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Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6
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K-, L- and M-shell X-ray productions induced by argon ions in the 0.8–1.6 MeV/amu range N. Gluchshenko a, I. Gorlachev 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, Ibragimov 1, 050032, Almaty, Kazakhstan L.N. Gumilyov Eurasian National University, Mirzoyan 2, Astana, Kazakhstan Ural Federal University, 620002, Yekaterinburg, Russia
a r t i c l e
i n f o
Article history: Received 21 December 2015 Received in revised form 13 January 2016 Accepted 15 January 2016
Keywords: X-ray production cross section Argon ions ECPSSR theory
a b s t r a c t The X-ray emissions induced by argon ions for the elements from Mg to Bi were measured on mono-elemental thin films. K-, L- and M-shells X-ray production cross section were obtained for the 40 Ar projectile energies of 32, 40, 48, 56 and 64 MeV, considering absorption corrections. For the most of target elements the approach used is based on the calculation of X-ray production cross sections through the cross section of Rutherford backscattering. The efficiency of the X-ray detector was determined using standard calibrated radioactive sources. The experimental results are compared to the predictions of the ECPSSR and PWBA theories calculated with the ISICS code. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction The phenomenon of characteristic X-ray emission, i.e., ionization followed by the radiative de-excitation filling of an inner shell vacancy, induced by the impact of photons, electrons or heavier charged particles on atoms, has been known for several decades [1]. Specifically, the impact of ions heavier than protons and deuterons, which involves a number of processes that have not been fully described neither by theories or experiments due to their complexity [2], is still a problem subject to investigation. At the same time, there is an increasing interest in the application of heavy ions for analysis with particle induced X-ray emission (PIXE), as they present higher X-ray yields, possibly improving PIXE sensitivity [3,4]. These papers proved that an exact knowledge of the ionization and further emission of X-rays due to heavy ion impact is necessary to obtain accurate results in quantitative analyses. The developed theoretical approaches have a fairly good description of the mechanism of X-ray generation under light ions irradiation. The ECPSSR theory of Brandt and Lapicki [5] is the most successful model in describing the ionization by light ions, such as protons [6]. This theory is a modification of the Plane Wave Born Approximation (PWBA). It considers effects such as the ion energy loss during the collision (E), the Coulomb deflection in the ion trajectory (C), the modification of the atomic electron energy states
⇑ Corresponding author. http://dx.doi.org/10.1016/j.nimb.2016.01.027 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
through a perturbed stationary states model (PSS), and an adjustment in the mass of the electron, due to relativistic effects (R). The United Atom (UA) correction to the ECPSSR model (ECPSSR UA) considers a modification in the binding energies of the target electrons due to the presence of the projectile [7]. However, in the case of heavy ion PIXE, the theoretical approaches do not always provide reliable data of X-ray production cross section, especially considering the complexity of describing the processes occurring at interaction of heavy ion with target atom. In this situation, the experimental research of the fundamental parameters for HIPIXE on accelerated heavy ion beams becomes important. The present work provides a study of K-shell X-ray production cross sections of the fourteen thin films Mg, 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, Ta, W, Pb, Bi and M-shell X-ray productions of the targets Ta, W induced by 40Ar with incident energies ranging from 32 to 64 MeV. L-shell Ag, Cd, In, Sn, Sb and M-shell Pb, Bi X-ray production cross sections weren’t measured because large overlaps detected X-rays with radiation from the projectiles. 40Ar projectiles were produced at the DC-60 cyclotron [8] of the Institute of Nuclear Physics. The obtained data were compared with the theoretical predictions of PWBA and ECPSSR models calculated by us with the ISICS code [9]. These activities are a continuation of researches on the measurement of proton [10] and nitrogen [11,12] induced X-ray production cross sections performed during 2013 and 2014.
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2. Experiment Samples were prepared in the form of metal thin films deposited onto Mylar backings by the magnetron plasma deposition method. The thicknesses of the metal films were measured by Rutherford backscattering using 14 MeV 14N2+ ions. Results varied from 53 lg/cm2 (copper) up to 280 lg/cm2 (tantalum). The estimated precision of the target thicknesses calculated with the RUMP code [13] was about ±8%. For these thicknesses the energy loss of the 32 MeV argon beam does not exceed 7%. Argon beams were produced in energies from 32 MeV to 64 MeV, in 8 MeV steps. The target foils were positioned perpendicular to the beam direction. The argon beam had a 2 mm diameter, typical ion beam currents were about 1 nA. The Si(Li) detector with an active area of 12 mm2 had an energy resolution of 135 eV at 5.9 keV was used for X-ray detection. It was placed at an angle of 135° with respect to the incoming beam. For the detection of K-lines of Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb and L-lines of Ta, W, Pb, Bi a 0.1 mm Mylar absorber was placed in front of the Si(Li) detector to absorb the intense yield of low energy X-rays. All M-lines, L-lines of Zn, Zr, Nb, Mo and Mg, Al K-lines were detected without the Mylar absorber. The efficiency of the X-ray detector was determined using standard calibrated radioactive sources 152Eu, 154Eu, 155Eu, 133Ba, 109Cd, 57Co, 241Am and 55Fe. The specified set of calibrated sources covers the energy range of X-ray range from 5.9 (55Fe) to 45 keV (152Eu). The points in the range of 1–5.9 keV without absorber were calculated taking into account the X-ray absorption in 200 nm organic window and 100 nm dead layer. The points in the range of 3–20 keV with absorber were calculated using the mass coefficient of X-ray attenuation in Mylar absorber. Finally, the efficiencies were extrapolated by a least-square fit with an estimated error of 7%. The measured and calculated curves of the X-ray detection efficiencies with and without Mylar absorber are presented in Fig. 1. The technique of simultaneous detection of X-rays and Rutherford backscattered particles was employed to obtain the X-ray production cross section. The simultaneous measurement of induced X-ray emission and elastically scattered ions allows the X-ray production cross sections to be calculated from the differential Rutherford cross sections. This method eliminates the uncertainties associated with target thickness and charge collection. A 50 mm2 silicon barrier detector mounted at 160° to the incident beam direction was used to record ions backscattered from the target. The angle subtended by the detector was 9.7 msr. Cross section productions could not be measured using this approach for the Mg, Al, Ti and Cr targets because argon ions are not be scattered at back angles for the Mg and Al films and for the Ti and Cr films the
rX ¼
NX DX XR rR K K eX NR DR f t
ð1Þ
Kf ¼
1 elf qf x
ð2Þ
Kt ¼
lt t
ð3Þ
1 elt t
where NX and NR are the measured X-ray and backscattering argon ions intensities corrected for dead time DX and DR; XR (sr) is the particle detector solid angle; eX (EX) is the Si(Li) detector efficiency for X-ray energy EX; rR is the elastic scattering cross section; lf (cm2/g), qf (g/cm3) and x (cm) are the mass coefficient of X-ray attenuation in the Mylar absorber, density and thickness of the Mylar absorber respectively; lt (cm2/g) and t (g/cm2) are the mass coefficient of Xray attenuation in the irradiated film and metal film thickness respectively. K f and K t take into account the X-rays absorption in the Mylar absorber and self-absorption in the target. The relative uncertainties of the X-ray cross section productions were calculated by the formula:
dr
r
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 2 2 2 2 2ffi dK f dNX deX dNN dX dK t ¼ þ þ þ þ þ NX eX NN Kf Kt X ð4Þ
16
where dNX and NX – the error in determining and the number of detected X-rays, respectively; deX and eX – the calculation error and the efficiency of X-ray detection, respectively; dNN b NN – the error in determining and the number of scattered ions, respectively; dX and X – the error in calculation and the solid angle subtended
14
by the surface-barrier detector, respectively; term
12
error of X-ray attenuation in the Mylar absorber and term
10
relative error of target X-rays self-absorption. The errors in correcting the effect of self-absorption and the determining of X-rays number because high background level are basic for soft X-ray lines. For K-lines of heavy elements the error in the determining of X-rays number is basic because poor statistics.
20 18
Efficiency*10(-5)
backscattering cross sections were too low to provide sufficient particle counting statistics. In this case, the X-ray cross section productions were calculated using the measured foil thicknesses and the beam integrated charge. At that, it is important to ensure complete suppression of delta secondary and Auger electrons for the accuracy charge measurement. However, the nonconducting samples (Mylar substrates), the small values of the measured beam currents (sometimes less than 0.1 nA) and a large number of high-energy (up to 30 keV) Auger electrons significantly complicate the accuracy charge measurement from the irradiated target. Therefore, for the Mg, Al, Ti and Cr targets it was developed the alternative approach based on the use of a molybdenum grid (the transparency is of the order of 50%) with a deposited layer of 500 nm thickness bismuth as a beam monitor. The grid was placed in the path of the argon beam and elastic recoiled ions were detected by a surface barrier detector. The number of ions backscattered by the bismuth layer was then employed to determine the total number of incident ions. The experimental X-ray production cross section for an individual X-ray line is given by
8 6 4 2
dK f Kf
is the relative dK t Kt
is the
0 0
5
10
15 20 25 X-ray e ne rgy, ke V
30
35
40
Fig. 1. The measured curves of the X-ray detection efficiencies with (pink square points) and without (black rhombic points) Mylar absorber. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Results and discussion Based on the approach described above, there were measured the X-ray production cross sections at the interaction of argon beams and target atoms. Tables 1 (K-line), 2 (L-line) and 3 (M-line) present individual and total X-ray productions of the
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N. Gluchshenko et al. / Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6 Table 1 The measured and calculated K-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Mg
Ka
Kb
Ktot
Ktot ECPSSR
Ktot PWBA
32 40 48 56 64
16,300 ± 2700 29,700 ± 4900 26,600 ± 4400 42,300 ± 7000 53,300 ± 8500
240,330 478,080 725,970 948,430 1,126,300
227,210 275,290 312,650 341,220 362,780
Al
32 40 48 56 64
20,900 ± 3500 34,800 ± 5800 28,200 ± 4700 41,400 ± 6900 56,100 ± 8900
103,090 237,460 395,270 551,720 691,910
173,020 216,890 252,960 282,120 305,420
Ti
32 40 48 56 64
2220 ± 290 4380 ± 580 5370 ± 710 8250 ± 1100 9160 ± 1450
316 ± 42 702 ± 94 800 ± 100 1290 ± 170 1520 ± 240
2540 ± 330 5080 ± 670 6170 ± 810 9530 ± 1300 10,700 ± 1700
145 594 1801 4332 8711
13,417 21,690 30,988 40,850 50,937
Cr
32 40 48 56 64
738 ± 98 2030 ± 270 3260 ± 430 4890 ± 650 6110 ± 970
98 ± 13 272 ± 38 490 ± 70 495 ± 75 1220 ± 200
840 ± 110 2300 ± 310 3750 ± 500 5380 ± 730 7300 ± 1200
57 224 671 1641 3418
7567 12,762 18,885 25,648 32,813
Cu
32 40 48 56 64
50.7 ± 5.1 149 ± 17 302 ± 39 684 ± 91 1380 ± 310
5.8 ± 0.8 13.2 ± 2.2 35.1 ± 7.3 112 ± 17 115 ± 27
56.5 ± 5.1 162 ± 17 337 ± 40 800 ± 110 1500 ± 310
9.5 32 90 211 440
1808 3323 5292 7659 10,360
Zn
32 40 48 56 64
25.0 ± 2.5 74.7 ± 6.9 203 ± 23 468 ± 48 675 ± 71
3.0 ± 0.4 9.8 ± 1.2 21.9 ± 3.1 56.5 ± 7.5 75.8 ± 9.8
28.0 ± 2.5 84.4 ± 7.0 225 ± 24 524 ± 49 751 ± 71
7.1 24 64 148 307
1358 2534 4087 5982 8171
Zr
32 40 48 56 64
0.463 ± 0.049 1.21 ± 0.13 3.06 ± 0.35 8.54 ± 0.93 11.8 ± 1.6
0.08 ± 0.03 0.22 ± 0.11 0.55 ± 0.25 1.53 ± 0.48 2.11 ± 0.64
0.545 ± 0.060 1.42 ± 0.17 3.61 ± 0.43 10.1 ± 1.1 13.9 ± 1.7
0.647 1.8 4.3 8.9 16.8
80.2 167.0 296.0 472.0 697.0
Nb
32 40 48 56 64
0.347 ± 0.037 0.97 ± 0.12 2.41 ± 0.28 5.90 ± 0.64 8.83 ± 1.08
0.068 ± 0.031 0.19 ± 0.10 0.47 ± 0.22 1.15 ± 0.46 1.73 ± 0.54
0.415 ± 0.048 1.15 ± 0.15 2.88 ± 0.36 7.05 ± 0.79 10.6 ± 1.2
0.532 1.5 3.5 7.2 13.4
61.2 128.0 229.0 368.0 547.0
Mo
32 40 48 56 64
0.299 ± 0.032 0.87 ± 0.10 2.09 ± 0.21 4.56 ± 0.48 6.61 ± 0.68
0.054 ± 0.011 0.16 ± 0.08 0.38 ± 0.11 0.87 ± 0.20 1.25 ± 0.38
0.353 ± 0.034 1.03 ± 0.12 2.46 ± 0.23 5.42 ± 0.52 7.86 ± 0.78
0.443 1.2 2.9 5.8 10.7
47.0 99.0 178.0 288.0 431.0
Ag
32 40 48 56 64
0.093 ± 0.014 0.320 ± 0.038 0.734 ± 0.083 1.40 ± 0.23 2.69 ± 0.36
0.021 ± 0.012 0.071 ± 0.037 0.162 ± 0.072 0.30 ± 0.11 0.62 ± 0.31
0.114 ± 0.018 0.391 ± 0.053 0.90 ± 0.11 1.71 ± 0.25 3.31 ± 0.47
0.190 0.51 1.14 2.23 4.00
13.00 28.20 52.30 86.70 133.00
Cd
32 40 48 56 64
0.075 ± 0.016 0.254 ± 0.037 0.653 ± 0.074 1.31 ± 0.15 2.00 ± 0.28
0.010 ± 0.004 0.032 ± 0.016 0.085 ± 0.043 0.22 ± 0.11 0.34 ± 0.07
0.085 ± 0.018 0.286 ± 0.041 0.740 ± 0.086 1.54 ± 0.19 2.34 ± 0.29
0.164 0.44 0.97 1.88 3.35
10.20 22.20 41.20 68.70 106.00
In
32 40 48 56 64
0.068 ± 0.010 0.222 ± 0.044 0.565 ± 0.083 1.39 ± 0.20 1.84 ± 0.28
0.008 ± 0.004 0.028 ± 0.009 0.069 ± 0.048 0.16 ± 0.08 0.26 ± 0.16
0.077 ± 0.011 0.250 ± 0.069 0.634 ± 0.090 1.55 ± 0.22 2.10 ± 0.32
0.141 0.38 0.83 1.60 2.82
7.94 17.40 32.50 54.40 84.10
Sn
32 40 48 56 64
0.053 ± 0.018 0.164 ± 0.033 0.398 ± 0.093 1.04 ± 0.18 1.56 ± 0.19
0.012 ± 0.010 0.038 ± 0.019 0.093 ± 0.047 0.13 ± 0.07 0.20 ± 0.10
0.065 ± 0.013 0.203 ± 0.039 0.49 ± 0.11 1.17 ± 0.19 1.76 ± 0.21
0.122 0.32 0.71 1.36 2.39
6.22 13.70 25.70 43.20 67.00
Sb
32 40 48 56 64
0.045 ± 0.006 0.129 ± 0.013 0.307 ± 0.035 0.757 ± 0.072 1.26 ± 0.15
0.006 ± 0.003 0.017 ± 0.005 0.040 ± 0.013 0.098 ± 0.021 0.16 ± 0.08
0.051 ± 0.007 0.146 ± 0.014 0.347 ± 0.038 0.854 ± 0.075 1.42 ± 0.23
0.106 0.28 0.61 1.16 2.04
4.89 10.80 20.40 34.40 53.50
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Table 2 The measured and calculated L-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Zn
La + Ll
Lb
Lc
Ltot
Ltot ECPSSR
Ltot PWBA
32 40 48 56 64
98,400 ± 12,800 129,000 ± 17,000 167,000 ± 22,000 228,000 ± 39,700 251,000 ± 39,000
303,400 509,000 703,390 869,710 1,003,900
622,520 724,020 797,480 849,890 886,550
Zr
32 40 48 56 64
36,300 ± 4900 42,900 ± 5700 58,900 ± 8300 109,000 ± 17,300 141,000 ± 23,000
15,463 35,805 65,896 103,950 147,080
154,250 208,990 259,370 304,390 343,950
Nb
32 40 48 56 64
30,000 ± 3900 33,500 ± 4400 41,800 ± 5700 71,100 ± 10,300 128,000 ± 19,000
12,119 28,474 53,220 85,337 122,690
135,020 185,390 232,630 275,520 313,740
Mo
32 40 48 56 64
30,500 ± 3900 29,600 ± 3800 37,900 ± 4900 59,000 ± 8030 120,000 ± 17,000
9604 22,853 43,280 70,396 102,670
118,340 164,560 208,670 249,330 286,050
Ta
32 40 48 56 64
328 ± 28 688 ± 60 1030 ± 90 2030 ± 180 2510 ± 220
102 ± 9 233 ± 21 380 ± 33 752 ± 67 985 ± 88
8.3 ± 1.0 22.9 ± 2.9 39.7 ± 3.7 91 ± 10 48 ± 16
439 ± 30 944 ± 63 1450 ± 100 2870 ± 190 3540 ± 240
90 211 418 740 1203
2527 4365 6664 9402 12,554
W
32 40 48 56 64
292 ± 25 619 ± 55 816 ± 71 1610 ± 150 2160 ± 200
100 ± 9 208 ± 19 295 ± 26 607 ± 58 771 ± 75
3.5 ± 1.8 15.1 ± 4.8 13.9 ± 2.2 46 ± 13 58 ± 19
396 ± 27 842 ± 58 1130 ± 80 2260 ± 160 2990 ± 220
82 192 380 671 1090
2266 3938 6036 8538 11,425
Pb
32 40 48 56 64
67.2 ± 5.9 174 ± 16 247 ± 22 548 ± 50 723 ± 71
35.9 ± 3.4 89.0 ± 8.4 163 ± 14 335 ± 31 415 ± 44
3.8 ± 1.0 11.4 ± 2.1 27.1 ± 3.1 35.2 ± 5.4 55 ± 10
107 ± 7 275 ± 18 438 ± 26 921 ± 59 1200 ± 80
40.3 93.2 182.0 317.0 510.0
926 1700.0 2704.0 3923.0 5345.0
Bi
32 40 48 56 64
59.3 ± 5.2 160 ± 14 239 ± 21 465 ± 44 639 ± 63
31.5 ± 3.1 80.8 ± 7.8 155 ± 14 259 ± 27 380 ± 42
3.5 ± 1.0 10.1 ± 1.8 19.1 ± 3.4 40.9 ± 6.8 68 ± 13
94.5 ± 6.1 252 ± 16 414 ± 26 767 ± 52 1090 ± 80
36.9 85.7 167.0 292.0 469.0
827 1530.0 2449.0 3569.0 4879.0
series Ktot, Ltot and Mtot respectively, being the sum of the individual lines for 32 MeV, 40 MeV, 56 MeV 40Ar6+ and 48 MeV, 64 MeV 40 Ar7+. In some cases, since the energy separation between some X-ray lines of one element is smaller than the resolution of the detector only group of lines can be identified. Therefore, only the total K-cross sections are presented in Table 1 for the Mg and Al targets, only the total L-cross sections are presented in Tables 2 for the Zn, Zr, Nb, Mo targets and only the total M-cross sections are presented in Table 3. Tables 1–3 include the uncertainties in
Table 3 The measured and calculated M-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Mtot
Mtot ECPSSR
Mtot PWBA
Ta
32 40 48 56 64
97,700 ± 13,000 123,000 ± 17,000 141,000 ± 19,000 172,000 ± 23,000 194,000 ± 27,000
32,016 47,875 64,575 82,163 100,550
368,020 477,870 579,190 669,850 749,490
W
32 40 48 56 64
75,300 ± 10,000 115,000 ± 16,000 124,000 ± 17,000 129,000 ± 18,000 189,000 ± 27,000
29,783 44,804 60,603 77,217 94,600
338,300 441,530 537,830 624,900 702,120
the measurement of the X-ray production cross sections obtained from Eq. (4). 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 by means of the ISICS code [9]. Figs. 2 and 3 show graphically the Ktot and Ltot X-ray production cross sections respectively as a function of atomic number of the target nucleus for 32–64 MeV 40Ar ions. The measured Ktot and Ltot X-ray production cross sections for 64 MeV 40Ar7+ as well as the calculated cross sections in the frame of the ECPSSR and PWBA approaches are presented in Fig. 4. For other 40Ar energies a similar behavior of the curves is observed. As shown in [9], the experimental data of nitrogen induced X-ray production cross sections and the theoretical predictions of the ECPSSR theory have similar trends. However, for 40Ar ions (this work) the situation looks completely different. As it follows from Fig. 4, for the K shells ECPSSR like trend is observed only for heavy elements (Z > 40). In the middle mass region (30 > Z > 22), the experimental cross sections are anomalously high, and for Mg and Al are also anomalously low in comparison with the ECPSSR theory. In case of L-shell ionization, the lack of experimental data for the target region between Ag (Z = 47) and Sb (Z = 51) makes it difficult to reveal general trends. However, for the high atomic
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N. Gluchshenko et al. / Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6
100000
X--ray production c ross-sectiom (b)
10000
1000
100
10 64 MeV
1
56 MeV 48 MeV 40 MeV
0.1
32 MeV
0.01 10
15
20
25
30
35
40
45
50
55
m ic number Targett atom Fig. 2. Energy variations of the
40
Ar Ktot X-ray production cross sections.
regions: 1. For Mg and Al ratios are 1.5 > Z1/Z2 > 1.38 and 0.67 > v1/vK > 0.38. Points are located in the region of validity of the approaches extending the first Born approximation [14]. 2. For the elements with atomic number 30 > Z > 24 the ratios are 0.82 > Z1/Z2 > 0.6 and 0.18 > v1/vK > 0.045. In this case, all points are located in the region of validity of the molecular orbital method. The ECPSSR model in this region describes the ion–atom collision process rather poorly. This should be accompanied by increasing in absolute values of the ionization cross sections compared with the predictions of the ECPSSR model, what we observe 3. For the elements with atomic number 83 > Z > 40 the ratios are 0.45 > Z1/Z2 > 0.22 and 0.049 > v1/vK > 0.0048. Points are located close to the boundary of the region of validity of the molecular orbital method. Thus, the ECPSSR model can correctly describe the interactions between the incident ion and the target atom not for all targets. As a result, the experimentally obtained curve of X-ray production cross section against target atomic number can depart from the theoretically calculated within the ECPSSR model. In the literature experimental data of 1 MeV/amu argon induced X-ray production cross section are not available or scanty. For K-shell V, Cu Nb and L-shell Nb, Ta, Pt, in 1984 O’Kelley et al. [17] reported X-ray production cross section in the argon energy
number targets (Z > 73) the experimental cross sections exceed several times the ECPSSR model data that is not typical in the case of nuclei excitation by nitrogen ions [9]. Observed large deviations between the experimental values and the theoretical predictions obtained in argon induced X-ray emission studies can be explained by the existence of the regions of validity of the different theoretical models [14]. The colliding systems have been classified according to the parameters: Z1/Z2 and v1/vK, where Z1 are Z2 respectively the atomic numbers of the incident ion and target atom, v1 is the ion velocity and vK is the velocity of the electron in the inner shell of the target. For asymmetric and fast collisions, where 0.3 < Z1/Z2 and v1/vK > 0.3, the ECPSSR approximation is appropriate [14]. For symmetric and slow collisions, where Z1/Z2 1 and v1/vK 6 1, molecular orbital theory [15,16] promotion comes into play. The molecular orbital theory takes into account the mutual distortion in the atomic orbitals of the collision partners and, as a result, the formation of a quasimolecule. For the less symmetric collisions capture of target electrons becomes important, holding for the region Z1/Z2 6 1 and v1/vK 6 1. In the present work in K-shell ionization the Z1/Z2 and v1/vK values are in the ranges of 0.22 < Z1/Z2 < 1.5 and 0.0048 < v1/vK < 0.67. The full range of Z1/Z2 and v1/vK ratios can be divided into three
X-ray p rod d uctii on cross se ectt ion (b)
1000000
100000
10000
64 MeV
1000
56 MeV 48 MeV 40 MeV
100
32 MeV
10 20
30
40
50
60
70
80
Target a tomic numb b er Fig. 3. Energy variations of the
40
Ar Ltot X-ray production cross sections.
90
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N. Gluchshenko et al. / Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6
1000000.00 ECPSSR
100000.00 X-ray production cross sectiom (b)
PWBA Ar
PWBA ECPSSR
Ar
10000.00
1000.00
Ltot 100.00
Ktot 10.00
1.00 10
20
30
40 50 60 Target att omicc number
70
80
90
Fig. 4. Comparison of the measured Ktot and Ltot X-ray production cross sections (red squares) and calculated in the frame of the ECPSSR (blue rhombuses) and PWBA (green triangles) approaches for 64 MeV 40Ar7+. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
range of 36.0–103 MeV. In case of 1.4 MeV/amu argon, their results are 24–62% lower than that of our work. However, they used thick films (1 mg/cm2) as a target that can lead to additional uncertainties in the cross section calculation. 4. Conclusions This work presents experimentally measured X-ray production cross sections using 40Ar ions impinging on thin metal targets across the periodic table between Mg and Bi. Argon beams were produced in energies from 32 MeV to 64 MeV, in 8 MeV steps. The obtained data were compared with the theoretical predictions of PWBA and ECPSSR models calculated by us with the ISICS code. Observed large deviations between the experimental values and the theoretical predictions obtained in argon induced X-ray emission studies can be explained by the existence of the regions of validity of the different theoretical models. The ECPSSR model can correctly describe the interactions between the incident ion and the target atom not for all targets. As a result, the experimentally obtained curve of X-ray production cross section against target atomic number can depart from the theoretically calculated within the ECPSSR model. Acknowledgments The works, the results of which 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] R.E. Van Geleken, A.A. Markovicz (Eds.), Handbook of X-ray Spectrometry, 2nd ed., John Wiley, New York, 2002. [2] W. Wolfli, Heavy Ion Physics. In: V. Ceausescu and I.A. Dorobantu, (Eds.) Predeal International Summer School (Central Institute of Physics, Bucharest, 1976) p. 43. [3] M.J. Orafran et al., Nucl. Instrum. Meth. B 74 (1993) 542. [4] M.J. Orafran et al., Nucl. Instrum. Meth. B 99 (1995) 384. [5] W. Brandt, G. Lapicki, Phys. Rev. A 23 (1981) 1717. [6] G. Lapicki, J. Phys. B 41 (2008) 115201. [7] L. Sarkadi, T. Mukoyama, Nucl. Instrum. Meth. B 61 (1991) 167. [8] B. Gikal et al., Phys. Part. Nucl. Lett. 5 (7) (2008) 642. [9] Z. Lie, S.J. Cipolla, Comput. Phys. Commun. 97 (1996) 315. [10] E. Batyrbekov, I. Gorlachev, I. Ivanov, A. Platov, Nucl. Instrum. Meth. B 325 (2014) 84. [11] E. Batyrbekov, N. Gluchshenko, I. Gorlachev, I. Ivanov, A. Platov, Nucl. Instrum. Meth. B 330 (2014) 86. [12] N. Gluchshenko, I. Gorlachev, I. Ivanov, A. Platov, M. Zdorovets, A. Kurahmedov, in: Proceedings of the 22nd International Conference on Ion Beam Analysis (Opatija, Croatia, 2015) p. 142. [13] L.R. Doolittle, Nucl. Instrum. Meth. B 15 (1986) 227. [14] G. Lapicki, W. Lichten, Phys. Rev. 31 (3) (1985) 1354. [15] U. Fano, W. Lichten, Phys. Rev. Lett. 14 (1965) 627. [16] H.L. Sun, Y.C. Yu, E.K. Lin, C.W. Wang, J.L. Duggan, A.R. Azordegan, F.D. McDaniel, G. Lapicki, Phys. Rev. A 53 (1996) 4190. [17] G.D. O’Kelley et al., Nucl. Instrum. Meth. 3 (1–3) (1984) 78.
Contents lists available at ScienceDirect
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 argon ions in the 0.8–1.6 MeV/amu range N. Gluchshenko a, I. Gorlachev 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, Ibragimov 1, 050032, Almaty, Kazakhstan L.N. Gumilyov Eurasian National University, Mirzoyan 2, Astana, Kazakhstan Ural Federal University, 620002, Yekaterinburg, Russia
a r t i c l e
i n f o
Article history: Received 21 December 2015 Received in revised form 13 January 2016 Accepted 15 January 2016
Keywords: X-ray production cross section Argon ions ECPSSR theory
a b s t r a c t The X-ray emissions induced by argon ions for the elements from Mg to Bi were measured on mono-elemental thin films. K-, L- and M-shells X-ray production cross section were obtained for the 40 Ar projectile energies of 32, 40, 48, 56 and 64 MeV, considering absorption corrections. For the most of target elements the approach used is based on the calculation of X-ray production cross sections through the cross section of Rutherford backscattering. The efficiency of the X-ray detector was determined using standard calibrated radioactive sources. The experimental results are compared to the predictions of the ECPSSR and PWBA theories calculated with the ISICS code. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction The phenomenon of characteristic X-ray emission, i.e., ionization followed by the radiative de-excitation filling of an inner shell vacancy, induced by the impact of photons, electrons or heavier charged particles on atoms, has been known for several decades [1]. Specifically, the impact of ions heavier than protons and deuterons, which involves a number of processes that have not been fully described neither by theories or experiments due to their complexity [2], is still a problem subject to investigation. At the same time, there is an increasing interest in the application of heavy ions for analysis with particle induced X-ray emission (PIXE), as they present higher X-ray yields, possibly improving PIXE sensitivity [3,4]. These papers proved that an exact knowledge of the ionization and further emission of X-rays due to heavy ion impact is necessary to obtain accurate results in quantitative analyses. The developed theoretical approaches have a fairly good description of the mechanism of X-ray generation under light ions irradiation. The ECPSSR theory of Brandt and Lapicki [5] is the most successful model in describing the ionization by light ions, such as protons [6]. This theory is a modification of the Plane Wave Born Approximation (PWBA). It considers effects such as the ion energy loss during the collision (E), the Coulomb deflection in the ion trajectory (C), the modification of the atomic electron energy states
⇑ Corresponding author. http://dx.doi.org/10.1016/j.nimb.2016.01.027 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
through a perturbed stationary states model (PSS), and an adjustment in the mass of the electron, due to relativistic effects (R). The United Atom (UA) correction to the ECPSSR model (ECPSSR UA) considers a modification in the binding energies of the target electrons due to the presence of the projectile [7]. However, in the case of heavy ion PIXE, the theoretical approaches do not always provide reliable data of X-ray production cross section, especially considering the complexity of describing the processes occurring at interaction of heavy ion with target atom. In this situation, the experimental research of the fundamental parameters for HIPIXE on accelerated heavy ion beams becomes important. The present work provides a study of K-shell X-ray production cross sections of the fourteen thin films Mg, 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, Ta, W, Pb, Bi and M-shell X-ray productions of the targets Ta, W induced by 40Ar with incident energies ranging from 32 to 64 MeV. L-shell Ag, Cd, In, Sn, Sb and M-shell Pb, Bi X-ray production cross sections weren’t measured because large overlaps detected X-rays with radiation from the projectiles. 40Ar projectiles were produced at the DC-60 cyclotron [8] of the Institute of Nuclear Physics. The obtained data were compared with the theoretical predictions of PWBA and ECPSSR models calculated by us with the ISICS code [9]. These activities are a continuation of researches on the measurement of proton [10] and nitrogen [11,12] induced X-ray production cross sections performed during 2013 and 2014.
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N. Gluchshenko et al. / Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6
2. Experiment Samples were prepared in the form of metal thin films deposited onto Mylar backings by the magnetron plasma deposition method. The thicknesses of the metal films were measured by Rutherford backscattering using 14 MeV 14N2+ ions. Results varied from 53 lg/cm2 (copper) up to 280 lg/cm2 (tantalum). The estimated precision of the target thicknesses calculated with the RUMP code [13] was about ±8%. For these thicknesses the energy loss of the 32 MeV argon beam does not exceed 7%. Argon beams were produced in energies from 32 MeV to 64 MeV, in 8 MeV steps. The target foils were positioned perpendicular to the beam direction. The argon beam had a 2 mm diameter, typical ion beam currents were about 1 nA. The Si(Li) detector with an active area of 12 mm2 had an energy resolution of 135 eV at 5.9 keV was used for X-ray detection. It was placed at an angle of 135° with respect to the incoming beam. For the detection of K-lines of Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb and L-lines of Ta, W, Pb, Bi a 0.1 mm Mylar absorber was placed in front of the Si(Li) detector to absorb the intense yield of low energy X-rays. All M-lines, L-lines of Zn, Zr, Nb, Mo and Mg, Al K-lines were detected without the Mylar absorber. The efficiency of the X-ray detector was determined using standard calibrated radioactive sources 152Eu, 154Eu, 155Eu, 133Ba, 109Cd, 57Co, 241Am and 55Fe. The specified set of calibrated sources covers the energy range of X-ray range from 5.9 (55Fe) to 45 keV (152Eu). The points in the range of 1–5.9 keV without absorber were calculated taking into account the X-ray absorption in 200 nm organic window and 100 nm dead layer. The points in the range of 3–20 keV with absorber were calculated using the mass coefficient of X-ray attenuation in Mylar absorber. Finally, the efficiencies were extrapolated by a least-square fit with an estimated error of 7%. The measured and calculated curves of the X-ray detection efficiencies with and without Mylar absorber are presented in Fig. 1. The technique of simultaneous detection of X-rays and Rutherford backscattered particles was employed to obtain the X-ray production cross section. The simultaneous measurement of induced X-ray emission and elastically scattered ions allows the X-ray production cross sections to be calculated from the differential Rutherford cross sections. This method eliminates the uncertainties associated with target thickness and charge collection. A 50 mm2 silicon barrier detector mounted at 160° to the incident beam direction was used to record ions backscattered from the target. The angle subtended by the detector was 9.7 msr. Cross section productions could not be measured using this approach for the Mg, Al, Ti and Cr targets because argon ions are not be scattered at back angles for the Mg and Al films and for the Ti and Cr films the
rX ¼
NX DX XR rR K K eX NR DR f t
ð1Þ
Kf ¼
1 elf qf x
ð2Þ
Kt ¼
lt t
ð3Þ
1 elt t
where NX and NR are the measured X-ray and backscattering argon ions intensities corrected for dead time DX and DR; XR (sr) is the particle detector solid angle; eX (EX) is the Si(Li) detector efficiency for X-ray energy EX; rR is the elastic scattering cross section; lf (cm2/g), qf (g/cm3) and x (cm) are the mass coefficient of X-ray attenuation in the Mylar absorber, density and thickness of the Mylar absorber respectively; lt (cm2/g) and t (g/cm2) are the mass coefficient of Xray attenuation in the irradiated film and metal film thickness respectively. K f and K t take into account the X-rays absorption in the Mylar absorber and self-absorption in the target. The relative uncertainties of the X-ray cross section productions were calculated by the formula:
dr
r
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 2 2 2 2 2ffi dK f dNX deX dNN dX dK t ¼ þ þ þ þ þ NX eX NN Kf Kt X ð4Þ
16
where dNX and NX – the error in determining and the number of detected X-rays, respectively; deX and eX – the calculation error and the efficiency of X-ray detection, respectively; dNN b NN – the error in determining and the number of scattered ions, respectively; dX and X – the error in calculation and the solid angle subtended
14
by the surface-barrier detector, respectively; term
12
error of X-ray attenuation in the Mylar absorber and term
10
relative error of target X-rays self-absorption. The errors in correcting the effect of self-absorption and the determining of X-rays number because high background level are basic for soft X-ray lines. For K-lines of heavy elements the error in the determining of X-rays number is basic because poor statistics.
20 18
Efficiency*10(-5)
backscattering cross sections were too low to provide sufficient particle counting statistics. In this case, the X-ray cross section productions were calculated using the measured foil thicknesses and the beam integrated charge. At that, it is important to ensure complete suppression of delta secondary and Auger electrons for the accuracy charge measurement. However, the nonconducting samples (Mylar substrates), the small values of the measured beam currents (sometimes less than 0.1 nA) and a large number of high-energy (up to 30 keV) Auger electrons significantly complicate the accuracy charge measurement from the irradiated target. Therefore, for the Mg, Al, Ti and Cr targets it was developed the alternative approach based on the use of a molybdenum grid (the transparency is of the order of 50%) with a deposited layer of 500 nm thickness bismuth as a beam monitor. The grid was placed in the path of the argon beam and elastic recoiled ions were detected by a surface barrier detector. The number of ions backscattered by the bismuth layer was then employed to determine the total number of incident ions. The experimental X-ray production cross section for an individual X-ray line is given by
8 6 4 2
dK f Kf
is the relative dK t Kt
is the
0 0
5
10
15 20 25 X-ray e ne rgy, ke V
30
35
40
Fig. 1. The measured curves of the X-ray detection efficiencies with (pink square points) and without (black rhombic points) Mylar absorber. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3. Results and discussion Based on the approach described above, there were measured the X-ray production cross sections at the interaction of argon beams and target atoms. Tables 1 (K-line), 2 (L-line) and 3 (M-line) present individual and total X-ray productions of the
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N. Gluchshenko et al. / Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6 Table 1 The measured and calculated K-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Mg
Ka
Kb
Ktot
Ktot ECPSSR
Ktot PWBA
32 40 48 56 64
16,300 ± 2700 29,700 ± 4900 26,600 ± 4400 42,300 ± 7000 53,300 ± 8500
240,330 478,080 725,970 948,430 1,126,300
227,210 275,290 312,650 341,220 362,780
Al
32 40 48 56 64
20,900 ± 3500 34,800 ± 5800 28,200 ± 4700 41,400 ± 6900 56,100 ± 8900
103,090 237,460 395,270 551,720 691,910
173,020 216,890 252,960 282,120 305,420
Ti
32 40 48 56 64
2220 ± 290 4380 ± 580 5370 ± 710 8250 ± 1100 9160 ± 1450
316 ± 42 702 ± 94 800 ± 100 1290 ± 170 1520 ± 240
2540 ± 330 5080 ± 670 6170 ± 810 9530 ± 1300 10,700 ± 1700
145 594 1801 4332 8711
13,417 21,690 30,988 40,850 50,937
Cr
32 40 48 56 64
738 ± 98 2030 ± 270 3260 ± 430 4890 ± 650 6110 ± 970
98 ± 13 272 ± 38 490 ± 70 495 ± 75 1220 ± 200
840 ± 110 2300 ± 310 3750 ± 500 5380 ± 730 7300 ± 1200
57 224 671 1641 3418
7567 12,762 18,885 25,648 32,813
Cu
32 40 48 56 64
50.7 ± 5.1 149 ± 17 302 ± 39 684 ± 91 1380 ± 310
5.8 ± 0.8 13.2 ± 2.2 35.1 ± 7.3 112 ± 17 115 ± 27
56.5 ± 5.1 162 ± 17 337 ± 40 800 ± 110 1500 ± 310
9.5 32 90 211 440
1808 3323 5292 7659 10,360
Zn
32 40 48 56 64
25.0 ± 2.5 74.7 ± 6.9 203 ± 23 468 ± 48 675 ± 71
3.0 ± 0.4 9.8 ± 1.2 21.9 ± 3.1 56.5 ± 7.5 75.8 ± 9.8
28.0 ± 2.5 84.4 ± 7.0 225 ± 24 524 ± 49 751 ± 71
7.1 24 64 148 307
1358 2534 4087 5982 8171
Zr
32 40 48 56 64
0.463 ± 0.049 1.21 ± 0.13 3.06 ± 0.35 8.54 ± 0.93 11.8 ± 1.6
0.08 ± 0.03 0.22 ± 0.11 0.55 ± 0.25 1.53 ± 0.48 2.11 ± 0.64
0.545 ± 0.060 1.42 ± 0.17 3.61 ± 0.43 10.1 ± 1.1 13.9 ± 1.7
0.647 1.8 4.3 8.9 16.8
80.2 167.0 296.0 472.0 697.0
Nb
32 40 48 56 64
0.347 ± 0.037 0.97 ± 0.12 2.41 ± 0.28 5.90 ± 0.64 8.83 ± 1.08
0.068 ± 0.031 0.19 ± 0.10 0.47 ± 0.22 1.15 ± 0.46 1.73 ± 0.54
0.415 ± 0.048 1.15 ± 0.15 2.88 ± 0.36 7.05 ± 0.79 10.6 ± 1.2
0.532 1.5 3.5 7.2 13.4
61.2 128.0 229.0 368.0 547.0
Mo
32 40 48 56 64
0.299 ± 0.032 0.87 ± 0.10 2.09 ± 0.21 4.56 ± 0.48 6.61 ± 0.68
0.054 ± 0.011 0.16 ± 0.08 0.38 ± 0.11 0.87 ± 0.20 1.25 ± 0.38
0.353 ± 0.034 1.03 ± 0.12 2.46 ± 0.23 5.42 ± 0.52 7.86 ± 0.78
0.443 1.2 2.9 5.8 10.7
47.0 99.0 178.0 288.0 431.0
Ag
32 40 48 56 64
0.093 ± 0.014 0.320 ± 0.038 0.734 ± 0.083 1.40 ± 0.23 2.69 ± 0.36
0.021 ± 0.012 0.071 ± 0.037 0.162 ± 0.072 0.30 ± 0.11 0.62 ± 0.31
0.114 ± 0.018 0.391 ± 0.053 0.90 ± 0.11 1.71 ± 0.25 3.31 ± 0.47
0.190 0.51 1.14 2.23 4.00
13.00 28.20 52.30 86.70 133.00
Cd
32 40 48 56 64
0.075 ± 0.016 0.254 ± 0.037 0.653 ± 0.074 1.31 ± 0.15 2.00 ± 0.28
0.010 ± 0.004 0.032 ± 0.016 0.085 ± 0.043 0.22 ± 0.11 0.34 ± 0.07
0.085 ± 0.018 0.286 ± 0.041 0.740 ± 0.086 1.54 ± 0.19 2.34 ± 0.29
0.164 0.44 0.97 1.88 3.35
10.20 22.20 41.20 68.70 106.00
In
32 40 48 56 64
0.068 ± 0.010 0.222 ± 0.044 0.565 ± 0.083 1.39 ± 0.20 1.84 ± 0.28
0.008 ± 0.004 0.028 ± 0.009 0.069 ± 0.048 0.16 ± 0.08 0.26 ± 0.16
0.077 ± 0.011 0.250 ± 0.069 0.634 ± 0.090 1.55 ± 0.22 2.10 ± 0.32
0.141 0.38 0.83 1.60 2.82
7.94 17.40 32.50 54.40 84.10
Sn
32 40 48 56 64
0.053 ± 0.018 0.164 ± 0.033 0.398 ± 0.093 1.04 ± 0.18 1.56 ± 0.19
0.012 ± 0.010 0.038 ± 0.019 0.093 ± 0.047 0.13 ± 0.07 0.20 ± 0.10
0.065 ± 0.013 0.203 ± 0.039 0.49 ± 0.11 1.17 ± 0.19 1.76 ± 0.21
0.122 0.32 0.71 1.36 2.39
6.22 13.70 25.70 43.20 67.00
Sb
32 40 48 56 64
0.045 ± 0.006 0.129 ± 0.013 0.307 ± 0.035 0.757 ± 0.072 1.26 ± 0.15
0.006 ± 0.003 0.017 ± 0.005 0.040 ± 0.013 0.098 ± 0.021 0.16 ± 0.08
0.051 ± 0.007 0.146 ± 0.014 0.347 ± 0.038 0.854 ± 0.075 1.42 ± 0.23
0.106 0.28 0.61 1.16 2.04
4.89 10.80 20.40 34.40 53.50
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N. Gluchshenko et al. / Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6
Table 2 The measured and calculated L-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Zn
La + Ll
Lb
Lc
Ltot
Ltot ECPSSR
Ltot PWBA
32 40 48 56 64
98,400 ± 12,800 129,000 ± 17,000 167,000 ± 22,000 228,000 ± 39,700 251,000 ± 39,000
303,400 509,000 703,390 869,710 1,003,900
622,520 724,020 797,480 849,890 886,550
Zr
32 40 48 56 64
36,300 ± 4900 42,900 ± 5700 58,900 ± 8300 109,000 ± 17,300 141,000 ± 23,000
15,463 35,805 65,896 103,950 147,080
154,250 208,990 259,370 304,390 343,950
Nb
32 40 48 56 64
30,000 ± 3900 33,500 ± 4400 41,800 ± 5700 71,100 ± 10,300 128,000 ± 19,000
12,119 28,474 53,220 85,337 122,690
135,020 185,390 232,630 275,520 313,740
Mo
32 40 48 56 64
30,500 ± 3900 29,600 ± 3800 37,900 ± 4900 59,000 ± 8030 120,000 ± 17,000
9604 22,853 43,280 70,396 102,670
118,340 164,560 208,670 249,330 286,050
Ta
32 40 48 56 64
328 ± 28 688 ± 60 1030 ± 90 2030 ± 180 2510 ± 220
102 ± 9 233 ± 21 380 ± 33 752 ± 67 985 ± 88
8.3 ± 1.0 22.9 ± 2.9 39.7 ± 3.7 91 ± 10 48 ± 16
439 ± 30 944 ± 63 1450 ± 100 2870 ± 190 3540 ± 240
90 211 418 740 1203
2527 4365 6664 9402 12,554
W
32 40 48 56 64
292 ± 25 619 ± 55 816 ± 71 1610 ± 150 2160 ± 200
100 ± 9 208 ± 19 295 ± 26 607 ± 58 771 ± 75
3.5 ± 1.8 15.1 ± 4.8 13.9 ± 2.2 46 ± 13 58 ± 19
396 ± 27 842 ± 58 1130 ± 80 2260 ± 160 2990 ± 220
82 192 380 671 1090
2266 3938 6036 8538 11,425
Pb
32 40 48 56 64
67.2 ± 5.9 174 ± 16 247 ± 22 548 ± 50 723 ± 71
35.9 ± 3.4 89.0 ± 8.4 163 ± 14 335 ± 31 415 ± 44
3.8 ± 1.0 11.4 ± 2.1 27.1 ± 3.1 35.2 ± 5.4 55 ± 10
107 ± 7 275 ± 18 438 ± 26 921 ± 59 1200 ± 80
40.3 93.2 182.0 317.0 510.0
926 1700.0 2704.0 3923.0 5345.0
Bi
32 40 48 56 64
59.3 ± 5.2 160 ± 14 239 ± 21 465 ± 44 639 ± 63
31.5 ± 3.1 80.8 ± 7.8 155 ± 14 259 ± 27 380 ± 42
3.5 ± 1.0 10.1 ± 1.8 19.1 ± 3.4 40.9 ± 6.8 68 ± 13
94.5 ± 6.1 252 ± 16 414 ± 26 767 ± 52 1090 ± 80
36.9 85.7 167.0 292.0 469.0
827 1530.0 2449.0 3569.0 4879.0
series Ktot, Ltot and Mtot respectively, being the sum of the individual lines for 32 MeV, 40 MeV, 56 MeV 40Ar6+ and 48 MeV, 64 MeV 40 Ar7+. In some cases, since the energy separation between some X-ray lines of one element is smaller than the resolution of the detector only group of lines can be identified. Therefore, only the total K-cross sections are presented in Table 1 for the Mg and Al targets, only the total L-cross sections are presented in Tables 2 for the Zn, Zr, Nb, Mo targets and only the total M-cross sections are presented in Table 3. Tables 1–3 include the uncertainties in
Table 3 The measured and calculated M-shell X-ray production cross sections (in barns). Target
EAr (MeV)
Mtot
Mtot ECPSSR
Mtot PWBA
Ta
32 40 48 56 64
97,700 ± 13,000 123,000 ± 17,000 141,000 ± 19,000 172,000 ± 23,000 194,000 ± 27,000
32,016 47,875 64,575 82,163 100,550
368,020 477,870 579,190 669,850 749,490
W
32 40 48 56 64
75,300 ± 10,000 115,000 ± 16,000 124,000 ± 17,000 129,000 ± 18,000 189,000 ± 27,000
29,783 44,804 60,603 77,217 94,600
338,300 441,530 537,830 624,900 702,120
the measurement of the X-ray production cross sections obtained from Eq. (4). 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 by means of the ISICS code [9]. Figs. 2 and 3 show graphically the Ktot and Ltot X-ray production cross sections respectively as a function of atomic number of the target nucleus for 32–64 MeV 40Ar ions. The measured Ktot and Ltot X-ray production cross sections for 64 MeV 40Ar7+ as well as the calculated cross sections in the frame of the ECPSSR and PWBA approaches are presented in Fig. 4. For other 40Ar energies a similar behavior of the curves is observed. As shown in [9], the experimental data of nitrogen induced X-ray production cross sections and the theoretical predictions of the ECPSSR theory have similar trends. However, for 40Ar ions (this work) the situation looks completely different. As it follows from Fig. 4, for the K shells ECPSSR like trend is observed only for heavy elements (Z > 40). In the middle mass region (30 > Z > 22), the experimental cross sections are anomalously high, and for Mg and Al are also anomalously low in comparison with the ECPSSR theory. In case of L-shell ionization, the lack of experimental data for the target region between Ag (Z = 47) and Sb (Z = 51) makes it difficult to reveal general trends. However, for the high atomic
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N. Gluchshenko et al. / Nuclear Instruments and Methods in Physics Research B 372 (2016) 1–6
100000
X--ray production c ross-sectiom (b)
10000
1000
100
10 64 MeV
1
56 MeV 48 MeV 40 MeV
0.1
32 MeV
0.01 10
15
20
25
30
35
40
45
50
55
m ic number Targett atom Fig. 2. Energy variations of the
40
Ar Ktot X-ray production cross sections.
regions: 1. For Mg and Al ratios are 1.5 > Z1/Z2 > 1.38 and 0.67 > v1/vK > 0.38. Points are located in the region of validity of the approaches extending the first Born approximation [14]. 2. For the elements with atomic number 30 > Z > 24 the ratios are 0.82 > Z1/Z2 > 0.6 and 0.18 > v1/vK > 0.045. In this case, all points are located in the region of validity of the molecular orbital method. The ECPSSR model in this region describes the ion–atom collision process rather poorly. This should be accompanied by increasing in absolute values of the ionization cross sections compared with the predictions of the ECPSSR model, what we observe 3. For the elements with atomic number 83 > Z > 40 the ratios are 0.45 > Z1/Z2 > 0.22 and 0.049 > v1/vK > 0.0048. Points are located close to the boundary of the region of validity of the molecular orbital method. Thus, the ECPSSR model can correctly describe the interactions between the incident ion and the target atom not for all targets. As a result, the experimentally obtained curve of X-ray production cross section against target atomic number can depart from the theoretically calculated within the ECPSSR model. In the literature experimental data of 1 MeV/amu argon induced X-ray production cross section are not available or scanty. For K-shell V, Cu Nb and L-shell Nb, Ta, Pt, in 1984 O’Kelley et al. [17] reported X-ray production cross section in the argon energy
number targets (Z > 73) the experimental cross sections exceed several times the ECPSSR model data that is not typical in the case of nuclei excitation by nitrogen ions [9]. Observed large deviations between the experimental values and the theoretical predictions obtained in argon induced X-ray emission studies can be explained by the existence of the regions of validity of the different theoretical models [14]. The colliding systems have been classified according to the parameters: Z1/Z2 and v1/vK, where Z1 are Z2 respectively the atomic numbers of the incident ion and target atom, v1 is the ion velocity and vK is the velocity of the electron in the inner shell of the target. For asymmetric and fast collisions, where 0.3 < Z1/Z2 and v1/vK > 0.3, the ECPSSR approximation is appropriate [14]. For symmetric and slow collisions, where Z1/Z2 1 and v1/vK 6 1, molecular orbital theory [15,16] promotion comes into play. The molecular orbital theory takes into account the mutual distortion in the atomic orbitals of the collision partners and, as a result, the formation of a quasimolecule. For the less symmetric collisions capture of target electrons becomes important, holding for the region Z1/Z2 6 1 and v1/vK 6 1. In the present work in K-shell ionization the Z1/Z2 and v1/vK values are in the ranges of 0.22 < Z1/Z2 < 1.5 and 0.0048 < v1/vK < 0.67. The full range of Z1/Z2 and v1/vK ratios can be divided into three
X-ray p rod d uctii on cross se ectt ion (b)
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Ar Ltot X-ray production cross sections.
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Fig. 4. Comparison of the measured Ktot and Ltot X-ray production cross sections (red squares) and calculated in the frame of the ECPSSR (blue rhombuses) and PWBA (green triangles) approaches for 64 MeV 40Ar7+. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
range of 36.0–103 MeV. In case of 1.4 MeV/amu argon, their results are 24–62% lower than that of our work. However, they used thick films (1 mg/cm2) as a target that can lead to additional uncertainties in the cross section calculation. 4. Conclusions This work presents experimentally measured X-ray production cross sections using 40Ar ions impinging on thin metal targets across the periodic table between Mg and Bi. Argon beams were produced in energies from 32 MeV to 64 MeV, in 8 MeV steps. The obtained data were compared with the theoretical predictions of PWBA and ECPSSR models calculated by us with the ISICS code. Observed large deviations between the experimental values and the theoretical predictions obtained in argon induced X-ray emission studies can be explained by the existence of the regions of validity of the different theoretical models. The ECPSSR model can correctly describe the interactions between the incident ion and the target atom not for all targets. As a result, the experimentally obtained curve of X-ray production cross section against target atomic number can depart from the theoretically calculated within the ECPSSR model. Acknowledgments The works, the results of which 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] R.E. Van Geleken, A.A. Markovicz (Eds.), Handbook of X-ray Spectrometry, 2nd ed., John Wiley, New York, 2002. [2] W. Wolfli, Heavy Ion Physics. In: V. Ceausescu and I.A. Dorobantu, (Eds.) Predeal International Summer School (Central Institute of Physics, Bucharest, 1976) p. 43. [3] M.J. Orafran et al., Nucl. Instrum. Meth. B 74 (1993) 542. [4] M.J. Orafran et al., Nucl. Instrum. Meth. B 99 (1995) 384. [5] W. Brandt, G. Lapicki, Phys. Rev. A 23 (1981) 1717. [6] G. Lapicki, J. Phys. B 41 (2008) 115201. [7] L. Sarkadi, T. Mukoyama, Nucl. Instrum. Meth. B 61 (1991) 167. [8] B. Gikal et al., Phys. Part. Nucl. Lett. 5 (7) (2008) 642. [9] Z. Lie, S.J. Cipolla, Comput. Phys. Commun. 97 (1996) 315. [10] E. Batyrbekov, I. Gorlachev, I. Ivanov, A. Platov, Nucl. Instrum. Meth. B 325 (2014) 84. [11] E. Batyrbekov, N. Gluchshenko, I. Gorlachev, I. Ivanov, A. Platov, Nucl. Instrum. Meth. B 330 (2014) 86. [12] N. Gluchshenko, I. Gorlachev, I. Ivanov, A. Platov, M. Zdorovets, A. Kurahmedov, in: Proceedings of the 22nd International Conference on Ion Beam Analysis (Opatija, Croatia, 2015) p. 142. [13] L.R. Doolittle, Nucl. Instrum. Meth. B 15 (1986) 227. [14] G. Lapicki, W. Lichten, Phys. Rev. 31 (3) (1985) 1354. [15] U. Fano, W. Lichten, Phys. Rev. Lett. 14 (1965) 627. [16] H.L. Sun, Y.C. Yu, E.K. Lin, C.W. Wang, J.L. Duggan, A.R. Azordegan, F.D. McDaniel, G. Lapicki, Phys. Rev. A 53 (1996) 4190. [17] G.D. O’Kelley et al., Nucl. Instrum. Meth. 3 (1–3) (1984) 78.