Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

Seguí, Silvina; Dingfelder, M.; Salvat, F.

doi:10.1103/physreva.67.062710

Cited by 109 publications

(120 citation statements)

References 36 publications

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“…Explicitly, the values adopted in the present work are K = 0.523 and ⌫ L 2,3 -K / ⌫ Total-K = 0.8680. [3], respectively, the analytical formulas of Gryzinski [24] and Casnati et al [23], and the experimental measurements of Shima et al [11] and Tang et al [27]. Our measured values lie between the DWBA and PWBA calculations, and agree with both calculations within experimental uncertainties.…”

Section: A K-shell Ionizationsupporting

confidence: 85%

“…In their approach, the generalized oscillator strength is obtained from the cross section for photoelectric absorption of photons in the considered atomic shell; the formulation also incorporates exchange corrections, through the Ochkur approximation, and an empirical Coulomb correction. The second theoretical approach considered here is the DWBA, as implemented in a robust calculation algorithm developed recently by Segui et al [3]. As mentioned previously, in the DWBA, the wave functions for the initial and final states of the projectile include the distortion caused by the atomic field; this feature allows the description of exchange effects in a consistent way.…”

Section: Resultsmentioning

confidence: 99%

“…Various semiempirical modifications to the PWBA have been proposed to account for these effects [1,2]. A more rigorous approach is to use the distorted-wave Born approximation (DWBA), in which the initial and final projectile wave functions include the distortion caused by the atomic field and, which also allows the description of exchange effects in a consistent way [3]. DWBA calculations are however extremely time consuming and, moreover, they are feasible only for a limited range of incident electron energies, which makes their use difficult in practical applications.…”

Section: Introductionmentioning

confidence: 99%

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Measurements of absoluteK-shell ionization cross sections andL-shell x-ray production cross sections of Ge by electron impact

2004

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Results from measurements of absolute K-shell ionization cross sections and L␣ x-ray production cross sections of Ge by impact of electrons with kinetic energies ranging from the ionization threshold up to 40 keV are presented. The cross sections were obtained by measuring K␣ and L␣ x-ray intensities emitted from ultrathin Ge films deposited onto self-supporting carbon backing films. Recorded x-ray intensities were converted to absolute cross sections by using estimated values of the sample thicknesses, the number of incident electrons, and the detector efficiency. Experimental data are compared with the results of widely used simple analytical formulas, with calculated cross sections obtained from the plane-wave and distorted-wave Born approximations and with experimental data from the literature.

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Section: A K-shell Ionizationsupporting

confidence: 85%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Measurements of absoluteK-shell ionization cross sections andL-shell x-ray production cross sections of Ge by electron impact

2004

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“…The experimental results are compared with the results of Monte Carlo (MC) simulation obtained by using the general-purpose MC code PENELOPE [5], together with ionization cross sections computed from the distorted-wave Born approximation [6]. Results are also compared with various analytical φ(0) expressions commonly used in EPMA and AES.…”

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confidence: 99%

New Measurements of the Surface Ionization at Low Energies

Merlet

Llovet

2005

MAM

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In electron probe microanalysis (EPMA), the surface ionization φ(0) describes the increase of ionizations in a thin layer of a given element located at the sample surface due to electrons backscattered from the substrate. Accurate knowledge of this parameter, for incident electron energies from ionization threshold up to 40 keV, is of interest for both theoretical and practical uses. On the one hand, φ(0) appears in most of the analytical parameterizations of the depth distribution of ionizations or φ(ρz) function used in quantitative EPMA procedures. While for bulk specimens the evaluated concentrations depend on this parameter especially when x-ray absorption is important, for thin films and multilayers, EPMA results are largely sensitive to the accuracy of the adopted φ(0) values. On the other hand, the surface ionization is also used in quantitative Auger electron spectroscopy (AES), where it is commonly referred to as the Auger backscattering factor (r), and it describes the increase of the Auger current due to backscattered electrons. Last but not least, the surface ionization is an excellent test to check the reliability of electron transport calculations. Indeed, φ(0) is not only sensitive to the cross sections adopted to describe elastic scattering and slowing down of electrons but also to the model adopted for inner-shell ionization.Measurements of the surface ionization have been performed by several groups over the past years. In our previous works [1,2,3,4], we have measured the surface ionization for bulk samples and thinfilm and multilayer samples deposited on a wide variety of substrates. In spite of the experimental uncertainties (of about 5%) and the limited set of incident electron energies for which φ(0) was measured, the data obtained made it possible to asses the reliability of φ(0) calculations at moderately high energies and to guide the development of new analytical formulas. However, it is still difficult to asses the reliability of φ(0) calculations at very low energies, especially close to the ionization threshold and the need for improved experimental measurements at low energies remains open.In this communication, new measurements of the surface ionization are presented. We have determined φ(0) by using the tracer method, i.e. by measuring the characteristic x-ray intensity emitted from an ultra-thin tracer layer deposited on a bulk substrate and, according to Castaing's definition, normalizing it to the intensity emitted from an equivalent, self-supporting tracer layer. Although conceptually simple, the determination of φ(0) faces numerous difficulties, from sample preparation to the measurement itself. Indeed, the tracer layer should be as thin as possible to minimize multiple-scattering effects (finite-thickness effect), especially at low accelerating voltages, but should be thick enough to yield acceptable signal-to-noise ratios so as to minimize statistical uncertainties and systematic errors in spectral background subtraction. In this work, we have used tracer layers with thic...

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“…For instance, the cross sections for ionization of inner shells (by electron impact) implemented by default, which were evaluated using the method of virtual quanta, are reliable only for electrons with kinetic energies well above the ionization threshold. In the present simulations we have replaced these cross sections by more accurate values calculated from the distorted-wave Born approximation [3].…”

mentioning

confidence: 99%

PENELOPE-2005. A Monte Carlo Code System Suitable for Simulation of X-ray Spectra

Llovet

Fernández-Varea

Sempau

et al. 2005

MAM

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Monte Carlo (MC) simulation of x-ray spectra emitted from targets bombarded by electron beams is of interest in x-ray microanalysis, especially for the quantitative interpretation of measurements under unconventional conditions. Examples are the analysis of non-homogeneous samples (at the micron scale) such as particulate matter, multilayer films or samples with rough surfaces, the analysis at grazing-angle incidence or at very-low incident electron energies. The usefulness of MC simulation stems from its ability to incorporate realistic interaction models devoted to describing the evolution of electrons in the sample and to track not only primary electrons but also all secondary radiations (electrons and photons) generated within the sample.penelope is a general-purpose MC code that allows the simulation of coupled electron-photon transport in targets consisting of bodies with arbitrary composition, for an energy range from 100 eV to 1 GeV [1]. The interaction models implemented in the code are based on the most reliable information available at present, limited only by the required generality of the code. These models combine results from first-principles calculations, semi-empirical models and evaluated data bases. penelope is coded as a set of FORTRAN subroutines that perform the random sampling of interactions and the tracking of electrons and photons. Hence, the user must provide a main program so as to follow the particle tracks through the target and keep score of the quantities of interest.The latest public version of penelope was released in 2003 and it is available from the OECD Nuclear Energy Agency Data Bank (http://www.nea.fr). We are now preparing a new version 2005 of the code that contains substantial improvements in the interaction models and in the geometry routines, which will be released in a few months. Namely, it incorporates numerical differential cross sections for elastic scattering obtained from partial-wave analysis using DiracFock atomic electron densities and the exchange potential of Furness and McCarthy. These cross sections were obtained by using the code elsepa [2]. Another improvement is that it allows the simulation of characteristic x rays and Auger electrons that result from vacancies produced in M-shells. The structure of the code is still flexible enough to enable the use of alternative, more elaborate interaction models when available. For instance, the cross sections for ionization of inner shells (by electron impact) implemented by default, which were evaluated using the method of virtual quanta, are reliable only for electrons with kinetic energies well above the ionization threshold. In the present simulations we have replaced these cross sections by more accurate values calculated from the distorted-wave Born approximation [3].As in previous versions of penelope, the tracking of particles in the target can be done automatically with the aid of the subroutine package pengeom, provided the target is defined as a

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Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

Cited by 109 publications

References 36 publications

Measurements of absoluteK-shell ionization cross sections andL-shell x-ray production cross sections of Ge by electron impact

Measurements of absoluteK-shell ionization cross sections andL-shell x-ray production cross sections of Ge by electron impact

New Measurements of the Surface Ionization at Low Energies

PENELOPE-2005. A Monte Carlo Code System Suitable for Simulation of X-ray Spectra

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