A semi-empirical approach to the calculation of absolute inner-shell electron impact ionization cross sections

Abstract

Abstract. Extending a recently developed semiclassical approach, we report the development of a formula which allows the satisfactory description and prediction of absolute electron impact ionization cross sections for K, L, and M inner-shell ionization in the energy range from threshold up to 109 eV for all elements. The present formulation also allows to derive and extend a previously noted scaling law for K-shell ionization. The present results are compared with previous theoretical and experimental determinations where available.

The quantitative analysis of thin specimens: a review of progress from the Cliff‐Lorimer to the new ζ‐factor methods

“…The average value of the ζ-factor weighted by the individual errors can then be expressed as (e.g. Galassi et al, 2002) Mott & Massey (1949) 1.801 ± 0.046 1.252 1.211 ± 0.030 1.997 Worthington & Tomlin (1956) 1.801 ± 0.046 1.252 1.211 ± 0.030 1.997 Drawin (1961) 1.111 ± 0.028 1.304 0.761 ± 0.019 1.719 Green & Cosslett (1961) 1.256 ± 0.032 1.291 0.858 ± 0.021 1.745 Gryzinski (1965) 1.294 ± 0.031 1.331 0.856 ± 0.021 2.326 Kolbenstvedt (1967) 0.735 ± 0.012 1.328 0.585 ± 0.015 2.336 Lotz (1967) 0.998 ± 0.025 1.290 0.682 ± 0.017 1.745 Brown (1974), Powell (1976a) 1.313 ± 0.033 1.251 0.900 ± 0.022 1.987 Powell (1976b) 0.952 ± 0.024 1.360 0.657 ± 0.016 1.642 Quarles (1976) 0.625 ± 0.016 1.309 0.513 ± 0.012 1.720 Schreiber & Wims (1981) 0.780 ± 0.020 1.656 0.555 ± 0.014 1.638 Casnati et al (1982) 0.569 ± 0.014 1.363 0.465 ± 0.011 1.641 Ogilvie (1984) 1.761 ± 0.032 1.402 1.442 ± 0.036 2.396 Zaluzec (1984) 0.632 ± 0.016 1.833 0.533 ± 0.013 1.569 Jakoby et al (1987) 0.618 ± 0.015 1.628 0.503 ± 0.056 1.570 Paterson et al (1989) 0.929 ± 0.023 1.323 0.759 ± 0.019 1.694 Pouchou & Pichoir (1991) 0.861 ± 0.021 1.966 0.638 ± 0.016 1.592 Pouchou (1994) 0.861 ± 0.021 1.966 0.638 ± 0.016 1.592 Deutsch et al (1994) 0.536 ± 0.010 1.502 0.429 ± 0.011 2.515 SIGMAK2 (Egerton, 1986) 0.631 ± 0.016 1.242 0.489 ± 0.012 1.843 SIGMAK3 (Egerton, 1996) 0.642 ± 0.016 1.266 0.496 ± 0.012 1.833 ATW, atmospheric thin window; WL, windowless; XEDS, X-ray energy dispersive spectrometry. …”

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

“…Quasi-linear variation of the ionization cross-section, or of the ionization efficiency curve, σ(E j ) ≈ σ(E m )(E -E i )/(E m -E i ), in the entire interval [9] between E i , the ionization energy of the species considered and E m , rather than close to E i only [4] has been found [18] to lead to significant deviations where tested. In order to perform semi-empirical calculations of ionization cross-sections for molecules (see below), Gryzinski's formula was modified [167,168] by replacing the first constant by the square of the orbital radii [140] and by introducing orbital weighting factors [169].…”

“…The modified Gryzinski-Binary Encounter model for atoms [167,168] is the basis for an additivity rule with atomic weighting factors calculated from a Mulliken analysis of the molecular orbital populations [179] and explains [180] why σ SiF > σ SiF 2 > σ SiF 3 .…”

Experimental Electron-Impact K-Shell Ionization Cross Sections

“…[23], Jakoby et al [24], and Deutsch et al [25]) and of some theoretical results (of Gryzinski [19,20], Khare and Wadehra [13], and Luo and Joy [14]) with experimental data of K -shell ionization cross sections for C, N, O, Ne, Al, Ar, Fe, Ni, Cu, Mo, and Ag. He concluded that the empirical formula of Casnati et al was superior to the equation of Gryzinski and to the empirical formulae of Jakoby et al and Deutsch et al, that the theoretical results of Khare and Wadehra [13] were generally larger than the experimental values, and that the theoretical results of Luo and Joy [14] agree reasonably well with the measured data.…”