ECPSSR Theory Research Articles

New data base for Lα, Lβ, Lγ x-ray production by protons, new empirical fits, extraction of L-subshell ionization cross sections with various atomic parameters, and their comparison with the ECPSSR theory and its modifications: a recommendation for reliable choice of atomic parameters and ionization theory for PIXE analysis

Tables of L-shell and L-subshell x-ray production cross sections by protons from 1994 are updated, and the so constructed data base is fitted to formulas for empirical Lα, Lβ, Lγ x-ray production cross sections. Based on these fits, empirical L-subshell ionization cross sections are generated with various sets of atomic parameters with and without alteration for multiple ionizations. The extracted ionization cross sections are compared with the predictions of the ECPSSR theory and it modifications. Based on comparisons with different choice of the atomic parameters and theories, we will recommend an optimal combination of the atomic parameters and ionization theory for a reliable input in PIXE applications software.

L x-ray production cross sections from 50-300 keV proton impact on selected 4d transition elements

L x-rays were measured from the impact on thick targets of protons in the 50-300 keV energy range. The derived L sub-shell cross sections were compared with the ECPSSR theory and with measurements by others. It was found that ECPSSR over-predicts the measurements as the impact energy decreases.

L sub-shell cross sections for proton impact on selected 4d transition elements

L x-rays excited from thick elemental targets of Y, Zr, Nb, Mo, Rh, Pd, Ag and Sn by proton impact in the energy range 50–300 keV were measured with a high-resolution Si(Li) detector equipped with an ultra-thin window. The L sub-shell x-ray production cross sections were determined from a thick-target analysis of the x-ray yields. These were compared with the ECPSSR theory along with various atomic parameter databases and including modifications using the united-atom (UA) binding energy correction.

Evaluation of cross sections for Lα x-ray production by up to 4 MeV protons in representative elements from silver to uranium

Over the last two decades, Lα x-ray production cross sections have been fitted with a number of empirical formulae. Cross sections obtained from these formulae are averaged and fitted to a new empirical formula. These new empirical cross sections are compared with the results of the plane-wave Born approximation and the ECPSSR theory of Brandt and Lapicki (1981 Phys. Rev. A 23 1717). They are also gauged by the ECPSSR theory that has been corrected with a united atom approach in slow collisions, evaluated with Dirac–Hartree–Slater instead of screened hydrogenic wavefunctions, modified for intra-shell couplings as well as the change of the atomic parameters due to multiple ionizations. The effects of appropriately normalized intra-shell coupling factors and of multiple ionization were found to be small and essentially offset each other. The role of different sets of atomic parameters in conversion of the predictions of these ionization theories for Lα x-ray production in elements from the 47 ⩽ Z2 ⩽ 92 range of target atoms bombarded by up to 4 MeV protons is examined, and the selection of the optimal combination of ionization theory and atomic parameters for a reliable data base for PIXE analysis of elements heavier than palladium is discussed.

ISICS2008: An expanded version of ISICS for calculating K-, L-, and M-shell cross sections from PWBA and ECPSSR theory

New version program summary Program title: ISICS2008 Catalogue identifier: ADDS_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADDS_v4_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5420 No. of bytes in distributed program, including test data, etc.: 107 669 Distribution format: tar.gz Programming language: C Computer: 80 486 or higher level PCs Operating system: Windows XP and all earlier operating systems Classification: 16.7 Catalogue identifier of previous version: ADDS_v3_0 Journal reference of previous version: Comput. Phys. Comm. 179 (2008) 616 Does the new version supersede the previous version?: Yes Nature of problem: Ionization and X-ray production cross section calculations for ion–atom collisions. Solution method: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits. Reasons for new version: Addition of relativistic treatment of both projectile and K-shell electrons. Summary of revisions: A new addition to ISICS is the option (R) to calculate ECPSSR cross sections that account for the relativistic treatment of both projectile and K-shell electron, as proposed recently by Lapicki [1], accordingly as σ K RECPSSR = C K ⋅ ( 1 + 0.07 ( θ K ς K ) 8 ( m K R υ 1 R Z z K ) 2 ) ⋅ σ PWBA ( ( m K R υ 1 R ) / Z z K , ς K θ K ) , where υ 1 R is the relativistic projectile velocity. The option can also be invoked in calculating ECPSShsR, where hsR stands for the Hartree–Slater description of the K-shell electron, which was already incorporated into ISICS2006 [2,3], and is now expressed in this option as, σ K RECPSShsR = C K ⋅ hsR ( ( 2 υ 1 R ) / ( Z z K ς K θ K ) , Z z / 137 ) ⋅ ( 1 + 0.07 ( θ K ς K ) 8 ( υ 1 R / Z z K ) 2 ) ⋅ σ PWBA ( υ 1 R / Z z K , ς K θ K ) using the function hsR that is already incorporated into ISICS2006. It should be noted that these expressions are corrected versions [4] from the ones published in Ref. [1]. In this new version, ISICS2008, the option line in the main menu that read “Use Relativistic Proj. velocity” has been replaced by “R option for K-shell … Uses Rel. Proj. vel.”. As before, various combinations of options can be utilized and each is denoted in the output. Restrictions: The consumed CPU time increases with the atomic shell ( K , L , M ) , but execution is still very fast. Additional comments: A revised User Manual is included in the distribution file. Running time: This depends on which shell and the number of different energies to be used in the calculation. The running time is not significantly changed from the previous version. As before, to calculate K-shell cross sections for protons striking carbon for 19 different proton energies it took less than 10 s; to calculate M-shell cross sections for protons on gold for 21 proton energies it took 4.2 min.

Study of the L-subshell X-ray production cross sections of Au by 20—50 MeV O5+ bombardments

The experiments were performed at HI-13 tandem accelerator at the Chinese Institute of Atomic Energy （CIAE）, in which the L-shell X-ray relative production cross section was measured for solid targets Au bombarded by 20—50 MeV O5+ions. The ratios of Au L-subshell production cross sections σ（Lβ）/σ（Lα），σ（Lγ）/σ（Lα），σ（Ll）/σ（Lα） have been calculated according to the experimental data. The results are compared with the predictions of the ECPSSR theory. Reasonable agreement between theory and experiment was obtained.

ERCS08: A FORTRAN program equipped with a Windows graphics user interface that calculates ECPSSR cross sections for the removal of atomic electrons

ERCS08 is a program for computing the atomic electron removal cross sections. It is written in FORTRAN in order to make it more portable and easier to customize by a large community of physicists, but it also comes with a separate windows graphics user interface control application ERCS08w that makes it easy to quickly prepare the input file, run the program, as well as view and analyze the output. The calculations are based on the ECPSSR theory for direct (Coulomb) ionization and non-radiative electron capture. With versatility in mind, the program allows for selective inclusion or exclusion of individual contributions to the cross sections from effects such as projectile energy loss, Coulomb deflection of the projectile, perturbation of electron's stationary state (polarization and binding), as well as relativity. This makes it straightforward to assess the importance of each effect in a given collision regime. The control application also makes it easy to setup for calculations in inverse kinematics (i.e. ionization of projectile ions by target atoms or ions). Program summary Program title: ERCS08 Catalogue identifier: AECU_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12 832 No. of bytes in distributed program, including test data, etc.: 318 420 Distribution format: tar.gz Programming language: Once the input file is prepared (using a text editor or ERCS08w), all the calculations are done in FORTRAN using double precision. Computer: see “Operating system” below Operating system: The main program (ERCS08) can run on any computer equipped with a FORTRAN compiler. Its pre-compiled executable file (supplied) runs under DOS or Windows. The supplied graphics user interface control application (ERCS08w) requires a Windows operating system. ERCS08w is designed to be used along with a text editor. Any editor can be used, including the one that comes with the operating system (for example, Edit for DOS or Notepad for Windows). Classification: 16.7, 16.8 Nature of problem: ECPSSR has become a typical tag word for a theory that goes beyond the standard plane wave Born approximation (PWBA) in order to predict the cross sections for direct (Coulomb) ionization of atomic electrons by projectile ions, taking into account the energy loss (E) and Coulomb deflection (C) of the projectile, as well as the perturbed stationary state (PSS) and relativistic nature (R) of the target electron. Its treatment of non-radiative electron capture to the projectile goes beyond the Oppenheimer–Brinkman–Kramers approximation (OBK) to include the effects of C, PSS, and R. PSS is described in terms of increased target electron binding (B) due to the presence of the projectile in the vicinity of the target nucleus, and (for direct ionization only) polarization of the target electron cloud (P) while projectile is outside the electron's shell radius. Several modifications of the theory have been recently suggested or endorsed by one of its authors (Lapicki). These modifications are sometimes explicit in the tag word (for example, eCPSSR, eCUSR, ReCPSShsR, etc.) A cross section for the ionization of a target electron is assumed to equal the sum of the cross sections for direct ionization (DI) and electron capture (EC). Solution method: The calculations are based on the ECPSSR theory for direct (Coulomb) ionization and non-radiative electron capture. With versatility in mind, the program allows for selective inclusion or exclusion of individual contributions to the cross sections from effects such as projectile energy loss, Coulomb deflection of the projectile, perturbation of electron's stationary state (polarization and binding), as well as relativity. This makes it straightforward to assess the importance of each effect in a given collision regime. The control application also makes it easy to setup for calculations in inverse kinematics (i.e. ionization of projectile ions by target atoms or ions). Restrictions: The program is restricted to the ionization of K, L, and M electrons. The theory is non-relativistic, which effectively limits its applicability to projectile energies up to about 50 MeV/amu. However, the theory is extended to apply to relativistic light projectiles. Radiative electron capture is not taken into account, since its contribution is found to be negligible in the collision regimes covered by the ECPSSR theory. Unusual features: Windows graphics user interface along with a FORTRAN code for calculations, selective inclusion or exclusion of specific corrections, inclusion of the extension to relativistic light projectiles, inclusion of non-radiative electron capture. Running time: Running the program using the input data provided with the distribution only takes a few seconds.

New Geant4 cross section models for PIXE simulation

We have implemented in the Geant4 simulation toolkit a set of new ionisation cross sections for the simulation of particle induced X-ray emission (PIXE), based upon theoretical and semi-empirical models. The set provides a model based on the so-called ECPSSR theory for the computation of K-shell ionisation cross sections for proton and alpha particle impact. A second model is based upon semi-empirical expressions proposed by Orlic for the calculation of L i -subshells ionisation cross sections for proton impact. Our developments are compared to ionisation cross sections already existing in the Geant4 toolkit and to experimental data.

Empirical K-shell ionization cross-sections of elements from 4Be to 92U by proton impact

A large database containing about 5400 experimental K-shell ionization cross-sections by protons for elements from Be to U is collected from various sources and compilations available in the literature from 1953 to 1999. The data are divided into groups corresponding to their atomic numbers and fitted separately by analytical functions to deduce empirical K-shell ionization cross-sections. The deduced empirical K-shell ionization cross-sections are presented together with the reference ones obtained by Paul and Sacher for selected elements [H. Paul, J. Sacher, At. Data Nucl. Data Tables 42 (1989) 105]. The two sets of results are compared to the calculations within the ECPSSR theory and discussed.

An improved version of ISICS: A program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

The formatting of the M-shell atomic parameters imbedded in file XCSC.H in ISICS has been corrected. The problem only affected cross section calculations for Uranium and heavier elements. The corrected version of ISICS has been re-compiled and is now available. New version program summary Program title: ISICS Catalogue identifier: ADDS_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADDS_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4645 No. of bytes in distributed program, including test data, etc.: 106 731 Distribution format: tar.gz Programming language: C++ Computer: 80486 or higher-level PCs Operating system: WINDOWS 98 through WINDOWS XP Classification: 16.7 Does the new version supersede the previous version?: Yes Nature of problem: Ionization and X-ray production cross section calculations for ion-atom collisions. Solution method: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits. Reasons for new version: The formatting of the M-shell atomic parameters involving cross section calculations for Uranium and heavier elements needed to be corrected. Summary of revisions: The affected file XCSC.H in ISICS has been corrected and ISICS has been recompiled. Restrictions: The consumed CPU time increases with the atomic shell (K, L, M), but execution is still very fast. Running time: This depends on which shell and the number of different energies to be used in the calculation. For example, to calculate K-shell cross sections for protons striking carbon for 19 different proton energies it took less than 10 s; to calculate M-shell cross sections for protons on gold for 21 proton energies it took 4.2 min.

Scaling of analytical cross sections for K-shell ionization by nonrelativistic protons to cross sections by protons at relativistic velocities

A procedure is given by which nonrelativistic cross sections are scaled to the K-shell ionization cross sections by protons of any velocity up to the speed of light. To perform this scaling in an analytical manner, the ECPSSR theory of Brandt and Lapicki (1981 Phys. Rev. A 23 1717) and its recent modifications that go beyond the plane wave Born approximation with exact (e) limits on the energy and momentum transfers (ePWBA) are formulated analytically. They are expressed in terms of a formula that fits numerically evaluated ePWBA to within 3% for carbon and all heavier elements. With an extension to GeV protons, the ECPSSR and its relativistic modifications are reviewed to untangle consequences of various relativistic treatments of protons and different methods to account for the relativistic nature of the K-shell electron. The adequacy of the scaling to obtain the relativistic K-shell ionization cross sections is scrutinized through departures of the developed theories from a comprehensive compilation of the data. Excellent agreement with 1 GeV data of Vodopyanov et al (1996 J. Phys. B: At. Mol. Opt. Phys 29 2543) is demonstrated, and an apparent discrepancy with 4.88 GeV data of Anholt et al (1976 Phys. Rev. A 14 2103) is examined in light of other theories.

SEMI‐empirical and empirical formulas for calculation of K‐shell ionization cross sections by proton impact: a comparison

AbstractAccording to the plane wave Born approximation (PWBA) and the binary encounter approximation (BEA) models, it is possible to fit the cross sections obtained with any atomic element at any particle energy using a scaling law for a K‐shell. The semi‐empirical K‐shell ionization cross sections are then deduced by fitting the available experimental data normalized to their corresponding theoretical values. For the empirical K‐shell ionization cross sections, a third‐order polynomial was used to fit the same experimental data for protons. Our results are compared with the predictions of the ECPSSR theory and with other earlier works. Good agreement is obtained, but it is emphasized that the ultimate solution is to deduce the cross sections by fitting the available experimental data for each element separately. Copyright © 2008 John Wiley & Sons, Ltd.

Coupling and binding-saturation effects inL-subshell ionization of heavy atoms by 0.3–1.3-MeV/amu Si ions

The coupling and binding effects have been studied in $L$-subshell ionization of heavy Au, Bi, Th, and U atoms by an impact of ${^{28}\text{S}\text{i}}^{q+}$ ions in the energy range of 8.5--36.0 MeV. The measured $\mathit{L}$ x-ray spectra were analyzed taking into account the multiple ionization effects in outer $M$ and $N$ shells. The $L$-subshell ionization cross sections have been obtained from measured x-ray production cross sections using the $L$-shell fluorescence and Coster-Kronig yields which were modified for a reduced number of electrons and closed Coster-Kronig transitions in the multiply ionized atoms. The results are compared with the available calculations, which are based on the semiclassical approximation (SCA) as well as the plane-wave Born approximation (PWBA). We demonstrate that for silicon ion impact these theoretical approaches have to be modified to include the $L$-subshell coupling effect using the ``coupled subshell model'' (CSM) as well as the saturation of the binding effect at the united atom limit. The calculations modified for both effects are in much better agreement with the data. In particular, an order-of-magnitude improvement of agreement between the data and the SCA-CSM calculations including the binding-saturation effect is reported for low-energy Si ions for the ${L}_{2}$-subshell. The results are also compared with the predictions of the PWBA based ECPSSR and ECUSAR theories accounting for the energy-loss (E), Coulomb-deflection (C), and relativistic (R) effects treating the binding effect within the perturbed stationary state (PSS) approximation with correction for the binding-saturation effect introduced to describe the united-atom and separated-atom (USA) limits.

The united atom approximation option in the ISICS program to calculate K-, L- and M-shell cross sections from PWBA and ECPSSR theory

The C program, ISICS [Z. Liu, S. J. Cipolla, Comput. Phys. Commun. 97 (1996) 315], which calculates ionization and X-ray production cross sections using PWBA and ECPSSR theory, has been enhanced by the addition of new options, including the united atom approximation to the binding-energy correction. Other changes will also be briefly described.

L X-ray production cross-section ratios for protons incident on high- Z atoms: A test of ECPSSR theory and newly recommended vacancy de-excitation parameters

The X-ray intensity ratios Lβ/Lα and Lγ/Lα for six heavy elements have been measured using a Si(Li) detector coupled to both analog and digital signal processors. The proton energies were chosen to ensure that possible united atom (UA) and intra-shell (IS) effects would be small, thereby ensuring that the experiments were a direct test of the ECPSSR together with the L subshell fluorescence and Coster–Kronig probabilities. Careful attention was paid to reducing recognized uncertainties in the fitting of the spectra, with the desired intensity ratios being extracted from a procedure that assumed the DF radiative transition rates of Scofield to be correct. Experiment and ECPSSR theory agree closely when the fluorescence and CK probabilities from a recent critical review are adopted in preference to those commonly used in earlier work. This result provides a significant improvement in the database used for PIXE analysis, and it paves the way for more definitive studies at lower proton energies, aimed at testing predicted UA and IS corrections.

A ionization theory based on united and separated atom model

The direct Coulomb ionization process can be generally well described by the ECPSSR theory, which bases on the perturbed-stationary-state(PSS) and accounts for the energy-loss, Coulomb-deflection, and relativistic effects. But the ECPSSR calculation has significant deviations for heavy projectile at low impinging energies. In this paper we propose a new modified ECPSSR theory, i.e. MECUSAR, in which PSS is replaced by an united and separated atom model, and molecule-orbit effect is considered. The MECUSAR calculations give better agreement with the experimental data at lower impinging energies, and agree with the ECPSSR calculations at high energies. By using OBKN (Oppenheimer-Brinkman-Kramers formulas of Nikolaev) theory to describe the contribution of the electron capture, we further modified the proposed MECUSAR theory, and calculated the target ionization cross sections for different charge states of the projectile.

TargetK-vacancy production by2.5to25MeV∕amuAr, Kr, and Xe ions

Cross sections have been measured for $K\ensuremath{\alpha}$ x-ray production in targets of Al, Ti, Cu, Zr, Ag, Sm, and Ta by Ar, Kr, and Xe ions ranging in energy from $2.5\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}25\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{amu}$. In addition, the degree of simultaneous $L$-shell ionization and the enhancement of the $K\ensuremath{\alpha}$ diagram lines due to secondary ionization processes were assessed by performing high-resolution spectral measurements on Al, Ti, V, Co, and Cu targets. This information was used to correct for the $K\ensuremath{\alpha}$ x-ray yield produced by electron bombardment and photoionization, and to calculate the fluorescence yields needed to convert the $K\ensuremath{\alpha}$ x-ray production cross sections into $K$-vacancy production cross sections. The resulting cross sections were compared with the predictions of the perturbed stationary state approximation with corrections for projectile energy loss, Coulomb deflection, and relativistic effects (ECPSSR theory). Also, the scaling properties of the $K\ensuremath{\alpha}$ x-ray production cross sections were examined and a semiempirical (universal) curve was deduced that reproduces the measured cross sections to within $\ifmmode\pm\else\textpm\fi{}30%$ on average.

An improved version of ISICS: a program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

The C program, ISICS [Z. Liu, S.J. Cipolla, Comput. Phys. Comm. 97 (1996) 315–330], which calculates ionization and X-ray production cross-sections using PWBA and ECPSSR theory, has been enhanced to include new options, correct some minor flaws, and to make the program more versatile. Program summary Title of program: ISICS Catalog identifier: ADDS_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADDS_v2_0 Program available from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested: WINDOWS XP Program language used: C Computer: 80486 or higher-level PCs No. of lines in distributed program, including test data, etc.: 5343 No. of bytes in distributed program, including test data, etc.: 151 838 Distribution format: tar.gz Catalogue identifier of previous version: ADDS Journal reference of previous version: Comput. Phys. Comm. 97 (1996) 315–330 Does the new version supersede the previous version: Yes Nature of the physical problem: Ionization and X-ray production cross-section calculations for ion–atom collisions. Reasons for new version: Increased functionality and new options. Summary of revisions: Option for the united-atom approximation for binding-energy correction; easier inputting of updated atomic parameters; extension of projectile energy down to eV range; accounting for DHS wave function in K-shell ionization; other miscellaneous changes. Method of solution: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits. Restrictions on the complexity of the problem: The consumed CPU time increases with the atomic shell (K, L, M), but execution is still very fast. Typical running time: No change from previous version. Unusual features of the program: No

L-subshell and total M-shell X-ray production cross sections of Ta, W, Pt, Au, Pb and Bi by 0.7–2.4 MeV protons

The L-subshell and total M-shell X-ray production cross sections of Ta, W, Pt, Au, Pb and Bi have been measured by protons of energy between 0.7 and 2.4MeV. The obtained results for X-ray production cross sections have been compared with the existing experimental data, prediction of the ECPSSR theory and also with fitted empirical cross sections of Strivay and Weber.

M-shell ionization of heavy elements by0.1–1.0MeV∕amuH1,2andHe3,4ions

The $M$-shell ionization in high-$Z$ atoms by low-energy light $_{1}^{1}\mathrm{H}$, $_{1}^{2}\mathrm{H}$, $_{2}^{3}\mathrm{He}$, and $_{2}^{4}\mathrm{He}$ ions have been studied systematically in the energy range $0.1--1.0\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{amu}$ in order to verify the available theoretical approaches describing the $M$-shell ionization by charged particles in asymmetric collisions. The present low-energy data, combined with our earlier results reported for $M$-shell ionization by hydrogen and helium ions for higher energies, form a systematic experimental basis to test the theoretical predictions of $M$-shell ionization based on the plane-wave Born approximation (PWBA), the semiclassical approximation (SCA), and the binary-encounter approximation (BEA). In the PWBA based approaches the energy loss (E), Coulomb deflection (C), perturbed stationary state (PSS), and relativistic (R) effects were considered within the ECPSSR theory and its recent modification, called the ECUSAR theory, in which a description of the PSS effect was corrected to account for the united- and separated-atom (USA) electron binding energy limits. In the SCA calculations with relativistic wave functions the binding effect was included only in the limiting cases of separated-atom and united-atom limits. Possible contribution of the electron capture, multiple ionization, and recoil ionization to the $M$-shell vacancy production, which is dominated for light ions impact by direct single ionization process, are also discussed. The universal scaling of measured $M$-shell x-ray production and ionization cross sections was investigated in detail. Using the present data the isotopic effect has been studied by comparing the measured $M$-shell ionization cross-section ratios for equal-velocity hydrogen $_{1}^{1}\mathrm{H}$ and $_{1}^{2}\mathrm{H}$ as well as helium $_{2}^{3}\mathrm{He}$ and $_{2}^{4}\mathrm{He}$ isotopes. In addition, the ratios of measured ionization cross sections for $_{1}^{2}\mathrm{H}$ and $_{2}^{4}\mathrm{He}$ were used to investigate the role of the binding effect. The present results are of practical importance for the application of particle-induced x-ray emission technique in trace element studies.