Measurements of L-shell X-ray production cross-sections of Ag and Sb by low-energy electron impact

Radiation Physics and Chemistry 122 (2016) 66–72

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Measurements of L-shell X-ray production cross-sections of Ag and Sb by low-energy electron impact J.L. Zhao, Z. An n, J.J. Zhu n, W.J. Tan, M.T. Liu Key Laboratory of Radiation Physics and Technology of Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, PR China

H I G H L I G H T S


We measured L shell X-ray production cross-sections of Ag and Sb by keV electrons.
Corrections for effects of target substrates are made by MC simulations.
L shell production cross-sections measured are in good agreement with theories.

art ic l e i nf o

a b s t r a c t

Article history: Received 5 September 2015 Received in revised form 22 December 2015 Accepted 18 January 2016 Available online 19 January 2016

The total L-shell X-ray production cross-sections of Ag and Sb elements were measured by detecting the characteristic X-rays induced by the electron impact in the energy range of 6–28 keV. In this experiment, the thin films with thick aluminum substrates were used as the targets, and the experimental setup was improved. The influence of multiple scattering of electrons penetrating the targets films, electrons reflected from the thick aluminum substrates and bremsstrahlung photons produced when incident electrons impacted the targets were corrected by using the Monte Carlo method. The experimental results determined in this paper were compared with some theoretical models and other available experimental data in the literature. It was shown that the L-shell X-ray production cross-sections of Ag and Sb elements measured in this paper were in good agreement with the theoretical predictions within the uncertainties. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Electron impact Atomic inner-shell ionization X-ray production cross-section Monte Carlo simulation

1. Introduction The atomic inner-shell ionization caused by electron or positron impact is a process of great importance in atomic physics (Powell, 1976,1985), and it is helpful for better understanding electron or positron-atom interactions (Khare and Wadehra, 1996; Tian et al., 2012; Llovet et al., 2014; Pindzola, 2014, 2015). Moreover, the study of atomic inner-shell ionization cross-sections by electron impact is still an interesting subject both experimentally (An et al., 1996, 2006; Shanker and Hippler, 1997; Wu et al., 2004; Limandri et al., 2012; Sepúlveda et al., 2014; Merlet et al., 2014; Llovet et al., 2014) and theoretically (Segui et al., 2003; Colgan et al., 2006; Bote and Salvat, 2008; Bote et al., 2009; Pindzola, 2014, 2015). Up to now, there have been many theoretical models, such as Bethe's theory (Bethe, 1931), plane-wave Born approximation (PWBA) (Powell, 1976, 1985), PWBA-C-Ex (Hippler, 1990) n

Corresponding authors. E-mail addresses: [email protected] (Z. An), [email protected] (J.J. Zhu).

http://dx.doi.org/10.1016/j.radphyschem.2016.01.033 0969-806X/& 2016 Elsevier Ltd. All rights reserved.

and distorted-wave Born Approximation (DWBA) (Segui et al., 2003; Colgan et al., 2006), to describe the atomic inner-shell ionization process. Theoretical progress made recently for atomic inner-shell ionization is that Segui et al. (2003) and Colgan et al. (2006) have developed semirelativistic/relativistic DWBA calculations for neutral atoms and incident electron energies from threshold up to about 10 times the ionization energy, and Bote and Salvat, (2008) combined the DWBA with the PWBA to calculate the cross-sections for incident electron/positron energies from the ionization threshold to 1 GeV, and Pindzola (2014, 2015) performed the pertubative fully-relativistic distorted-wave calculations for the electron-impact inner-shell ionizations of U and Au elements in which the full two-body retarded electromagnetic interaction was included. In the DWBA theory, the distorting effect of the target atom on the projectiles wave functions was taken into account, which made the formalism valid for lower incident energies, particularly near the ionization threshold. Since then, the agreement between theory and experiment has been improved greatly. However, the review paper of Llovet et al. (2014) also

J.L. Zhao et al. / Radiation Physics and Chemistry 122 (2016) 66–72

indicated that inconsistencies still exist between experiment and theory, particularly for subshells other than the K shell. Therefore, the theoretical models still need to be tested by using accurate experimental data. Moreover, these accurate atomic inner-shell ionization cross-sections are also basic data for radiation physics, astrophysics, electron microprobe analysis, fusion research and for the simulation of radiation transport in matter (Powell, 1976, 1985; Salvat et al., 2008). Powell, (1976, 1985) reviewed the available measurements, calculations and predictive formulae for inner-shell ionization cross-sections developed during the past decades. Most recently, Llovet et al. (2014) provided additional information and supplied a more extensive comparison of measured with calculated ionization cross-sections. At present, most of the available experimental information pertains to K-shells ionization (An et al., 1996, 2003; Liu et al., 2000; Zhu et al., 2009; Limandri et al., 2012; Llovet et al., 2014); although slight discrepancy existed among available K-shells ionization experimental data from different authors, in general the experimental data showed a good agreement with the theoretical values, e.g., the DWBA theoretical values. However, for the L-shell ionization cross-sections or X-ray production crosssections, the measurements were relatively scarce and the agreement between some experimental data and the theoretical models was not satisfactory (Merlet et al., 2004; Wu et al., 2010, 2012; Llovet et al., 2014). As for M shells, there are very few measurements (Merlet et al., 2008, 2014; Moy et al., 2013, 2014a, 2014b). In one word, the review paper of Llovet et al. (2014) showed that available experimental data are still scarce for many elements, and when they are available for some elements, significant discrepancy exists between theory and experiment and between the results from different authors, which are often larger than the quoted experimental uncertainties. This fact indicates that the absolute measurements for atomic inner-shell ionization cross-sections or X-ray production cross-sections still face considerable difficulties and the accuracy for measurements needs to be improved. In this paper, the total L-shell X-ray production cross-sections for Ag and Sb by electron impact in the energy range of 6–28 keV have been measured, and the thin films deposited on thick substrates as the targets were also employed in these measurements (An et al., 1996; Wu et al., 2004). As for Ag element, Wu et al. (2004) measured the total L-shell X-ray production cross-sections by electron impact in the energy range of 5–25 keV by using the thin Ag film with the thick aluminum substrate as the target, and observed that the experimental data were about 9–18% lower than the PWBA-C-Ex calculations. Recently, Sepúlveda et al. (2014) determined three L-subshell ionization cross-sections of Ag for the first time and the total L-shell X-ray production cross-sections as well in the electron-impact energy range of 6–25 keV by using the thin Ag film with the thick carbon substrate as the target, and found that the total L-shell X-ray production cross-sections were about 25% higher than the DWBA theoretical values. Zhao et al. (2015) measured the total L-shell X-ray yields of thick Ag target by 6–29 keV electron impact and also obtained the corresponding X-ray production cross-sections based on some assumptions that were given in detail in Zhao et al. (2015), and observed that the experimental data lay between the experimental data of Wu et al. (2004) and Sepúlveda et al. (2014) and were about 10% higher than the DWBA theoretical values. Obviously, it is necessary to carry out additional experimental determinations to clarify the disagreement between the different sets of data. In addition, the atomic numbers of Ag (Z¼ 47) and Sb (Z¼ 51) are closer, and the experimental and theoretical values for the L-shell X-ray production cross-sections of Sb are comparable to those of Ag element. In the literature, to the best of our knowledge, there are no experimental data for Sb element. Hence, the L-shell X-ray production crosssections for Sb element were also measured in this paper.

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In order to obtain more accurate experimental data, the experimental setup in this paper has been improved and described in detail in Section 2. The influence of multiple scattering of electrons penetrating the targets films, electrons reflected from the thick aluminum substrates and bremsstrahlung photons produced by incident electrons impacting on the targets were corrected by simulating the electron and photon transports in the targets with a Monte Carlo (MC) code. The measured L-shell X-ray production cross-sections for Ag and Sb were compared with the corresponding results based on the DWBA and PWBA-C-Ex theories and experimental data available in the literature. This paper is organized as follows: Section 2 introduces the experimental setup, the efficiency calibration of a silicon drift detector (SDD) and Monte Carlo simulation. Section 3 presents the data processing and the experimental results for the L-shell X-ray production cross-sections of Ag and Sb elements by 6–28 keV electron impact. The conclusions are given in Section 4.

2. Experiments 2.1. Experimental setup The experimental setup is similar to that in Li et al. (2014) and Zhao et al. (2015). The 6–28 keV electron beams were provided by the electron gun in a scanning electron microscope (SEM) of KYKY2800B type (KYKY Technology Co., Ltd., Beijing, China). The focus of the electron beams by the electron optical lens in the SEM was much better than that in our previous experimental setup, in which the spot size of the electron beams was determined only by a carbon collimator (Wu et al., 2004). The Ag and Sb targets were placed inside a deep Faraday cup where a top hole and a side hole were drilled for incident electrons to pass through and X-ray photons to be detected, respectively. The electron beams vertically impacted through the top hole of the deep Faraday cup, and the targets were tilted by 45° with respect to the direction of incident electron beams. The beam current intensity was adjusted according to the dead-time correction, and the values of the dead-time were about 3%. The electron beam current was collected by the deep Faraday cup and fed into an ORTEC439 digital current integrator (ORTEC, Oak Ridge, Tennessee, USA). The spot area of the electron beam irradiated on the surface of the target was about 2  2 mm2. The X-ray photons were detected by a SDD detector (Model XR-100SDD, AMPTEK Inc., Bedford, MA, USA) which was placed horizontally towards to the side hole of the deep Faraday cup. The X-ray SDD detector used in this experiment has an energy resolution (full-width at half-maximum) of 125 eV for 55Fe 5.9 keV Kα X-ray, and its sensitive silicon layer is 0.5 mm thick and its window area is 20 mm2. Moreover, the peak time of the detector is 11.2 μs. This detector has an ultra-thin C2 window which consists of 40 nm thick Si3N4 film, 30 nm thick Al coating film and 15 μm thick Si grid supporter with 78% open area, therefore, it has much higher intrinsic efficiency at very low X-ray energies and is suitable for the measurements performed in this paper. The deep Faraday cup, the targets and the SDD detector were all placed in the vacuum chamber of the SEM. The deep Faraday cup used in this paper was redesigned (shown in Fig. 1). The wall of the deep Faraday cup was made of a Cu cylinder of 5 mm, instead of a Al cylinder previously used in our experiment, in order to greatly decrease the penetration of higherenergy bremsstrahlung photons. In front of the top hole of the deep Faraday cup, a Cu layer of 1 mm with a central hole, which was insulated from the deep Faraday cup, was placed and grounded to eliminate possible electron accumulations on the Faraday cup caused by the incident electron beams. Meanwhile, a negative 100 V bias voltage was also set in front of the top hole and side

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Fig. 1. The schematic of experimental setup.

hole of the deep Faraday cup to suppress the escape of secondary electrons while the escape of the electrons with the energies larger than 100 eV was estimated by the Monte Carlo calculations. These designs improved the accuracy of the measurements for the total incident electron numbers. Moreover, in order to prevent the backscattered electrons from entering the C2 ultra-thin window of the SDD detector, which may make the detector unable to work properly and produce additional bremsstrahlung background, a pair of parallel strong Nd–Fe–B permanent magnets were placed in front of the SDD detector to deflect the backscattered electrons. The software package CST PARTICLE STUDIO (Spachmann and Becker, 2006) was used for the design of the permanent magnet assembly. Our experiments showed that the permanent magnet assembly worked very well in the incident electron energies of interest here. The targets used in present experiment were prepared by depositing Ag and Sb elements on thick Al substrates. The thickness of Ag and Sb films was determined by Rutherford backscattering spectrometry (RBS) (Jeynes et al., 2003). The 1 MeV alpha-particles were provided by the Van de Graaff electrostatic accelerator (Shanghai Xianfeng Motor Factory Co., Ltd., Shanghai, China) and vertically impacted on the sample surfaces. A semiconductor Au (Si) surface barrier detector (Beijing Nuclear Instruments Factory, Beijing, China) for detecting the backscattered particles was placed at an angle of 160° with respect to the incident beam direction. The SIMNRA software (Mayer, 1997) was used to fit the experimental results. The homogeneity of the thickness of the target was checked by performing the RBS measurements at two or three points for each targets and it was found that the target homogeneity was very good. The thickness of Ag and Sb films was determined to be 15.26 70.90 μg/cm2 and 8.65 70.50 μg/cm2, respectively. After the analysis of the RBS spectrum of Ag film, a diffusion of Ag atoms into the Al substrate was found. 2.2. Efficiency calibration of SDD detector A key factor in determining the experimental L-shell X-ray production cross-sections is the detection efficiency of the X-ray detector. In the higher energy region the accurate detection efficiency can be measured by means of standard radioactive sources, but it is difficult for X-ray energies below 3.3 keV, because the adequate standard radioactive sources are not generally available. In this paper, the detection efficiency of the SDD detector was determined by using the method adopted in Zhu et al. (2009), i.e., firstly, the relative detection efficiency curve in the lower energy region was obtained from the ratio of the experimental and

theoretical bremsstrahlung spectra of 19 keV electron beams bombarding a high pure thick carbon (  1 mm thick), and then the absolute values of detection efficiency were determined by normalizing relative detection efficiency curve to the absolute efficiency values which were measured by using standard radioactive sources in the higher energy region. The theoretical bremsstrahlung spectrum was calculated by using the Monte Carlo PENELOPE code (Salvat et al., 2008). The standard X-ray point sources, i.e., 55Fe, 57Co, 137Cs, 241Am, were supplied by PhysikalischTechnische Bundesanstalt (PTB), Germany and the accuracies of activities were  1–3% (k¼ 2). The X-ray full-energy peaks for 3.30, 11.89, 13.90, 17.81, 20.82 and 26.34 keV of 241Am, 4.70, 32.10, 36.50 and 37.35 keV of 137Cs, 6.40, 7.06 and 14.41 keV of 57Co, 5.9 and 6.49 keV of 55Fe were used for the detection efficiency determination. The half-lives, X-ray energies and emission probabilities of 55 Fe, 57Co, 137Cs and 241Am sources were taken from the values recommended by the International Atomic Energy Agency (IAEA) (Bé et al., 2005), and for the 3.3 keV X-ray of 241Am source the emission probability was taken from the paper of Gallagher and Cipolla (1974). In Fig. 2 the absolute values of detection efficiency determined by using the standard radioactive sources and the normalized relative detection efficiency curve were shown. The two peaks appeared in the normalized relative detection efficiency curve originated from the K-shell X-rays of carbon target and Si and Al materials in the SDD detector. The detection efficiency for the SDD detector can be calculated with a simple model (Uzonyi et al., 2003; Zhao et al., 2015) as follows:

ϵ(E ) = cT (E ) Tcol (E ) A (E ),

(1)

where T(E) represents the transmittance of the successive absorbing layers of X-ray detector, Tcol(E) denotes the transmittance of detector's collimator, and A(E) describes the absorption of X-rays in the detector sensitive volume, c is a normalization constant. These transmittance and absorption factors are expressed as follows:

(

)

T (E ) = exp −μSi3N4 xSi3N4 − μAl xAl ,

(2)

⎡ ⎤ 1−η Tcol (E ) = η ⎢ 1 + exp ( − μgird xgrid ) ⎥, ⎣ ⎦ η

(3)

A (E ) = 1 − exp ( −τ Si x det ector ),

(4)

J.L. Zhao et al. / Radiation Physics and Chemistry 122 (2016) 66–72

Fig. 2. The detection efficiency of the SDD X-ray detector with an ultra-thin C2 window. The absolute efficiency values obtained with 55Fe, 57Co, 137Cs and 241Am standard sources, the normalized relative efficiency curve and the calculated efficiency curve are shown.

where μ's are the total mass attenuation coefficients of X-rays in Si3N4 foil, Al foil and Si grid supporter, x's are the mass thickness of Si3N4 foil, Al foil, Si grid supporter and Si sensitive layer, respectively. τSi is the photoelectric absorption mass attenuation coefficient of X-rays in Si. η denotes the ratio of the area not covered by the grid supporter to the total Si3N4 window area. The total and photoelectric absorption mass attenuation coefficients were taken from the database of the PENELOPE code and the thickness of the Si3N4 foil, the Al foil, the Si grid supporter, Si sensitive layer and the ratio η were provided by the manufacturer, which were given in the last section. Based on Eq. (1), the calculated efficiency curve, also shown in Fig. 2, was in very good agreement with the experimental efficiency values. The errors for the efficiency calibration with this method, which stemmed mainly from the use of the standard X-ray sources, can be estimated based on the activity errors, the emission probability errors, the thickness errors of polyethylene/polyester cover films of the standard X-ray sources and the statistical errors of the peak areas. The errors for the efficiency calibration were estimated to be about 9.5% in the lower energy region (  1–5 keV), and 4.7% in the higher energy region (4 5 keV).

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Faraday cup. For speeding up the MC simulations, in general, the half angle of the X-ray detector subtended to the target center was assumed to be 30°, and our calculations showed that the simulation results for the half angles of 30° and 5° were almost identical; but for the bremsstrahlung spectrum calculation of thick carbon target, the half angle was assumed to be 5°. In addition, the geometrical configuration for the Monte Carlo simulations which is the same as the experimental setup was used to calculate the escape rates from the deep Faraday cup, and a two-layer geometry file for a thin film target with a thick substrate was used to calculate the K correction factors and our simulation calculations also showed that the results for the K correction factors were almost identical with or without the deep Faraday cup. Because the negative 100 V bias voltage was already set in front of the top hole and side hole of the deep Faraday cup to suppress the escape of electrons with the energies less than 100 eV, the electron escape rates were estimated by the PENELOPE Monte Carlo calculations only for the electrons with the energies larger than 100 eV. The electron escape rates were about 2.2–2.8% for the thin Ag and Sb targets with the thick Al substrates placed in the deep Faraday cup in the electron impact energies of interest here. The number of incident electrons, Ne, in Eq. (5) was corrected by the electron escape rates.

3. Data processing 3.1. K correction factor Fig. 3 showed the experimental X-ray spectrum for the thin Ag film with the thick Al substrate by 10 keV electron bombard and a bremsstrahlung background which was calculated based on the PENELOPE code and was subtracted when the L-shell X-ray net peak area was calculated. The total L-shell X-ray production crosssections s(Ee) were given from the measured total L-shell X-ray counts N(Ee) by the following formula (Wu et al., 2004):

σ (Ee ) =

4πA ⎡⎣ 1 − K (Ee ) ⎤⎦ cos θ NA tNe ϵ(Eph ) Ω

N (Ee ),

(5)

where A is the atomic weigh, Ee is the incident electron energy, θ is the angle between the incident electron beams and the normal of the target surface, NA is the Avogadro constant, Ne is the number of incident electron, Eph is the produced photon energy, ε(Eph) is the intrinsic efficiency, Ω is the solid angle subtended by the beam

2.3. Monte Carlo simulations The PENELOPE code performs Monte Carlo simulation of coupled electron–photon transport in arbitrary materials for a wide energy range, from 50 eV up to 1 GeV (Salvat et al., 2008). The simulation algorithm is based on a scattering model that combines numerical databases with analytical cross-section models for the interactions of the electrons and photos with matter. The subroutine package PENGEOM can be used to flexibly handle arbitrary quadric geometries (Salvat et al., 2008). The scaled cross-section tables of Seltzer and Berger, (1985, 1986) and the corresponding analytical angular distribution (Acosta et al., 2002) determined by fitting the benchmark partial-wave shape functions of Kissel et al. (1983) are used to simulate the bremsstrahlung radiation emission; the electron-impact inner-shell ionization cross-sections calculated from the DWBA (Segui et al., 2003; Bote and Salvat, 2008) are used to simulate characteristic X-ray photon emission. In this paper, the Monte Carlo code PENELOPE was employed to calculate the bremsstrahlung spectrum of thick carbon target, the K correction factors and the electron escape rates from the deep

Fig. 3. A typical experimental X-ray spectrum for the thin Ag film with the thick Al substrate by 10 keV electron impact and a bremsstrahlung background calculated based on the PENELOPE code.

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spot to the detector effective area and t is the mass thickness value of the target film, K(Ee) is the so-called K correction factor which was used to correct the combined effect of multiple scattering of electrons penetrating the targets films, electrons reflected from the thick aluminum substrates and bremsstrahlung photons produced when incident electrons impact the targets. As we know, when the incident electrons penetrate the target films, the multiple scattering would make the electron mean path longer than the target thickness, consequently more X-rays could be excited along the path. Moreover, the electrons reflected from the thick aluminum substrates and bremsstrahlung photons produced by incident electrons impacting on the targets would also excite more X-rays. These effects would result in a systematic overestimation of the X-ray production cross-sections. Corrections could be made for these effects by the K correction factor in Eq. (5) which is defined as the ratio of the additional characteristic X-ray counts induced by these effects to the total characteristic X-ray counts. The K correction factors could be obtained through the Monte Carlo calculations with the PENELOPE code. Firstly, a twolayer geometry file for the thin film target with a thick substrate is prepared for the subroutine package PENGEOM, and then the characteristic X-ray counts NL,MC could be obtained through the PENELOPE Monte Carlo simulations, and the total uncorrected L-shell X-ray production cross-sections by electron impact could be calculated by the following equation:

σ MC

4πA cos θ = NL,MC, Ne NA tΩ

(6)

where A, Ne, NA, t, θ and Ω are defined as in Eq. (5). Meanwhile, the total L-shell X-ray production cross-sections could be expressed as follows:

σ L,th = ω3 ⎡⎣ σ L3 + σ L2 f23 + σ L1 ( f13 + f12 f23 + f ′13 ) ⎤⎦ + ω2 ( σ L1 f12 + σ L2 ) + ω1σ L1,

(7)

where ωLi is the fluorescence yields for the Li shell, fij is the Coster– Kronig coefficients, f13′ is the radiative transition Coster–Kronig coefficient between the L1 and L3 subshells and σ Li is the ionization cross-section of the Li subshell. All data of ωLi , fij, f13′ and σ Li are taken from the database of the PENELOPE code. The data of ωLi , fij, f13′ for Ag and Sb elements are listed in Table 1. Finally, the K correction factors are calculated by the following equation:

K=

σ MC − σ L,th , σ MC

(8)

By this method, the K correction factors of Ag and Sb elements have been obtained and shown in Fig. 4. The diffusion of Ag atoms into the Al substrate is taken into account in the calculations of the K correction factors of Ag element. The curves of K correction factors for Ag and Sb elements shown in Fig. 4 are used for the eye-guide.

Fig. 4. K correction factors of Ag and Sb L-shell X-ray productions cross-sections verse incident electron energies. The curves were used for the eye-guide. Table 2 Ag and Sb L-shell X-ray production cross-sections by electron impact measured in this paper. Ee (keV)

X-ray production cross-sections (barn) Ag L Sb L

6 7 8 9 10 11 12 13 14 16 18 20 22 24 26 28

5577 67

3757 45 5007 60 5477 66 6107 73 6357 76 6427 77 6497 78 629 7 75 6407 77 625 7 75 608 7 73 589 7 71 582 7 70 5737 69 556 7 67 5487 66

6797 81 7117 85 7087 85 6837 82 6657 80 6477 78 6277 75 592 771 573 769 563 768 5377 64

3.2. Results and discussion The Ag and Sb L-shell X-ray production cross-sections by electron impact in the energy range of 6–28 keV measured in this paper are summarized in Table 2. The errors of the experimental data are mainly from the peak counts (  1.3% for Ag, 2.0% for Sb), the detection efficiency (  9.5%), the (1  K) factor (  2.8% for Ag,  5.0% for Sb) and the target thickness (  6.0% for Ag,  5.8% for Sb) which consists of the counting statistics of RBS spectra (  3%), the homogeneity of targets (  1.2% for Ag, negligible for Sb) and

Table 1 The data of ωLi , fij, f13′ for Ag and Sb elements taken from the database of the PENELOPE code (Salvat et al., 2008) and the errors of ωLi and fij for Ag and Sb elements estimated from Campbell (2003). Elements

Ag Errors Sb Errors

Fluorescence yields

Coster–Kronig transition coefficients

ωL1

ωL2

ωL 3

f12

f13

f23

f13′

0.0149 7 31% 0.0378 7 25%

0.0547 7 6% 0.0737 7 6%

0.0570 78% 0.0757 79%

0.0921 7 35% 0.1969 7 35%

0.6644 7 30% 0.3221 7 30%

0.1604 7 25% 0.1718 7 25%

1.4367  10  4 2.9392  10  4

J.L. Zhao et al. / Radiation Physics and Chemistry 122 (2016) 66–72

Fig. 5. The comparison of the present experimental data of Ag L shell X-ray production cross-sections by electron impact with the experimental data of Wu et al. (2004), Sepúlveda et al. (2014), Zhao et al. (2015) and the DWBA (Segui et al., 2003) and PWBA-C-Ex (Hippler, 1990; Khare and Wadehra, 1996; An et al., 2001) theoretical data. The error band for the DWBA theoretical results due to the errors of the atomic relaxation parameters was also shown by the gray shaded area.

the stopping powers (  5%) used in the RBS spectrum fittings with the SIMNRA code. The total errors by quadratic addition are estimated to be about 12% for the L-shell X-ray production crosssections of Ag and Sb elements. The incident energies of electron beams were checked by the endpoints of experimental bremsstrahlung spectra, it was found that the incident energies of electron beams determined by the endpoints of experimental bremsstrahlung spectra were about 0.2 keV lower than the digital voltage readings given by the SEM in the energy region higher than 20 keV, and in the lower energy region ( 6–18 keV), they were in good agreement. In Figs. 5 and 6, the experimental data measured in this paper for Ag and Sb elements are compared with those of the DWBA (Segui et al., 2003) and PWBA-C-Ex (Hippler, 1990; Khare and Wadehra, 1996; An et al., 2001) theoretical results and available experimental data in the literature (Wu et al., 2004; Sepúlveda et al., 2014). From the review paper of Campbell (2003), the errors of fluorescence yields and Coster–Kronig coefficients for Ag and Sb

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elements could be conservatively estimated and also listed in Table 1, and therefore, based on Eq. (7) and the standard rules of error propagation, the errors for the DWBA Ag and Sb L shell X-ray production cross-sections could also be estimated and are shown as error bands in Figs. 5 and 6. It is clearly shown that the experimental data for Ag and Sb elements in the present work are in very good agreement with the theoretical predictions of DWBA and PWBA-C-Ex theories within the errors. In Fig. 5, it is also observed that the present experimental data for Ag element are in reasonable agreement with the data of Zhao et al. (2015) within the experimental errors. The experimental data of Wu et al. (2004) are about 20% lower than the theoretical results and our present data, the possible reason, i.e., the error of target thickness determination, has been discussed in Zhao et al. (2015). Recently, Sepúlveda et al. (2014) also measured the total L-shell X-ray production cross-sections in the electron-impact energy range of 6– 25 keV by using the thin Ag film target with the thick carbon substrate, their experimental data are about 30% higher than the theoretical values and our present data. The tentative explanation for this discrepancy may be due to several reasons. First, the detection efficiency calibration in the present work has been performed by using the standard radioactive sources in combination with the bremsstrahlung spectrum of thick carbon sample and the model calculations, this allows us to obtain reliable detection efficiencies; second, by the method presented here with the PENELOPE Monte Carlo simulations, the corrections for the electron multiple scattering, backscattered electrons and bremsstrahlung photons have been fully accounted for in this work; moreover, a larger incident electron beam spot, i.e., about 2  2 mm2, was used in this work to decrease possible inaccuracy induced by the target inhomogeneity, as compared with a very small beam spot like that used in Sepúlveda et al. (2014).

4. Conclusions In this paper, the experimental setup has been redesigned in some aspects in order to improve the accuracy of experimental data, and the total L-shell X-ray production cross-sections of Ag and Sb elements by electron impact in the energy region of 6– 28 keV have been measured. The corrections for the electron multiple scattering, backscattered electrons and bremsstrahlung photons have been made for the experimental data based on the PENELOPE Monte Carlo simulations. The experimental data measured in this paper are in good agreement with the DWBA and PWBA-C-Ex theoretical results. As for Ag element, the present data are also compared with the experimental data available in the literature and the possible reasons for the discrepancies between the different datasets have been discussed. Based on the agreement between our present experimental data with the theories, it should be concluded that the theories developed recently for the inner-shell ionizations, in conjunction with the reliable atomic relaxation parameters, can predict reliable X-ray production crosssections in the energy region of interest here, at least for the element studied here.

Acknowledgment This work was financially supported by National Natural Science Foundation of China (Grant nos. 10674097 and 11175123). Fig. 6. The comparison of the present experimental data of Sb L shell X-ray production cross-sections by electron impact with the DWBA (Segui et al., 2003) and PWBA-C-Ex (Hippler, 1990; Khare and Wadehra, 1996; An et al., 2001) theoretical data. The error band for the DWBA theoretical results due to the errors of the atomic relaxation parameters was also shown by the gray shaded area.

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