K X-ray production by 3–4 MeV proton impact on selected lanthanoids J. Reyes-Herrera, J. Miranda n Instituto de Fı ´sica, Universidad Nacional Auto ´noma de Me ´xico, Apartado Postal 20-364, 01000 Me ´xico, D.F., Mexico article info Article history: Received 21 April 2009 Accepted 27 May 2010 Keywords: Ionization cross sections X-rays Lanthanoids PIXE abstract Measurements of K-shell X-ray production cross sections induced by proton beams with energies between 3 MeV and 4 MeV are presented. The studied elements were Ce, Nd, Gd, Dy, and Ho, as thick targets. The measured cross sections are evaluated through comparisons with the ECPSSR model, the eECPSShsR-UA theory, the adiabatic perturbation (also known as direct molecular orbital, or MO) theory, and the empirical fits of Kahoul et al. using a scaling based on the reduced velocity parameter x R K in every case. Consideration is given to multiple ionization effects and electron capture contribution to K-shell ionization. It is shown that the experimental results are in good agreement with the theoretical predictions in the whole measured x R K range. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction There is a growing interest in the use of particle induced X-ray emission (PIXE), for analysis of lanthanoids (Jime ´ nez-Reyes, 1993), as they are more frequently used in technological applications (Hirano and Suzuki, 1996), or they might be used as tracers of natural (Hashimoto et al., 1994; Avino et al., 2006; Muhs and Budahn, 2009; Castillo et al., 2008) or anthropogenic (Georgi et al., 1987; Moreno et al., 2008) atmospheric aerosols. An important problem in the measurement of concentration of lanthanoids, also known as rare earth elements (REE), in many kinds of samples using any energy-dispersive X-ray spectrometry, especially particle induced X-ray emission (PIXE), is the inter- ference of the L-lines produced by the REE with the K X-rays from more abundant lighter elements, such as Mn and Fe. Thus, the possibility of using proton beams with energies higher than the usual 2–3 MeV to induce the K X-rays of the rare earths might be explored, although information about ionization cross sections or other atomic parameters is still scarce. In this regard, accurate data of X-ray relative intensity ratios, fluorescence yields and ionization cross sections is increasingly important, both for accurate results in quantitative analyses and in fundamental studies of atomic and nuclear processes. Hence, a reliable knowledge of the K-shell ionization cross sections of lanthanoids is necessary. Characteristic X-ray emission, that is, ionization followed by radiative relaxation filling an inner shell vacancy, produced by the impact of ions on atoms, is a phenomenon known for several decades (W¨ olfli, 1976). Especially, the production of K X-rays by proton impact was studied by many authors (Lapicki, 2008 and references cited therein), but the development of theoretical models that describe and predict the X-ray production cross sections by protons has seen only recent advancement in the relativistic velocity range of the projectiles (Lapicki, 2008). The ECPSSR theory of Brandt and Lapicki (1981) is a very successful model in describing the ionization by light ions, such as protons (Lapicki, 2002, 2008). This theory is a modification of the plane wave Born approximation (PWBA). It considers effects such as the ion energy loss after the collision (E), the Coulomb deflection in the ion trajectory (C), the modification of the atomic electron energy states through a perturbed stationary states model (PSS), and an adjustment in the mass of the electron, due to relativistic effects (R). Recently, the consideration of exact limits of integra- tion and the use of Hartree–Slater atomic wave functions were included, resulting in the model known as eECPSShsR (Lapicki, 2008). The United Atom correction to the eECPSShsR model (or eECPSShsR-UA) considers a modification in the binding energies of the target electrons due to the presence of the projectile (Sarkadi and Mukoyama, 1991; Lapicki, 2008). In contrast, Montenegro and Sigaud (1985) developed analytical expressions for computing the ionization cross sections through adiabatic perturbations, which they called a direct MO model. In the adiabatic limit, the ionization is predominant at internuclear distances smaller than the K-shell radius. Here, the Coulomb excitation of an electron occupying a MO can be seen as a superposition of two components, each one corresponding to the two involved nuclei. So far, an evaluation of these theories for lanthanoids in the light of experimental results has been very limited. Following a different approach, Kahoul et al. (2008) fitted analytical expressions to all existing K-shell ionization cross sections, based on a scaling similar to that given by Johansson and Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/radphyschem Radiation Physics and Chemistry 0969-806X/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2010.05.007 n Corresponding author. Tel.: + 52 55 56225073; fax: + 52 55 56225009. E-mail address: miranda@fisica.unam.mx (J. Miranda). Radiation Physics and Chemistry 79 (2010) 1013–1017