single ionization of hydrogen-like ions and the formula derived can be used to rationalize the empirically-based scaling law for the ionization cross section of hydrogen-like ions, i.e. the Z 4 power dependence, where Z is the nuclear charge. The results obtained are compared with previous experimental and theoretical ionization cross section functions.