Inner-shell ionization cross sections

A particular strength of Equation (7) is that the intensity ratio is formed between mea-surements of the same X-ray energy in both the unknown and standard. This procedure has significant advant es First, there is no need to know the spectrometer s efficiency, a value that is very difficult to calibrate absolutely, since it appears as a multiplicative factor in both terms and therefore cancels. Second, an exact knowledge of the inner shell ionization cross section or fluorescence yields is not needed, since they also cancel in the ratio. 

In this section we describe experiments whose aim has been to determine explicitly inner shell ionization cross sections (or ratios of electron and positron cross sections). Section 5.5 contained an account of the influence of inner shell processes on multiple ionization of the heavier noble gases. 

Abstract Electron impact inner-shell ionization cross-section (EIICS) calculations of neutral atoms with atomic numbers Z = 6-92 for /6-shell, Z = 18-92 for E-shell, and Z = 79-92 for M-shell have been reviewed. In this work, the evaluations of the EIICS are discussed using our recently propounded easy-to-use models that are found adequately successful in describing the experimental cross sections. The selection of the range of atomic number Z for different inner-shells was guided by the availability of the EIICS data either from experiments or from rigorous quantal calculations. Details of the models have been... 

C.J. Powell, Inner-shell ionization cross sections, in T.D. Mark, D.H. Dunn (Eds.), Electron Impact Ionization, Springer, Berlin, 1985, p. 198. 

C.J. Powell, Inner-shell Ionization cross-sections, in J.R. Michael, P. Ingram (Eds.), Microbeam Analysis, Sun Francisco Press, San Francisco, 1990, pp. 13-20. 

S.A.H. Seif el Naser, D. Berenyi, G. Bibok, Inner shell ionization cross sections for relativistic electrons, Z. Phys. 267 (1974) 169. 

Abstract The momentum representation of the electron wave functions is obtained for the nonrelativistic hydrogenic, the Hartree-Fock-Roothaan, the relativistic hy-drogenic, and the relativistic Hartree-Fock-Roothaan models by means of Fourier transformation. All the momentum wave functions are expressed in terms of Gauss-type hypergeometric functions. The electron momentum distributions are calculated by the use of these expressions, and the relativistic effect is demonstrated. The results are applied for calculations of inner-shell ionization cross sections by charged-particle impact in the binary-encounter approximation. The reiativistic effect and the wave-function effect on the ionization cross sections are discussed. 

In quantum chemistry, the state of a physical system is usually described by a wave function in the position space. However, it is also well known that a wave function in the momentum space can provide complementary information for electronic structure of atoms or molecules [1]. The momentum-space wave function is especially useful to analyse the experimental results of scattering problems, such as Compton profiles [2] and e,2e) measurements [3]. Recently it is also applied to study quantum similarity in atoms and molecules [4]. In the present work, we focus our attention on the inner-shell ionization processes of atoms by charged-particle impact and study how the electron momentum distribution affects on the inner-shell ionization cross sections. 

The momentum wave functions thus obtained are used to calculate inner-shell ionization cross sections by charged-particle impact in the binary-encounter approximation (BEA) [5]. The wave-function effect and the electronic relativistic effect on the inner-shell ionization processes are studied. 

These facts indicate that the initial velocity of the target electron has a strong influence on the BEA cross sections and it is important to take into consideration the electron velocity (momentum) distribution in the BEA. The inner-shell ionization cross sections in the BEA with realistic velocity distribution are found to be in agreement with those in the PWBA and in the semi-classical approximation (SCA) [23],... 

Present results indicate that the inner-shell ionization cross section in the BEA is sensitive to the momentum distribution of the target electron in the initial state. The momentum distribution is useful to study the relativistic and wave-function effects on the ionization cross sections. 

Based on the effective charge, the theoretical cross-section values can be calculated using the first-order theories. Theoretically, the PWBA is not accurate to reproduce the experimental inner-shell ionization cross-sections for collision systems with Z1/Z2 > 0.1 in the v (velocity of projectile) orbital velocity of the electron) region. For comparison, velocity v in atomic units can be calculated using 6.35[ (MeV)/M] / while velocity V2 in atomic units is calculated using [BE(eV)/13.6] /. ... 

As mentioned in the previous chapter, for inner-shell ionization of heavy target atoms, the effects of the projectile Coulomb trajectory and of binding or antibinding should be enhanced as compared with the manifestations of polarization and saddle-point ionization.The possibility for an investigation of the former effects through a comparison of inner-shell ionization cross sections measured with proton and antiproton impact was realized by Andersen et al. [3.52]. Although preliminary data for impact on Ti, Cu, Se, and Nb exist (see Morenzoni [4.22]), no final results from this investigation have yet been published. 

Theoretical treatments of inner-shell ionization cross section Oj point to approximately universal curves for all Z of the product of Oj by Ef as a function of Eg in units of E, where Ej is the ionization energy of the subshell. Electron energy Eg varies from Ej to high values (see [11]). The curves show maxima of Oj Ef. 

D.H.H. Hoffmann, C. Brendel, H. Genz, W. Low, S. Muller, A. Richter, Inner-shell ionization by relativistic electron impact, Z. Phys. A 293 (1979)187 D.H.H. Hoffmann, H. Genz, W. Low, A. Richter, Z and E dependence and scaling behaviour of the K-shell ionization cross section for relativistic electron impact, Phys. Lett. A 65 (1978) 304. 

In this section we discuss the more important experimental results for continuum oscillator strengths measured by electron spectroscopy that have been reported up to mid 1978. The discussion is divided on the basis of target species rather than the type of experiment since this stresses the interrelation and complementary nature of many of the experiments. As the experimental work is far from complete in many cases, only a limited picture of the overall breakdown processes is available at present. In particular, a very limited amount of work has been reported for inner shells. More data are generally available for mass fragmentation (photoionization mass spectrometry) than for partial ionization cross sections (photoelectron spectroscopy). 

Schneider, H., Tobehn, I., Ebel, F. and Hippier, R. (1993). Absolute cross sections for inner shell ionization by lepton impact. Phys. Rev. Lett. 71 2707-2709. 

In a typical EEL spectrum, the count rate Ia (area under the excitation edge after background subtraction, for element A) is a product of the incident electron current density, J0, the number of atoms Na of element A per unit area, and oa> the total ionization cross-section per atom for the excitation of the appropriate inner-shell by the incident electrons. However, to preserve good energy resolution, an aperture is placed after the specimen which limits scattering to angles less than P and hence only a fraction of the core loss signal Ia(P) is measured. Moreover, in most... 

S. Segui, M. Dingfelder, F. Salvat, Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact, Phys. Rev. A 67 (2007) 062710. 

H. Deutsch, K. Becker, B. Gstir, T.D. Mark, A semi-empirical approach to the calculation of absolute inner-shell electron impact ionization cross sections, Z. Phys. D 29 (1994) 31. 

G. Glupe, W. Mehlhorn, Absolute electron impact ionization cross sections of N, O and Ne, J. Phys. Suppl. 32 (1971) C4—40 G. Glupe, W. Mehlhorn, A new method for measuring electron impact ionization cross sections of inner shells, Phys. Lett. A 25 (1967) 274. 

X-ray spectra are distinguished from ordinary visible light or UV spectra by the fact that these photons can excite inner shell electrons from the absorbing atoms with consequent sharp steps in the absorption cross section as the X-ray energy is increased through an inner-shell ionization threshold. The resulting spectrum (Fig. 4) can be analyzed in two different regions ... 

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