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Nuclear Instruments and Methods in Physics Research B 381 (2016) 34–38
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
K-, L- and M-shell X-ray productions induced by oxygen ions in the 0.8–1.6 MeV/amu range I. Gorlachev a,⇑, N. Gluchshenko a, I. Ivanov a,b, A. Kireyev a, S. Kozin a,b, A. Kurakhmedov a,b, A. Platov a, M. Zdorovets a,c a b c
Institute of Nuclear Physics, 050032 Ibragimov 1, Almaty, Kazakhstan L.N. Gumilyov Eurasian National University, Mirzoyan 2, Astana, Kazakhstan Ural Federal University, Yekaterinburg 620002, Russia
a r t i c l e
i n f o
Article history: Received 19 April 2016 Received in revised form 19 May 2016 Accepted 19 May 2016 Available online 30 May 2016 Keywords: X-ray production cross section Argon ions ECPSSR theory
a b s t r a c t The X-ray production cross sections induced by oxygen ions with projectile energies from 12.8 to 25.6 MeV for the elements from Al to Bi were measured. The applied approach is based on calculation of X-ray production cross sections through the cross section of Rutherford backscattering, which can be calculated with high accuracy using the Rutherford formula. The experimental results are compared to the predictions of ECPSSR and PWBA theories calculated with the ISICS code. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Particle induced X-ray emission (PIXE) is a powerful nondestructive elemental analysis technique currently used routinely for determination of major, minor and trace constituents of metallurgical, biological, environmental and other samples [1–4]. The PIXE technique provides simultaneous analysis of 72 elements from sodium to uranium on the periodic table in various samples. The PIXE technique offers the advantage of analysis without the necessity for sample preparation, thereby minimizing the potential errors resulting from sample preparation. As a rule, proton and helium beams with the energies in the range of 1–3 MeV are used for analysis with the PIXE technique. It can be explained by widespread application of light ion accelerators in the world and simplicity of the X-ray spectra obtained using the advanced software. Recently, however, the research groups working on the accelerated beams of charged particles show a growing interest for heavy ions application (HIPIXE technique). In this case, a greater production of characteristic X-rays per incident ion can provide the improving PIXE sensitivity [5–8]. As shown in [5], the analysis of heavy water samples from the nuclear power plant with 50 MeV 16O can provide the detection limit less than 0.01 ppb (part per billion) for the chemical elements
⇑ Corresponding author. E-mail address: [email protected] (I. Gorlachev). http://dx.doi.org/10.1016/j.nimb.2016.05.020 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
from Cr to Zn. Such sensitivity is not available not only for the proton induced X-ray emission technique, but for ICP MS technique that is normally used for water analysis. The main features of HIPIXE technique, restraining its application for analytical goals, are the limited X-ray production cross sections database and the complexity of X-ray spectra processing. In recent years, several research groups have obtained the experimental data on X-ray productions in the interaction of heavy ions with target atoms [9–12]. However, these works are sporadic yet. The complexity of HIPIXE spectra processing is explained by shifting and broadening of X-ray lines as the result of multiple ionization effect of the target atoms. Therefore, for analytical goals it is advisable to use the relatively light ions like C, N, O, for which this effect is not so much significant. The aim of this work is updating of the database for oxygen induced X-ray production cross sections. The K-shell X-ray production cross sections of thirteen thin films Al, Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, L-shell X-ray productions of the targets Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, Ta, W, Pb, Bi and M-shell X-ray productions of the targets Ta, W, Pb and Bi induced by 16O with incident energies ranging from 12.8 to 25.6 MeV with the step of 3.2 MeV were obtained. The X-ray productions were calculated through the Rutherford backscattering cross sections which can be calculated from the Rutherford formula with high accuracy. This approach eliminates the uncertainties associated with target thickness and charge collection. The obtained experimental data were compared with the theoretical values calculated within the framework of
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Plane Wave Born Approximation (PWBA) and its improved model – ECPSSR theory. The theoretical values were obtained by us using the ISICS code [13].
1.0E+06
X-ray production cross-section (b)
1.0E+05
1.0E+04
2. Results and discussion 1.0E+03
1.0E+02
1.0E+01 5 4
1.0E+00
3 2 1
1.0E-01 10
15
20
25
30
35
40
45
50
55
Target atomic number
Fig. 1. Energy variations of 16O induced Ktot X-ray production cross sections (1–12.8 MeV, 2–16.0 MeV, 3–19.2 MeV, 4–22.4 MeV, 5–25.6 MeV).
Reference [14], where inner-shell X-ray production by argon ions was reported, provides a detailed description of the experimental set up. Using the efficiency curve as shown in Fig. 1 therein, X-ray production cross sections extracted and the data uncertainties are calculated as given by Eqs. (1)–(4) in [14] Tables 1 (K-line), 2 (L-line) and 3 (M-line) include both individual and total X-ray cross sections of the Ktot, Ltot and Mtot series respectively, being the sum of the individual lines for 12.8 MeV, 16.0 MeV 16O2+ and 19.2 MeV, 22.4 MeV and 25.6 MeV 16O3+. In some cases, only the group of lines can be identified since the energy separation between some X-ray lines of one element is
Table 1 The measured and theoretical calculated K-shell X-ray production cross sections (in barns). Target
E (MeV)
Ktot
Ktot ECPSSR
Ktot PWBA
Al
12.8 16.0 19.2 22.4 25.6
8360 ± 1350 15,600 ± 3000 30,300 ± 5800 61,000 ± 12,000 189,000 ± 41,000
27,000 44,500 60,500 73,800 84,300
34,100 42,800 49,900 55,700 60,300
Ti
12.8 16.0 19.2 22.4 25.6
133 ± 14 375 ± 40 744 ± 80 1930 ± 250 4030 ± 690
18.0 ± 1.9 57.5 ± 6.2 122 ± 13 285 ± 36 660 ± 110
151 ± 14 432 ± 41 866 ± 81 2220 ± 170 4690 ± 700
300 793 1650 2900 4520
2640 4270 6100 8050 10,000
Cr
12.8 16.0 19.2 22.4 25.6
72.2 ± 7.8 197 ± 22 362 ± 39 940 ± 120 2190 ± 260
11.2 ± 1.2 32.4 ± 3.5 61.7 ± 6.7 169 ± 21 398 ± 47
83.4 ± 7.9 230 ± 22 424 ± 40 1110 ± 120 2580 ± 260
138 369 787 1430 2310
1490 2510 3720 5050 6470
Cu
12.8 16.0 19.2 22.4 25.6
18.3 ± 2.0 40.9 ± 4.4 71.0 ± 7.6 173 ± 19 368 ± 41
2.82 ± 0.32 6.64 ± 0.72 21.0 ± 1.3 30.9 ± 3.4 66.4 ± 7.5
21.1 ± 2.0 47.6 ± 4.4 82.9 ± 7.7 204 ± 19 435 ± 42
26.3 69.2 149 280 474
355 654 1040 1510 2040
Zn
12.8 16.0 19.2 22.4 25.6
13.4 ± 1.5 30.5 ± 3.3 54.0 ± 5.8 130 ± 15 250 ± 28
2.14 ± 0.27 4.99 ± 0.54 9.35 ± 1.02 22.1 ± 2.5 44.9 ± 5.0
15.6 ± 1.5 35.5 ± 3.3 63.4 ± 5.9 152 ± 15 295 ± 28
19.6 51.2 110 207 351
267 498 804 1180 1610
Zr
12.8 16.0 19.2 22.4 25.6 12.8 16.0 19.2 22.4 25.6
1.51 ± 0.16 3.55 ± 0.38 5.81 ± 0.63 12.0 ± 1.3 21.0 ± 2.3 1.19 ± 0.13 2.60 ± 0.28 4.28 ± 0.46 8.98 ± 0.97 14.6 ± 1.6
0.295 ± 0.035 0.610 ± 0.082 1.22 ± 0.15 2.34 ± 0.29 2.83 ± 0.50 0.207 ± 0.025 0.489 ± 0.062 0.89 ± 0.11 1.73 ± 0.23 3.05 ± 0.39
1.80 ± 0.17 4.16 ± 0.39 7.03 ± 0.65 14.3 ± 1.3 24.8 ± 2.4 1.40 ± 0.13 3.09 ± 0.29 5.17 ± 0.48 10.7 ± 1.0 17.7 ± 1.7
1.49 3.72 7.75 14.3 24.1 1.19 2.96 6.16 11.3 19.1
15.7 32.7 58.1 92.7 137 12.0 25.1 45.0 72.2 107
Mo
12.8 16.0 19.2 22.4 25.6
0.964 ± 0.104 2.04 ± 0.22 3.34 ± 0.36 7.49 ± 0.81 12.6 ± 1.4
0.195 ± 0.022 0.423 ± 0.051 0.687 ± 0.084 1.48 ± 0.19 2.39 ± 0.33
1.16 ± 0.11 2.46 ± 0.23 4.03 ± 0.37 8.97 ± 0.81 15.0 ± 1.4
0.96 2.39 4.95 9.08 15.3
9.22 19.5 35.0 56.6 84.7
Ag
12.8 16.0 19.2 22.4 25.6
0.278 ± 0.030 0.685 ± 0.076 1.13 ± 0.12 2.65 ± 0.29 3.52 ± 0.38
0.054 ± 0.008 0.176 ± 0.024 0.290 ± 0.043 0.497 ± 0.076 1.60 ± 0.19
0.332 ± 0.031 0.861 ± 0.079 1.42 ± 0.13 3.15 ± 0.30 5.12 ± 0.42
0.330 0.866 1.77 3.22 5.36
2.43 5.54 10.3 17.0 26.1
Cd
12.8 16.0
0.241 ± 0.028 0.548 ± 0.061
0.033 ± 0.012 0.117 ± 0.019
0.274 ± 0.031 0.665 ± 0.064
0.293 0.719
1.99 4.35
Nb
Ka
Kb
(continued on next page)
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Table 1 (continued) Target
E (MeV)
Ka
Kb
Ktot
Ktot ECPSSR
Ktot PWBA
19.2 22.4 25.6
0.97 ± 0.11 2.10 ± 0.23 3.67 ± 0.45
0.274 ± 0.038 0.434 ± 0.066 0.67 ± 0.18
1.25 ± 0.12 2.53 ± 0.24 4.35 ± 0.48
1.47 2.66 4.42
8.09 13.5 20.8
In
12.8 16.0 19.2 22.4 25.6
0.197 ± 0.024 0.469 ± 0.052 0.799 ± 0.091 1.73 ± 0.19 2.96 ± 0.33
0.035 ± 0.010 0.091 ± 0.017 0.141 ± 0.033 0.315 ± 0.064 0.65 ± 0.14
0.232 ± 0.026 0.560 ± 0.055 0.940 ± 0.096 2.05 ± 0.20 3.61 ± 0.36
0.244 0.598 1.22 2.20 3.65
1.55 3.42 6.38 10.7 16.5
Sn
12.8 16.0 19.2 22.4 25.6
0.148 ± 0.021 0.443 ± 0.049 0.685 ± 0.080 1.54 ± 0.16 2.40 ± 0.28
0.027 ± 0.011 0.063 ± 0.010 0.098 ± 0.017 0.286 ± 0.065 0.534 ± 0.076
0.175 ± 0.023 0.506 ± 0.050 0.784 ± 0.082 1.83 ± 0.18 2.94 ± 0.29
0.204 0.500 1.02 1.83 3.04
1.22 2.69 5.05 8.49 13.2
Sb
12.8 16.0 19.2 22.4 25.6
0.102 ± 0.011 0.260 ± 0.028 0.443 ± 0.048 1.04 ± 0.11 1.90 ± 0.23
0.019 ± 0.006 0.049 ± 0.008 0.083 ± 0.012 0.197 ± 0.047 0.43 ± 0.14
0.121 ± 0.012 0.308 ± 0.029 0.526 ± 0.049 1.24 ± 0.12 2.33 ± 0.27
0.172 0.419 0.852 1.53 2.53
0.958 2.12 4.00 6.75 10.5
Table 2 The measured and theoretical calculated L-shell X-ray production cross sections (in barns). Target
E (MeV)
Ltot
Ltot ECPSSR
Ltot PWBA
Zn
12.8 16.0 19.2 22.4 25.6
La + Ll
Lb
Lc
57,000 ± 9000 69,000 ± 11,000 75,000 ± 12,000 112,000 ± 19,000 123,000 ± 21,000
84,900 118,000 144,000 165,000 180,000
123,000 143,000 157,000 168,000 175,000
Zr
12.8 16.0 19.2 22.4 25.6
19,900 ± 3300 33,100 ± 5300 38,700 ± 6100 60,000 ± 10,000 76,000 ± 12,000
9800 17,500 26,400 35,800 45,100
30,400 41,200 51,200 60,100 67,900
Nb
12.8 16.0 19.2 22.4 25.6
15,200 ± 2400 24,300 ± 3800 34,400 ± 5500 52,400 ± 8400 57,500 ± 9000
8130 14,700 22,600 31,000 39,500
26,600 36,600 45,900 54,400 61,900
Mo
12.8 16.0 19.2 22.4 25.6
13,800 ± 2200 18,800 ± 2900 26,600 ± 4200 50,000 ± 8100 57,100 ± 9000
6780 12,400 19,300 26,800 34,600
23,300 32,400 41,200 49,200 56,400
Ag
12.8 16.0 19.2 22.4 25.6
4980 ± 790 9300 ± 1500 14,500 ± 2300 22,400 ± 3600 27,300 ± 4300
2630 5250 8580 12,600 17,000
11,300 17,000 22,600 28,200 33,600
Cd
12.8 16.0 19.2 22.4 25.6
4050 ± 650 7200 ± 1100 12,000 ± 1900 19,600 ± 3200 25,800 ± 4500
2330 4490 7400 10,900 14,900
10,100 15,000 20,200 25,400 30,500
In
12.8 16.0 19.2 22.4 25.6
2900 ± 520 6500 ± 1000 9700 ± 1500 17,200 ± 2700 23,800 ± 3800
1970 3830 6350 9450 13,000
8800 13,200 18,000 22,800 27,600
Sn
12.8 16.0 19.2 22.4 25.6
2360 ± 380 5750 ± 900 8400 ± 1300 12,300 ± 2000 15,000 ± 2400
1670 3250 5420 8120 11,300
7610 11,600 15,900 20,300 24,700
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I. Gorlachev et al. / Nuclear Instruments and Methods in Physics Research B 381 (2016) 34–38 Table 2 (continued) E (MeV)
Sb
12.8 16.0 19.2 22.4 25.6
La + Ll
Lb
Lc
Ltot
Ltot ECPSSR
Ltot PWBA
1950 ± 300 3680 ± 570 5530 ± 860 10,000 ± 1600 11,000 ± 1800
1420 2790 4680 7050 9820
6650 10,200 14,100 18,100 22,200
Ta
12.8 16.0 19.2 22.4 25.6
92.8 ± 9.9 154 ± 16 214 ± 23 447 ± 48 700 ± 76
56.9 ± 6.2 93.0 ± 9.9 128 ± 14 252 ± 27 391 ± 43
8.8 ± 1.0 12.7 ± 1.4 15.5 ± 1.7 35.0 ± 3.9 52.6 ± 6.1
159 ± 12 259 ± 19 357 ± 27 734 ± 55 1140 ± 90
98.8 204 359 568 835
497 859 1310 1850 2470
W
12.8 16.0 19.2 22.4 25.6
82.2 ± 8.8 145 ± 15 216 ± 23 385 ± 41 631 ± 67
51.5 ± 5.5 86.2 ± 9.2 124 ± 13 214 ± 23 343 ± 37
6.6 ± 0.8 11.7 ± 1.3 15.5 ± 1.7 28.8 ± 3.3 47.3 ± 5.1
140 ± 11 243 ± 18 356 ± 27 628 ± 41 1020 ± 68
89.4 185 326 516 760
446 775 1190 1680 2250
Pb
12.8 16.0 19.2 22.4 25.6
34.7 ± 3.7 62.6 ± 6.7 95 ± 10 170 ± 18 266 ± 29
24.0 ± 2.6 42.4 ± 4.5 61.2 ± 6.5 105 ± 11 160 ± 17
3.9 ± 0.5 7.41 ± 0.83 9.4 ± 1.0 16.9 ± 1.9 26.5 ± 3.1
62.8 ± 4.6 113 ± 8 166 ± 12 294 ± 22 453 ± 34
40.5 85.9 154 246 366
183 336 535 776 1060
Bi
12.8 16.0 19.2 22.4 25.6
32.1 ± 3.5 59.5 ± 6.4 94 ± 10 157 ± 17 243 ± 26
22.5 ± 2.4 38.5 ± 4.1 58.8 ± 6.3 96 ± 10 144 ± 16
3.9 ± 0.5 5.79 ± 0.66 8.56 ± 0.98 14.0 ± 1.7 21.9 ± 26
58.6 ± 4.3 104 ± 8 162 ± 12 268 ± 17 409 ± 31
36.6 77.9 140 224 333
163 301 482 702 960
Table 3 The measured and theoretical calculated M-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Mtot
Mtot ECPSSR
Mtot PWBA
Ta
12.8 16.0 19.2 22.4 25.6
40,300 ± 6400 51,300 ± 8000 50,100 ± 7800 90,000 ± 14,000 85,000 ± 14,000
24,700 34,100 43,800 53,500 62,700
72,600 94,300 114,000 132,000 148,000
12.8 16.0 19.2 22.4 25.6
37,600 ± 5900 50,000 ± 7800 51,800 ± 8100 77,000 ± 12,000 73,000 ± 12,000
22,700 31,400 40,500 49,600 58,400
66,700 87,100 106,000 123,000 139,000
12.8 16.0 19.2 22.4 25.6
23,000 ± 3600 34,100 ± 5300 39,200 ± 6100 55,200 ± 8700 63,000 ± 10,000
11,600 16,600 21,800 27,200 32,800
34,400 46,400 58,400 70,100 81,300
12.8 16.0 19.2 22.4 25.6
20,500 ± 3200 32,200 ± 5000 37,200 ± 5800 51,600 ± 8100 70,000 ± 11,000
10,700 15,300 20,100 25,200 30,400
31,400 42,400 53,500 64,500 75,000
W
Pb
Bi
smaller than the resolution of the X-ray detector. Therefore, only the total cross sections are presented in tables for Al K-line, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn and Sb L-lines and for all M-lines. The theoretical data presented in Tables 1–3 were calculated from the single vacancy fluorescence yield and cross section ionization in the frame of the ECPSSR and PWBA approaches using the ISICS code [13]. Figs. 1 and 2 graphically show the measured Ktot and Ltot X-ray productions as a function of target atomic number for the different energies of 16O ions. Such dependence is not given for Mtot productions due to small number of experimental points. As an illustration of the relation between the theory and experiment the measured cross sections for the 22.4 MeV oxygen beam are presented in Fig. 3 together with the theoretically calculated ones
1.0E+06
X-ray production cross-srection (b)
Target
1.0E+05
1.0E+04
1.0E+03 5 4 3 2 1
1.0E+02
1.0E+01 20
30
40
50
60
70
80
90
Target atomic number
Fig. 2. Energy variations of 16O induced Ltot X-ray production cross sections (1–12.8 MeV, 2–16.0 MeV, 3–19.2 MeV, 4–22.4 MeV, 5–25.6 MeV).
within ECPSSR and PWBA approaches. The similar trends are observed for other ion energies. In the scientific literature there are scanty experimental data on the X-ray productions induced by oxygen ions. As a rule, researchers limited to the several targets and narrow energy range of the projectiles. For example, J.S. Braich et al. [15] measured the M Xray production cross sections only for gold target, E.C. Montenegro et al. [16] limited to measuring the K X-ray productions for titanium and iron targets, H.R. Verma [17] researched the L X-ray production cross sections in 83Bi, W. Hink [18] published the experimental carbon K-shell excitation cross sections as a function of incident ion energy per mass unit for oxygen ions, in reference [11] presented by J. Reyes-Herrera and J. Miranda the target elements were selected lanthanoids (Ce, Gd, Dy, Ho and Er). In some cases, such as in [19], the measured cross sections are presented graphically in the logarithmic scale that complicates a comparison with the data presented in this article. Therefore, we are able to compare the experimental cross sections only with the theoretically calculated values. Tables 1–3 show that the ECPSSR data are in better agreement with the experiment than the cross sections obtained in the frame-
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1.0E+04
waves (ECPSSR, PWBA) cannot always correctly describe the interactions of accelerated ions with target atoms. The same reasons can cause the large discrepancies between the experimental and theoretical data for ionization of L- and Mshells (Tables 2 and 3).
1.0E+03
3. Conclusions
1.0E+06
Ktot
Mtot
Ltot
X-ray production cross section (b)
1.0E+05
1.0E+02
1.0E+01
1.0E+00 10
20
30
40
50
60
70
80
90
1.0E-01 Target atomic number
Fig. 3. Comparison between measured Ktot, Ltot and Mtot X-ray production cross sections (red squares) and calculated within the framework of ECPSSR (blue rhombuses) and PWBA (green triangles) theoretical models for 22.4 MeV 16O3+. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
work of PWBA approximation. It can be explained that the ECPSSR approach, unlike the PWBA theory, takes into account the effects such as ion energy loss during the collision, the Coulomb deflection of ion trajectory, modification of the atomic electron energy and adjustment in the electron mass due to relativistic effects. As follows from Table 1 in the case of K-shell ionization of the target atoms the best agreement between experimental and theoretical data, calculated under the ECPSSR theory, is attained for the elements with atomic numbers in the range of 40 < Z < 50. Typically, the deviations are not exceeding 20–25% and they are within the limits of experimental errors. The large uncertainties for Sb can be explained by scanty statistics of the X-ray peaks. For the elements with low Z (30 < Z) there are large discrepancies observed between the experimental and theoretical data that are not within the limits of the experimental error. The differences increase is accompanied with decreasing of atomic number reaching the value over 100% for Al. The large deviations observed in this case between experimental values and theoretical predictions can be explained by the existence of domain applicability for various theoretical models [20]. The colliding systems can be classified in accordance with the parameters: Z1/Z2 and v1/vK, where Z1 and Z2 are atomic numbers of incident ion and target atom respectively, v1 is ion velocity and vK is electron velocity in the inner shell of the target. In our case for the K shells parameters Z1/Z2 and v1/vK are in the ranges: 0.096 < Z1/Z2 < 0.67 and 0.069 < v1/vK < 0.748. For symmetric and fast collisions, where 0.3 < Z1/Z2 and v1/ vK > 0.3, models based on the Plane Wave Born Approximation (ECPSSR, PWBA) are appropriate to describe the ion-atom interactions. However, for symmetrical and slow collisions, where Z1/ Z2 1 and v1/vK 6 1, it is necessary to take into account the mutual distortion in the atomic orbitals of the colliding partners and, as a result, the formation of a quasi-molecule (molecular orbital theory). In our experiment for elements with low Z the points are located near the region of validity of the molecular orbital model. In this case, the theories based on the Born approximation of plane
In the presented work we studied the X-ray production cross sections at the interaction of oxygen ions with target atoms in the range of atomic numbers 13 < Z < 83. The energy of the accelerated ions was varied in the range of 12.8–25.6 MeV with a step of 3.2 MeV. The obtained data were compared with the theoretical predictions of the ECPSS model calculated by us using the ISICS code. For elements with atomic numbers in the range of 40 < Z < 50 the deviations usually do not exceed 20–25% and are within the limits of the experimental error. The observed large discrepancies between the experimental and theoretical values for K-shell Xray productions of light atoms and L- and M-shell X-ray productions of all studied elements can be explained by the existence of applicability domains for various theoretical models. The large uncertainties for Sb are explained by poor statistics of the X-ray peaks. The obtained experimental data will be used at the DC-60 accelerator to develop the HIPIXE technique for the analysis of a wide range of samples. Acknowledgment The works, which results are presented in this article, are made with the financial support of the Ministry of Energy of the Republic of Kazakhstan. We also express our gratitude to F. Penkov for active and useful participation in the discussions. References [1] I. Popescu, T. Badica, A. Olariu, C. Besliu, A. Ene, Al. Ivanescu, in: Radioanal. Nucl. Chem. Lett. 213 (1996) 369. [2] C. Stihi, I.V. Popescu, G. Busuioc, T. Badica, A. Olariu, G. Dima, Radioanal. Nucl. Chem. Lett. 246 (2000) 445. [3] A. Bancuta, C. Stihi, I.V. Popescu, T. Badica, Gh.V. Cimpoca, J. Phys: Conf. Ser. 41 (2006) 502. [4] C. Stihi, A. Bancuta, I.V. Popescu, M. Virgolici, V. Cimpoca, M. Gigiu, Gh. Vlaicu, J. Phys: Conf. Ser. 41 (2006) 565. [5] M.J. Orafran et al., Nucl. Instr. Meth. B 74 (1993) 542. [6] M.J. Orafran et al., Nucl. Instr. Meth. B 99 (1995) 384. [7] S.A.E. Johansson, J.L. Campbell, PIXE: A Novel Technique for Materials Analysis, John Wiley, Chichester, 1988. [8] K.H. Ecker, H.P. Weise, K.L. Merkle, Mikrochim. Acta 133 (2000) 313. [9] M.J. Orafran, M.E. Debray, R. Eusebi, A.J. Kreiner, M.E. Vazquez, A. Burlon, P. Stolier, Nucl. Instr. Meth. B 201 (2003) 317. [10] X. Zhou et al., Phys. Scr. 87 (2013) 055301. [11] J. Reyes-Herrera, J. Miranda, Nucl. Instr. Meth. B 267 (2009) 1767. [12] R.L. Watson, Y. Peng, V. Horvat, A.N. Perumal, Phys. Rev. A 74 (2006) 062709. [13] Z. Lie, S.J. Cipolla, Comput. Phys. Commun. 97 (1996) 315. [14] N. Gluchshenko, I. Gorlachev, I. Ivanov, A. Kireyev, S. Kozin, A. Kurakhmedov, A. Platov, M. Zdorovets, Nucl. Instr. Meth. B 372 (2016) 1. [15] J.S. Braich, P. Verma, D.P. Goyal, H.R. Verma, Nucl. Instr. Meth. 119 (1996) 317. [16] E.C. Montenegro et al., J. Phys. B: At. Mol. Phys. 19 (1986) 3287. [17] H.R. Verma, Rom. J. Phys. 58 (7) (2013) 947. [18] W. Hink, Revue de Physique Appliquee 11 (1) (1976) 31. [19] A.C. Scafes, C. Ciortea, D.E. Dumitriu, A. Enulescu, D. Fluerasu, M.M. Gugiu, M.D. Pena, M. Pentia, I. Piticu, Rom. Rep. Phys. 66 (2) (2014) 455. [20] G. Lapicki, W. Lichten, Phys. Rev. 31 (3) (1985) 1354.
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
K-, L- and M-shell X-ray productions induced by oxygen ions in the 0.8–1.6 MeV/amu range I. Gorlachev a,⇑, N. Gluchshenko a, I. Ivanov a,b, A. Kireyev a, S. Kozin a,b, A. Kurakhmedov a,b, A. Platov a, M. Zdorovets a,c a b c
Institute of Nuclear Physics, 050032 Ibragimov 1, Almaty, Kazakhstan L.N. Gumilyov Eurasian National University, Mirzoyan 2, Astana, Kazakhstan Ural Federal University, Yekaterinburg 620002, Russia
a r t i c l e
i n f o
Article history: Received 19 April 2016 Received in revised form 19 May 2016 Accepted 19 May 2016 Available online 30 May 2016 Keywords: X-ray production cross section Argon ions ECPSSR theory
a b s t r a c t The X-ray production cross sections induced by oxygen ions with projectile energies from 12.8 to 25.6 MeV for the elements from Al to Bi were measured. The applied approach is based on calculation of X-ray production cross sections through the cross section of Rutherford backscattering, which can be calculated with high accuracy using the Rutherford formula. The experimental results are compared to the predictions of ECPSSR and PWBA theories calculated with the ISICS code. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Particle induced X-ray emission (PIXE) is a powerful nondestructive elemental analysis technique currently used routinely for determination of major, minor and trace constituents of metallurgical, biological, environmental and other samples [1–4]. The PIXE technique provides simultaneous analysis of 72 elements from sodium to uranium on the periodic table in various samples. The PIXE technique offers the advantage of analysis without the necessity for sample preparation, thereby minimizing the potential errors resulting from sample preparation. As a rule, proton and helium beams with the energies in the range of 1–3 MeV are used for analysis with the PIXE technique. It can be explained by widespread application of light ion accelerators in the world and simplicity of the X-ray spectra obtained using the advanced software. Recently, however, the research groups working on the accelerated beams of charged particles show a growing interest for heavy ions application (HIPIXE technique). In this case, a greater production of characteristic X-rays per incident ion can provide the improving PIXE sensitivity [5–8]. As shown in [5], the analysis of heavy water samples from the nuclear power plant with 50 MeV 16O can provide the detection limit less than 0.01 ppb (part per billion) for the chemical elements
⇑ Corresponding author. E-mail address: [email protected] (I. Gorlachev). http://dx.doi.org/10.1016/j.nimb.2016.05.020 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
from Cr to Zn. Such sensitivity is not available not only for the proton induced X-ray emission technique, but for ICP MS technique that is normally used for water analysis. The main features of HIPIXE technique, restraining its application for analytical goals, are the limited X-ray production cross sections database and the complexity of X-ray spectra processing. In recent years, several research groups have obtained the experimental data on X-ray productions in the interaction of heavy ions with target atoms [9–12]. However, these works are sporadic yet. The complexity of HIPIXE spectra processing is explained by shifting and broadening of X-ray lines as the result of multiple ionization effect of the target atoms. Therefore, for analytical goals it is advisable to use the relatively light ions like C, N, O, for which this effect is not so much significant. The aim of this work is updating of the database for oxygen induced X-ray production cross sections. The K-shell X-ray production cross sections of thirteen thin films Al, Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, L-shell X-ray productions of the targets Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, Ta, W, Pb, Bi and M-shell X-ray productions of the targets Ta, W, Pb and Bi induced by 16O with incident energies ranging from 12.8 to 25.6 MeV with the step of 3.2 MeV were obtained. The X-ray productions were calculated through the Rutherford backscattering cross sections which can be calculated from the Rutherford formula with high accuracy. This approach eliminates the uncertainties associated with target thickness and charge collection. The obtained experimental data were compared with the theoretical values calculated within the framework of
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Plane Wave Born Approximation (PWBA) and its improved model – ECPSSR theory. The theoretical values were obtained by us using the ISICS code [13].
1.0E+06
X-ray production cross-section (b)
1.0E+05
1.0E+04
2. Results and discussion 1.0E+03
1.0E+02
1.0E+01 5 4
1.0E+00
3 2 1
1.0E-01 10
15
20
25
30
35
40
45
50
55
Target atomic number
Fig. 1. Energy variations of 16O induced Ktot X-ray production cross sections (1–12.8 MeV, 2–16.0 MeV, 3–19.2 MeV, 4–22.4 MeV, 5–25.6 MeV).
Reference [14], where inner-shell X-ray production by argon ions was reported, provides a detailed description of the experimental set up. Using the efficiency curve as shown in Fig. 1 therein, X-ray production cross sections extracted and the data uncertainties are calculated as given by Eqs. (1)–(4) in [14] Tables 1 (K-line), 2 (L-line) and 3 (M-line) include both individual and total X-ray cross sections of the Ktot, Ltot and Mtot series respectively, being the sum of the individual lines for 12.8 MeV, 16.0 MeV 16O2+ and 19.2 MeV, 22.4 MeV and 25.6 MeV 16O3+. In some cases, only the group of lines can be identified since the energy separation between some X-ray lines of one element is
Table 1 The measured and theoretical calculated K-shell X-ray production cross sections (in barns). Target
E (MeV)
Ktot
Ktot ECPSSR
Ktot PWBA
Al
12.8 16.0 19.2 22.4 25.6
8360 ± 1350 15,600 ± 3000 30,300 ± 5800 61,000 ± 12,000 189,000 ± 41,000
27,000 44,500 60,500 73,800 84,300
34,100 42,800 49,900 55,700 60,300
Ti
12.8 16.0 19.2 22.4 25.6
133 ± 14 375 ± 40 744 ± 80 1930 ± 250 4030 ± 690
18.0 ± 1.9 57.5 ± 6.2 122 ± 13 285 ± 36 660 ± 110
151 ± 14 432 ± 41 866 ± 81 2220 ± 170 4690 ± 700
300 793 1650 2900 4520
2640 4270 6100 8050 10,000
Cr
12.8 16.0 19.2 22.4 25.6
72.2 ± 7.8 197 ± 22 362 ± 39 940 ± 120 2190 ± 260
11.2 ± 1.2 32.4 ± 3.5 61.7 ± 6.7 169 ± 21 398 ± 47
83.4 ± 7.9 230 ± 22 424 ± 40 1110 ± 120 2580 ± 260
138 369 787 1430 2310
1490 2510 3720 5050 6470
Cu
12.8 16.0 19.2 22.4 25.6
18.3 ± 2.0 40.9 ± 4.4 71.0 ± 7.6 173 ± 19 368 ± 41
2.82 ± 0.32 6.64 ± 0.72 21.0 ± 1.3 30.9 ± 3.4 66.4 ± 7.5
21.1 ± 2.0 47.6 ± 4.4 82.9 ± 7.7 204 ± 19 435 ± 42
26.3 69.2 149 280 474
355 654 1040 1510 2040
Zn
12.8 16.0 19.2 22.4 25.6
13.4 ± 1.5 30.5 ± 3.3 54.0 ± 5.8 130 ± 15 250 ± 28
2.14 ± 0.27 4.99 ± 0.54 9.35 ± 1.02 22.1 ± 2.5 44.9 ± 5.0
15.6 ± 1.5 35.5 ± 3.3 63.4 ± 5.9 152 ± 15 295 ± 28
19.6 51.2 110 207 351
267 498 804 1180 1610
Zr
12.8 16.0 19.2 22.4 25.6 12.8 16.0 19.2 22.4 25.6
1.51 ± 0.16 3.55 ± 0.38 5.81 ± 0.63 12.0 ± 1.3 21.0 ± 2.3 1.19 ± 0.13 2.60 ± 0.28 4.28 ± 0.46 8.98 ± 0.97 14.6 ± 1.6
0.295 ± 0.035 0.610 ± 0.082 1.22 ± 0.15 2.34 ± 0.29 2.83 ± 0.50 0.207 ± 0.025 0.489 ± 0.062 0.89 ± 0.11 1.73 ± 0.23 3.05 ± 0.39
1.80 ± 0.17 4.16 ± 0.39 7.03 ± 0.65 14.3 ± 1.3 24.8 ± 2.4 1.40 ± 0.13 3.09 ± 0.29 5.17 ± 0.48 10.7 ± 1.0 17.7 ± 1.7
1.49 3.72 7.75 14.3 24.1 1.19 2.96 6.16 11.3 19.1
15.7 32.7 58.1 92.7 137 12.0 25.1 45.0 72.2 107
Mo
12.8 16.0 19.2 22.4 25.6
0.964 ± 0.104 2.04 ± 0.22 3.34 ± 0.36 7.49 ± 0.81 12.6 ± 1.4
0.195 ± 0.022 0.423 ± 0.051 0.687 ± 0.084 1.48 ± 0.19 2.39 ± 0.33
1.16 ± 0.11 2.46 ± 0.23 4.03 ± 0.37 8.97 ± 0.81 15.0 ± 1.4
0.96 2.39 4.95 9.08 15.3
9.22 19.5 35.0 56.6 84.7
Ag
12.8 16.0 19.2 22.4 25.6
0.278 ± 0.030 0.685 ± 0.076 1.13 ± 0.12 2.65 ± 0.29 3.52 ± 0.38
0.054 ± 0.008 0.176 ± 0.024 0.290 ± 0.043 0.497 ± 0.076 1.60 ± 0.19
0.332 ± 0.031 0.861 ± 0.079 1.42 ± 0.13 3.15 ± 0.30 5.12 ± 0.42
0.330 0.866 1.77 3.22 5.36
2.43 5.54 10.3 17.0 26.1
Cd
12.8 16.0
0.241 ± 0.028 0.548 ± 0.061
0.033 ± 0.012 0.117 ± 0.019
0.274 ± 0.031 0.665 ± 0.064
0.293 0.719
1.99 4.35
Nb
Ka
Kb
(continued on next page)
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Table 1 (continued) Target
E (MeV)
Ka
Kb
Ktot
Ktot ECPSSR
Ktot PWBA
19.2 22.4 25.6
0.97 ± 0.11 2.10 ± 0.23 3.67 ± 0.45
0.274 ± 0.038 0.434 ± 0.066 0.67 ± 0.18
1.25 ± 0.12 2.53 ± 0.24 4.35 ± 0.48
1.47 2.66 4.42
8.09 13.5 20.8
In
12.8 16.0 19.2 22.4 25.6
0.197 ± 0.024 0.469 ± 0.052 0.799 ± 0.091 1.73 ± 0.19 2.96 ± 0.33
0.035 ± 0.010 0.091 ± 0.017 0.141 ± 0.033 0.315 ± 0.064 0.65 ± 0.14
0.232 ± 0.026 0.560 ± 0.055 0.940 ± 0.096 2.05 ± 0.20 3.61 ± 0.36
0.244 0.598 1.22 2.20 3.65
1.55 3.42 6.38 10.7 16.5
Sn
12.8 16.0 19.2 22.4 25.6
0.148 ± 0.021 0.443 ± 0.049 0.685 ± 0.080 1.54 ± 0.16 2.40 ± 0.28
0.027 ± 0.011 0.063 ± 0.010 0.098 ± 0.017 0.286 ± 0.065 0.534 ± 0.076
0.175 ± 0.023 0.506 ± 0.050 0.784 ± 0.082 1.83 ± 0.18 2.94 ± 0.29
0.204 0.500 1.02 1.83 3.04
1.22 2.69 5.05 8.49 13.2
Sb
12.8 16.0 19.2 22.4 25.6
0.102 ± 0.011 0.260 ± 0.028 0.443 ± 0.048 1.04 ± 0.11 1.90 ± 0.23
0.019 ± 0.006 0.049 ± 0.008 0.083 ± 0.012 0.197 ± 0.047 0.43 ± 0.14
0.121 ± 0.012 0.308 ± 0.029 0.526 ± 0.049 1.24 ± 0.12 2.33 ± 0.27
0.172 0.419 0.852 1.53 2.53
0.958 2.12 4.00 6.75 10.5
Table 2 The measured and theoretical calculated L-shell X-ray production cross sections (in barns). Target
E (MeV)
Ltot
Ltot ECPSSR
Ltot PWBA
Zn
12.8 16.0 19.2 22.4 25.6
La + Ll
Lb
Lc
57,000 ± 9000 69,000 ± 11,000 75,000 ± 12,000 112,000 ± 19,000 123,000 ± 21,000
84,900 118,000 144,000 165,000 180,000
123,000 143,000 157,000 168,000 175,000
Zr
12.8 16.0 19.2 22.4 25.6
19,900 ± 3300 33,100 ± 5300 38,700 ± 6100 60,000 ± 10,000 76,000 ± 12,000
9800 17,500 26,400 35,800 45,100
30,400 41,200 51,200 60,100 67,900
Nb
12.8 16.0 19.2 22.4 25.6
15,200 ± 2400 24,300 ± 3800 34,400 ± 5500 52,400 ± 8400 57,500 ± 9000
8130 14,700 22,600 31,000 39,500
26,600 36,600 45,900 54,400 61,900
Mo
12.8 16.0 19.2 22.4 25.6
13,800 ± 2200 18,800 ± 2900 26,600 ± 4200 50,000 ± 8100 57,100 ± 9000
6780 12,400 19,300 26,800 34,600
23,300 32,400 41,200 49,200 56,400
Ag
12.8 16.0 19.2 22.4 25.6
4980 ± 790 9300 ± 1500 14,500 ± 2300 22,400 ± 3600 27,300 ± 4300
2630 5250 8580 12,600 17,000
11,300 17,000 22,600 28,200 33,600
Cd
12.8 16.0 19.2 22.4 25.6
4050 ± 650 7200 ± 1100 12,000 ± 1900 19,600 ± 3200 25,800 ± 4500
2330 4490 7400 10,900 14,900
10,100 15,000 20,200 25,400 30,500
In
12.8 16.0 19.2 22.4 25.6
2900 ± 520 6500 ± 1000 9700 ± 1500 17,200 ± 2700 23,800 ± 3800
1970 3830 6350 9450 13,000
8800 13,200 18,000 22,800 27,600
Sn
12.8 16.0 19.2 22.4 25.6
2360 ± 380 5750 ± 900 8400 ± 1300 12,300 ± 2000 15,000 ± 2400
1670 3250 5420 8120 11,300
7610 11,600 15,900 20,300 24,700
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I. Gorlachev et al. / Nuclear Instruments and Methods in Physics Research B 381 (2016) 34–38 Table 2 (continued) E (MeV)
Sb
12.8 16.0 19.2 22.4 25.6
La + Ll
Lb
Lc
Ltot
Ltot ECPSSR
Ltot PWBA
1950 ± 300 3680 ± 570 5530 ± 860 10,000 ± 1600 11,000 ± 1800
1420 2790 4680 7050 9820
6650 10,200 14,100 18,100 22,200
Ta
12.8 16.0 19.2 22.4 25.6
92.8 ± 9.9 154 ± 16 214 ± 23 447 ± 48 700 ± 76
56.9 ± 6.2 93.0 ± 9.9 128 ± 14 252 ± 27 391 ± 43
8.8 ± 1.0 12.7 ± 1.4 15.5 ± 1.7 35.0 ± 3.9 52.6 ± 6.1
159 ± 12 259 ± 19 357 ± 27 734 ± 55 1140 ± 90
98.8 204 359 568 835
497 859 1310 1850 2470
W
12.8 16.0 19.2 22.4 25.6
82.2 ± 8.8 145 ± 15 216 ± 23 385 ± 41 631 ± 67
51.5 ± 5.5 86.2 ± 9.2 124 ± 13 214 ± 23 343 ± 37
6.6 ± 0.8 11.7 ± 1.3 15.5 ± 1.7 28.8 ± 3.3 47.3 ± 5.1
140 ± 11 243 ± 18 356 ± 27 628 ± 41 1020 ± 68
89.4 185 326 516 760
446 775 1190 1680 2250
Pb
12.8 16.0 19.2 22.4 25.6
34.7 ± 3.7 62.6 ± 6.7 95 ± 10 170 ± 18 266 ± 29
24.0 ± 2.6 42.4 ± 4.5 61.2 ± 6.5 105 ± 11 160 ± 17
3.9 ± 0.5 7.41 ± 0.83 9.4 ± 1.0 16.9 ± 1.9 26.5 ± 3.1
62.8 ± 4.6 113 ± 8 166 ± 12 294 ± 22 453 ± 34
40.5 85.9 154 246 366
183 336 535 776 1060
Bi
12.8 16.0 19.2 22.4 25.6
32.1 ± 3.5 59.5 ± 6.4 94 ± 10 157 ± 17 243 ± 26
22.5 ± 2.4 38.5 ± 4.1 58.8 ± 6.3 96 ± 10 144 ± 16
3.9 ± 0.5 5.79 ± 0.66 8.56 ± 0.98 14.0 ± 1.7 21.9 ± 26
58.6 ± 4.3 104 ± 8 162 ± 12 268 ± 17 409 ± 31
36.6 77.9 140 224 333
163 301 482 702 960
Table 3 The measured and theoretical calculated M-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Mtot
Mtot ECPSSR
Mtot PWBA
Ta
12.8 16.0 19.2 22.4 25.6
40,300 ± 6400 51,300 ± 8000 50,100 ± 7800 90,000 ± 14,000 85,000 ± 14,000
24,700 34,100 43,800 53,500 62,700
72,600 94,300 114,000 132,000 148,000
12.8 16.0 19.2 22.4 25.6
37,600 ± 5900 50,000 ± 7800 51,800 ± 8100 77,000 ± 12,000 73,000 ± 12,000
22,700 31,400 40,500 49,600 58,400
66,700 87,100 106,000 123,000 139,000
12.8 16.0 19.2 22.4 25.6
23,000 ± 3600 34,100 ± 5300 39,200 ± 6100 55,200 ± 8700 63,000 ± 10,000
11,600 16,600 21,800 27,200 32,800
34,400 46,400 58,400 70,100 81,300
12.8 16.0 19.2 22.4 25.6
20,500 ± 3200 32,200 ± 5000 37,200 ± 5800 51,600 ± 8100 70,000 ± 11,000
10,700 15,300 20,100 25,200 30,400
31,400 42,400 53,500 64,500 75,000
W
Pb
Bi
smaller than the resolution of the X-ray detector. Therefore, only the total cross sections are presented in tables for Al K-line, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn and Sb L-lines and for all M-lines. The theoretical data presented in Tables 1–3 were calculated from the single vacancy fluorescence yield and cross section ionization in the frame of the ECPSSR and PWBA approaches using the ISICS code [13]. Figs. 1 and 2 graphically show the measured Ktot and Ltot X-ray productions as a function of target atomic number for the different energies of 16O ions. Such dependence is not given for Mtot productions due to small number of experimental points. As an illustration of the relation between the theory and experiment the measured cross sections for the 22.4 MeV oxygen beam are presented in Fig. 3 together with the theoretically calculated ones
1.0E+06
X-ray production cross-srection (b)
Target
1.0E+05
1.0E+04
1.0E+03 5 4 3 2 1
1.0E+02
1.0E+01 20
30
40
50
60
70
80
90
Target atomic number
Fig. 2. Energy variations of 16O induced Ltot X-ray production cross sections (1–12.8 MeV, 2–16.0 MeV, 3–19.2 MeV, 4–22.4 MeV, 5–25.6 MeV).
within ECPSSR and PWBA approaches. The similar trends are observed for other ion energies. In the scientific literature there are scanty experimental data on the X-ray productions induced by oxygen ions. As a rule, researchers limited to the several targets and narrow energy range of the projectiles. For example, J.S. Braich et al. [15] measured the M Xray production cross sections only for gold target, E.C. Montenegro et al. [16] limited to measuring the K X-ray productions for titanium and iron targets, H.R. Verma [17] researched the L X-ray production cross sections in 83Bi, W. Hink [18] published the experimental carbon K-shell excitation cross sections as a function of incident ion energy per mass unit for oxygen ions, in reference [11] presented by J. Reyes-Herrera and J. Miranda the target elements were selected lanthanoids (Ce, Gd, Dy, Ho and Er). In some cases, such as in [19], the measured cross sections are presented graphically in the logarithmic scale that complicates a comparison with the data presented in this article. Therefore, we are able to compare the experimental cross sections only with the theoretically calculated values. Tables 1–3 show that the ECPSSR data are in better agreement with the experiment than the cross sections obtained in the frame-
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1.0E+04
waves (ECPSSR, PWBA) cannot always correctly describe the interactions of accelerated ions with target atoms. The same reasons can cause the large discrepancies between the experimental and theoretical data for ionization of L- and Mshells (Tables 2 and 3).
1.0E+03
3. Conclusions
1.0E+06
Ktot
Mtot
Ltot
X-ray production cross section (b)
1.0E+05
1.0E+02
1.0E+01
1.0E+00 10
20
30
40
50
60
70
80
90
1.0E-01 Target atomic number
Fig. 3. Comparison between measured Ktot, Ltot and Mtot X-ray production cross sections (red squares) and calculated within the framework of ECPSSR (blue rhombuses) and PWBA (green triangles) theoretical models for 22.4 MeV 16O3+. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
work of PWBA approximation. It can be explained that the ECPSSR approach, unlike the PWBA theory, takes into account the effects such as ion energy loss during the collision, the Coulomb deflection of ion trajectory, modification of the atomic electron energy and adjustment in the electron mass due to relativistic effects. As follows from Table 1 in the case of K-shell ionization of the target atoms the best agreement between experimental and theoretical data, calculated under the ECPSSR theory, is attained for the elements with atomic numbers in the range of 40 < Z < 50. Typically, the deviations are not exceeding 20–25% and they are within the limits of experimental errors. The large uncertainties for Sb can be explained by scanty statistics of the X-ray peaks. For the elements with low Z (30 < Z) there are large discrepancies observed between the experimental and theoretical data that are not within the limits of the experimental error. The differences increase is accompanied with decreasing of atomic number reaching the value over 100% for Al. The large deviations observed in this case between experimental values and theoretical predictions can be explained by the existence of domain applicability for various theoretical models [20]. The colliding systems can be classified in accordance with the parameters: Z1/Z2 and v1/vK, where Z1 and Z2 are atomic numbers of incident ion and target atom respectively, v1 is ion velocity and vK is electron velocity in the inner shell of the target. In our case for the K shells parameters Z1/Z2 and v1/vK are in the ranges: 0.096 < Z1/Z2 < 0.67 and 0.069 < v1/vK < 0.748. For symmetric and fast collisions, where 0.3 < Z1/Z2 and v1/ vK > 0.3, models based on the Plane Wave Born Approximation (ECPSSR, PWBA) are appropriate to describe the ion-atom interactions. However, for symmetrical and slow collisions, where Z1/ Z2 1 and v1/vK 6 1, it is necessary to take into account the mutual distortion in the atomic orbitals of the colliding partners and, as a result, the formation of a quasi-molecule (molecular orbital theory). In our experiment for elements with low Z the points are located near the region of validity of the molecular orbital model. In this case, the theories based on the Born approximation of plane
In the presented work we studied the X-ray production cross sections at the interaction of oxygen ions with target atoms in the range of atomic numbers 13 < Z < 83. The energy of the accelerated ions was varied in the range of 12.8–25.6 MeV with a step of 3.2 MeV. The obtained data were compared with the theoretical predictions of the ECPSS model calculated by us using the ISICS code. For elements with atomic numbers in the range of 40 < Z < 50 the deviations usually do not exceed 20–25% and are within the limits of the experimental error. The observed large discrepancies between the experimental and theoretical values for K-shell Xray productions of light atoms and L- and M-shell X-ray productions of all studied elements can be explained by the existence of applicability domains for various theoretical models. The large uncertainties for Sb are explained by poor statistics of the X-ray peaks. The obtained experimental data will be used at the DC-60 accelerator to develop the HIPIXE technique for the analysis of a wide range of samples. Acknowledgment The works, which results are presented in this article, are made with the financial support of the Ministry of Energy of the Republic of Kazakhstan. We also express our gratitude to F. Penkov for active and useful participation in the discussions. References [1] I. Popescu, T. Badica, A. Olariu, C. Besliu, A. Ene, Al. Ivanescu, in: Radioanal. Nucl. Chem. Lett. 213 (1996) 369. [2] C. Stihi, I.V. Popescu, G. Busuioc, T. Badica, A. Olariu, G. Dima, Radioanal. Nucl. Chem. Lett. 246 (2000) 445. [3] A. Bancuta, C. Stihi, I.V. Popescu, T. Badica, Gh.V. Cimpoca, J. Phys: Conf. Ser. 41 (2006) 502. [4] C. Stihi, A. Bancuta, I.V. Popescu, M. Virgolici, V. Cimpoca, M. Gigiu, Gh. Vlaicu, J. Phys: Conf. Ser. 41 (2006) 565. [5] M.J. Orafran et al., Nucl. Instr. Meth. B 74 (1993) 542. [6] M.J. Orafran et al., Nucl. Instr. Meth. B 99 (1995) 384. [7] S.A.E. Johansson, J.L. Campbell, PIXE: A Novel Technique for Materials Analysis, John Wiley, Chichester, 1988. [8] K.H. Ecker, H.P. Weise, K.L. Merkle, Mikrochim. Acta 133 (2000) 313. [9] M.J. Orafran, M.E. Debray, R. Eusebi, A.J. Kreiner, M.E. Vazquez, A. Burlon, P. Stolier, Nucl. Instr. Meth. B 201 (2003) 317. [10] X. Zhou et al., Phys. Scr. 87 (2013) 055301. [11] J. Reyes-Herrera, J. Miranda, Nucl. Instr. Meth. B 267 (2009) 1767. [12] R.L. Watson, Y. Peng, V. Horvat, A.N. Perumal, Phys. Rev. A 74 (2006) 062709. [13] Z. Lie, S.J. Cipolla, Comput. Phys. Commun. 97 (1996) 315. [14] N. Gluchshenko, I. Gorlachev, I. Ivanov, A. Kireyev, S. Kozin, A. Kurakhmedov, A. Platov, M. Zdorovets, Nucl. Instr. Meth. B 372 (2016) 1. [15] J.S. Braich, P. Verma, D.P. Goyal, H.R. Verma, Nucl. Instr. Meth. 119 (1996) 317. [16] E.C. Montenegro et al., J. Phys. B: At. Mol. Phys. 19 (1986) 3287. [17] H.R. Verma, Rom. J. Phys. 58 (7) (2013) 947. [18] W. Hink, Revue de Physique Appliquee 11 (1) (1976) 31. [19] A.C. Scafes, C. Ciortea, D.E. Dumitriu, A. Enulescu, D. Fluerasu, M.M. Gugiu, M.D. Pena, M. Pentia, I. Piticu, Rom. Rep. Phys. 66 (2) (2014) 455. [20] G. Lapicki, W. Lichten, Phys. Rev. 31 (3) (1985) 1354.