Calculation Of Ionization Cross Sections Research Articles

Ionization of atomic hydrogen by slow protons

A theoretical model is suggested for the calculation of ionization cross sections in heavy particle collisions in the impact parameter formalism, considering the influence of coupling with the important bound states in direct as well as in rearrangement channels in a two-centered atomic state expansion. We solve the relevant time-dependent Schr\"odinger equation by a variational method in the two-state approximation. In the present paper, we calculate total ionization cross sections of a hydrogen atom by 5--300-keV proton impact. The results thus obtained are compared with the measured data and existing theoretical findings.

Analytical formulas for Coulomb integrals involved in scattering problems

Radial matrix elements of multipole type involving the product of two Coulomb functions appear in many problems of theoretical atomic physics. Here we investigate some of their properties, with a generalization which includes the possibility of having the two functions related to two different charges. These would typically appear in calculations of ionization cross sections, going beyond the well studied case where the two charges are equal (elastic scattering or discrete excitation). We provide analytical formulas for the evaluation of matrix elements and recursion relations connecting them, both in the exact quantal formulation and in the WKB approximation. These theoretical results are illustrated by considering, within the Coulomb projected Born model, the electron impact ionization of ${\mathrm{Mg}}^{+}$ and ${\mathrm{Ar}}^{7+}$ with a relatively moderate incident energy. The radial matrix elements are evaluated with our exact quantal formulas and in the WKB approximation. The agreement is impressive, and is reflected in the values of triple, double, and single differential cross sections. Finally, a further study shows how the semiclassical approximation yields a very good estimate of single cross sections.

Calculated ionization cross sections for proton-fullerene ion collisions

A simple jellium model is constructed in order to obtain one-electron wave functions for the valence electrons of the fullerene. With this jellium wave function we have calculated ionization cross sections for proton-C60+ collisions in the semiclassical approximation. For higher projectile velocities, for which the semiclassical approximation is valid also for electron impact, theoretical cross sections fit satisfactorily the experimental data of Volpel et al. [Phys. Rev. Lett.71 (1993) 3439].

Molecular treatment of electron detachment in H++H- collisions.

To confirm the appropriateness of ideas recently put forward [L. F. Errea, C. Harel, H. Jouin, L. M\'endez, B. Pons, and A. Riera, Phys. Rev. A 52, R2505 (1995)] concerning the validity of the molecular approach to calculate ionization cross sections, we treat the ${\mathrm{H}}^{+}$ +${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ reaction as a widely different benchmark. \textcopyright{} 1996 The American Physical Society.

Personal computer aided data handling and analysis for PIXE

Since our laboratory was established in 1990, we have developed several computer programs for the data handling and analysis: programs for converting binary or ASCII format of spectra and arrangement of data files, for X-ray spectrum analysis, for determining the efficiency of a Si(Li) detector, for determining the transmission curve of an X-ray absorber, and for calculating ionization cross sections. The latter threes are used for obtaining physical quantities which are required for determining quantitative concentrations of elements and must be prepared individually for each experimental conditions. These five computer programs have all been developed for two types of personal computers and some of them have already been distributed and widely used in Japan.

Simplified model of electron scattering using R-matrix methods.

The eigenchannel {ital R}-matrix method is used to describe a set of two-electron escape processes. This method is applied to calculate both bound state excitation and ionization cross sections for a simplified model of electron-hydrogen scattering and electron-He{sup +} scattering, in which only zero angular momentum states are considered. The results shown are calculated for incident electron energies ranging from 13.6--50 eV for electron-hydrogen scattering and from 54.4--200 eV for electron-He{sup +} scattering. A frame transformation technique is introduced to improve the stability of calculated ionization cross sections. The {ital R}-matrix results are compared with cross sections obtained from a convergent close-coupling approach and with other results.

A semi-empirical method to calculate cross-sections for the electron-impact ionization of clusters

The semi-classical Deutsch Märk (DM) formalism for the calculation of absolute cross-sections for the single ionization of atoms has been extended empirically to the calculation of cross-sections for the ionization of clusters. Comparison with the absolute effective ionization cross-sections measured for various average cluster size distributions for H 2 and CO 2 clusters shows good agreement with the present calculations.

An 18-state calculation of positron-hydrogen scattering

We report results for positron scattering by ground-state atomic hydrogen in the energy range 0 to 80 eV. The calculations have been performed in an 18-state Ps(1s, 2s, 3s, 4s, 2p, 3p, 4p, 3d, 4d)+H(1s, 2s, 3s, 4s, 2p, 3p, 4p, 3d, 4d) approximation where the pseudostates (denoted by a bar) have been taken from Fon et al. (1981). Cross sections are presented for elastic scattering, positronium formation, total scattering and ionization. The elastic scattering results are in good agreement with accurate variational numbers at low energies and with other sophisticated, but very different, theoretical approximations at higher energies. We estimate that the elastic cross section is now known to better than 10%. The cross section for positronium formation is dominated by capture into the 1s state and is in fairly good agreement with the measurements of Weber et al. (1994). The results for the total cross section are generally consistent with the upper and lower bounds of Zhou et al. (1994) but are a little larger than other theoretical estimates at the higher energies. There is also a general theoretical problem concerning the degree to which the total cross sections for electrons and positrons merge at energies above 31 eV. The calculated ionization cross section is in agreement with the measurements of Jones et al. (1993).

A semiclassical approach to the calculation of electron impact ionization cross-sections of atoms: From hydrogen to uranium

Absolute ionization cross-sections for single ionization by electron impact (from threshold up to 200 eV) of free gaseous atoms have been calculated by utilizing a recently proposed semiclassical approach (DM formulation). The formula used here is derived within the framework of classical and quantum mechanical approximations, and the necessary input parameters are determined and discussed. Where possible the calculated ionization cross-section functions are compared with experimental data sets and with the most widely used previous formulae such as the Gryzinski and Lotz formulae. It is concluded that the present approach leads on average to a better agreement with experimental results than previous classical, semiclassical and empirical treatments.

A semiclassical approach to the calculation of electron impact ionization cross-sections of atoms: from hydrogen to uranium

Absolute ionization cross-sections for single ionization by electron impact (from threshold up to 200 eV) of free gaseous atoms have been calculated by utilizing a recently proposed semiclassical approach (DM formulation). The formula used here is derived within the framework of classical and quantum mechanical approximations, and the necessary input parameters are determined and discussed. Where possible the calculated ionization cross-section functions are compared with experimental data sets and with the most widely used previous formulae such as the Gryzinski and Lotz formulae. It is concluded that the present approach leads on average to a better agreement with experimental results than previous classical, semiclassical and empirical treatments.

Measured and calculated absolute total cross-sections for the single ionization of CF x and NF x by electron impact

Various additivity rules and the Deutsch—Märk (DM) formalism have been used to calculate total absolute electron-impact cross-sections for single ionization of the CF x ( x = 1–3) free radicals, the NF x ( x = 1,2) free radicals and the NF 3 molecule. A comparison is made with experimentally determined total single ionization cross-sections which have been obtained from recently measured absolute partial ionization cross-sections for the parent and dissociative ionization of these species. The overall best agreement between the measured and the calculated cross-sections in terms of the absolute values, the shapes and the cross-section ordering was obtained using a recently proposed “new” additivity rule. Common trends and tendencies in the ionization cross-sections within each class of targets, CF x and NF x , and between the two target families CF x and NF x are highlighted and a comparison will be made with the previously measured and calculated ionization cross-sections for the SiF x ( x = 1–3) free radicals.

Interaction delocalization in characteristic X-ray emission from light elements

Recently the first observation of channeling effect in oxygen K-shell X-ray emission was reported in this journal by Qian et al. [Ultramicroscopy 41 (1992) 147], who pointed out that this would allow oxygen to be used as a reference site in atom location by channelling enhanced microanalysis (ALCHEMI) applied to oxides. Experimental results for characteristic X-ray emission in spinel are reported which confirm their results. Calculations of ionization cross sections and the effective ionization potential for each of the constituent atoms of the spinel MgAl 2O 4 have been carried out from first principles. This allows a quantitative theoretical insight into the channeling effect for the light elements Al, Mg and O which incorporates delocalization of the ionization interaction.

Three-photon ionization cross section calculations of Be

Three-photon perturbative photoionization cross sections from the ground state of beryllium have been calculated employing B-spline basis functions. Two-photon ionization cross sections are also calculated and compared to other L2 basis set calculations. Various approximations for the 1s2 core are discussed, calculations are performed in velocity and length gauges including electron correlations.

Ionization cross sections in e+-H2 scattering

In this paper a complete scheme for calculating ionization cross sections for molecular targets is given, and for the first time the cross sections for the e++H2 to e++e-+H2+ processes are calculated in the energy region 30-200 eV using the CPT model. The results show some conformity with recent experimental data.

Assessment of a self-consistent theoretical data base for L X-Ray relative intensities in proton-induced X-Ray emission analysis

Recent Dirac-Hartree-Slater and Dirac-Hartree-Fock calculations of ionization cross-sections, fluorescence and Coster-Kronig yields and X-ray emission rates offer a “self-consistent” theoretical data base for relative intensities of proton-induced L X-rays. Interpolation schemes for use with tables of these quantities are described. Theoretical intensity ratios for major line groups agree with compiled experimental data to within a few percent, justifying use of the data base in PIXE.

Background modeling alternatives in EELS and their implications on microanalysis

With the advent of parallel detectors, electron energy-loss spectroscopy (EELS) is expected to be employed increasingly in the routine microanalysis of light elements. The quantitation formulae that are used are relatively simple and straightforward and require only a measurement of the integrated core-loss intensity over a particular energy window beyond the ionization edge (Δi) and most often, a calculated ionization cross-section. Even though the hydrogenic cross-sections that are used routinely for microanalysis can be a source of error, it is observed that the procedure that largely determines the accuracy of quantification is the removal of the contribution of the background below the ionization edge. Based on empirical observations, an inverse power law function of the form I = AE-r, where the exponent ‘r’ takes values from 2 to 6, is now commonly used for the background. A background fitting region preceding the ionization edge (Δb) is chosen, the constants A and r determined by least squares refinement and the background extrapolated beyond the ionization edge for the required energy window (Δi).

One- and two-photon ionization of model atoms

The response to an ionizing radiation field of a simple one-electron atomic system modelled by an attractive Fermi-type pseudopotential is investigated under the assumption that the source intensity is sufficiently low for a perturbation theory treatment at appropriate order to be adequate in dealing with the radiation field-matter interaction. One- and two-photon ionization cross-sections are evaluated either in the length or in the velocity forms by using an approach recently put forward by the authors, which stresses the nature of such quantities as Fourier transforms of relevant time-dependent correlation functions. Some remarks concerning the merits of different gauges in approximate two-photon ionization cross-section calculations conclude the paper.

Mean-electric-field approximation to multiple ionization in distant collisions

The description of ion-atom collisions in a mean-electric-field approximation is discussed. In this method the sum of the interactions between the projectile and the electrons of the target is expressed as the sum of the Coulomb field acting on the center of charge of the target electrons and a residual interaction. For distant (high-energy) collisions the residual interaction can be neglected. The calculation of the scattering amplitude corresponding to the mean electric field is performed within the framework of the first Born approximation. It is shown that for high-energy collisions the scattering amplitude is a product of single-electron scattering amplitudes and the cross sections of the multiple ionization follow the binomial distribution. A simple expression is derived for the cross section of n-vacancy production. The calculated ionization cross sections and mean numbers of outer-shell vacancies in the presence of an inner-shell vacancy are in satisfactory agreement with experimental values for high projectile energies.

K-shell cross sections for analytical electron microscopy

There has during the last few years been a renewed interest in the calculation of ionization cross-sections for use in AEM-based x-ray analysis, due to the fact that modern AEM's can operate up to accelerating potentials of 400 kV. In this regime relativistic effects are considerable and the extrapolation of the “accepted” microprobe-based formulae to these levels is questionable and the relativistic Bethe equation is the most appropriate formulation.

Ionization of rare-gas targets by collisions of fast highly charged projectiles

We have determined the net ionization cross section for total slow-ion or slow-electron charge production in rare-gas targets by passage of a fast projectile both experimentally and theoretically. We have experimentally studied ionization in these targets by C, Fe, Nb, and Pb projectiles with energies ranging from 310 keV/amu to 4.75 MeV/amu and for charge states in the range of + 4 to + 54. Theoretical calculations employing the classical-trajectory Monte Carlo method are used to calculate ionization cross sections in the rare gases for projectiles at collision energies of 1-5 MeV/amu with charge states + 5 to + 80. Experiment and theory generally agree within a factor of 2 over this wide range of conditions. For a given rare-gas target, the cross sections for net ionization reduce to a common curve when plotted as cross section divided by charge state versus energy per nucleon divided by charge state.