Analytical expression forK- andL-shell cross sections of neutral atoms near ionization threshold by electron impact

Abstract

An analytical expression is proposed to describe the K-and L-shell ionization cross sections of neutral atoms by electron impact over a wide range of atomic numbers (4 Z 79) and over voltages U < 10. This study is based on the analysis of a calculated ionization cross section database using the distortedwave first-order Born approximation (DWBA). The expression proposed for cross sections relative to their maximum height involves only two parameters for each atomic shell, with no dependence on the atomic number. On the other hand, it is verified that these parameters exhibit a monotonic behaviour with the atomic number for the absolute ionization cross sections, which allows us to obtain analytical expressions for the latter.

Experimental determination of cross sections forK-shell ionization by electron impact for C, O, Al, Si, and Ti

“…In the case of the expression published by Talukder et al [28], alternative coefficients were recommended by one of the authors [45]. Campos et al [10] obtained analytical functions for the five elements reported in this work by fitting theoretical data calculated by Segui et al [5] based on DWBA. Bote et al [4] determined analytical functions from the parametrization of theoretical calculations, performed by the former authors combining DWBA and PWBA.…”

“…The formula proposed by Hombourger [9] adequately describes the behavior of Q in the range 1 < U < 20 and 5 < Z < 79. The analytical function fitted to theoretical data given by Campos et al [10] is applicable in a larger range of U for some atomic numbers.…”

“…The factors C j , A j , Q j , and ω j are, respectively, the mass concentration, the atomic weight, the K-shell ionization cross section, and the fluorescence yield, from element j . The analytical function used to describe the ionization cross section [10] and other parameters involved in the prediction of characteristic intensities are discussed elsewhere [33].…”

“…Thickness and density of the films were characterized by x-ray reflectivity (XRR). The results were compared with experimental data from other authors [11,[15][16][17][18][19][20][21][22] and with theoretical and semiempirical curves available in the literature [4,9,10,[23][24][25][26][27][28].…”

Monte Carlo simulation of X-ray spectra from low energy electrons using optical data

“…For inner-shell ionization we have used the expressions of Campos et al [13] which have been calculated using the distorted wave Born approximation (DWBA). Their expressions are suitable for energies ranging from the ionization threshold up to those as used in electron microscopy and for all elements from Z = 4 up to 79.…”