Electron contribution to photon transport in coupled photon-electron problems: inner-shell impact ionization correction to XRF Jorge E. Fernandez, a * Viviana Scot, a Luca Verardi b and Francesc Salvat c The Monte Carlo code PENELOPE (coupled electron-photon Monte Carlo) has been used to compute the effect of the secondary electrons on the X-ray fluorescence characteristic lines. The mechanism that produces this contribution is the inner-shell impact ionization. The ad hoc code KERNEL (which calls the PENELOPE library) has been used to simulate a forced first collision at the origin of coordinates. The electron correction (produced by the secondary electrons and their multiple scattering) has been studied in terms of angle, space and energy. The energy dependence has been quantified in the interval 1–150 keV, for all the emission lines (K, L and M) of the elements with atomic numbers Z = 11–92. For each characteristic line, the energy dependence is described by simple parametric expressions corresponding to the five energy regions delimited by the K, L1, L2 and L3 absorption edges. It has been introduced a new photon kernel comprising the correction due to inner-shell impact ionization. The new kernel is suitable to be adopted in photon transport codes (either deterministic or Monte Carlo) with a minimal effort. Finally, the new kernel has been studied for different elements and lines to trace a general behavior. Copyright © 2013 John Wiley & Sons, Ltd. Introduction The most accurate description of the radiation field in X-ray spec- trometry requires the modeling of coupled photon-electron transport, because Compton scattering and photoelectric effect give both photons and electrons as secondary particles. The solution for the coupled problem is time consuming because the electrons interact continuously with the medium and there- fore, the number of electron collisions is always very high. For this reason, transport codes usually neglect the electron contribu- tions shown in Fig. 1, and consequently, only photon transport is considered. Nevertheless, secondary electrons contribute to the photon field through electron-photon conversion mecha- nisms like bremsstrahlung (which produces a continuous photon spectrum) and inner-shell impact ionization (ISII) (which modifies the intensity of the characteristic lines) (Fig. 2). Other processes, not mentioned here, that contribute to the multiple scattering of electrons (Auger electrons, Coster-Kronig transitions, etc.) need to be also considered. In what follows, we will focus on ISII, which is the only effect that modifies the intensity of the charac- teristic lines, and therefore, it is of interest in X-ray fluorescence (XRF) analysis. Several authors have tried to describe the XRF due to secondary electrons by focusing separately on the contributions from K- photoelectrons, [1] Auger electrons, [2] both effects, [3] and Compton electrons. [4] The whole problem is very complex because all of these mechanisms (plus other not mentioned) have to be consid- ered together, and the fact that electrons interact continuously and locally (compared with the photons) makes it necessary to describe carefully the multiple scattering of the electrons. A prac- tical approach to study the mentioned mechanisms in presence of multiple scattering is to recur to a coupled photon-electron Monte Carlo (MC) code. Some authors [5,6] have developed ad hoc MC codes on the basis of simplified models of electron transport to evaluate the effect of secondary electrons in thin layers. To understand the extent of the electron contributions on multilayers, [5,7,8] some experiments have been performed using the polychromatic excitation of X-ray tubes, showing that the effect exists, but it is lower than expected. Kawahara et al. [8] described also an experiment with tunable monochromatic excitation at BESSY II. In this case, it appeared a very strong discontinuity of the Cr–L line intensity in correspondence with the Cr–K edge, which is due to the cascade effect. The apparent contradiction of these experiments needs to be explained by recourse to an MC code using a detailed description of the multi- ple scattering of electrons. In this work, it has been used the MC code PENELOPE [9] (coupled electron-photon MC) to compute the effect of the secondary electrons into the photon transport. In particular, PENELOPE has been used to compute a corrective term to the photon kernel, which fully describes the effect of ISII on the characteristic line emission. It is given a formal expression of a new photon kernel comprising the correction for ISII. The new kernel is suitable to be adopted in photon transport codes (either deterministic or MC) with a minimal increase in complexity. * Correspondence to: Jorge E. Fernandez, Laboratory of Montecuccolino- Department of Industrial Engineering (DIN), Alma Mater Studiorum University of Bologna, via dei Colli, 16, I-40136, Bologna, Italy. E-mail: jorge. fernandez@unibo.it a Laboratory of Montecuccolino (DIN), Alma Mater Studiorum University of Bologna, via dei Colli, 16, 40136 Bologna, Italy b Department of Electrical, Electronic and Information Engineering “Guglielmo Marconi” (DEI), Alma Mater Studiorum University of Bologna, Viale del Risorgi- mento 2, 40136 Bologna, Italy c Facultat de Física (ECM), Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain X-Ray Spectrom. 2013, 42, 189–196 Copyright © 2013 John Wiley & Sons, Ltd. Research article Accepted: 21 December 2012 Published online in Wiley Online Library: 22 May 2013 (wileyonlinelibrary.com) DOI 10.1002/xrs.2473 189