amu range

Nuclear Instruments and Methods in Physics Research B 407 (2017) 86–91

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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 krypton ions in the 0.8–1.6 MeV/amu range I. Gorlachev a,⇑, N. Gluchshenko a, I. Ivanov a,b, A. Kireyev a, V. Alexandrenko 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 7 March 2017 Received in revised form 1 June 2017 Accepted 1 June 2017

Keywords: X-ray production cross section Krypton ions Beam monitor ECPSSR theory

a b s t r a c t The K-, L- and M-shells X-ray production cross sections induced by krypton ions for a range target elements from Ti to Bi were measured. In the experiments the thin films were irradiated by 84Kr particles with projectile energies of 67.2, 84.0, 100.8, 117.6 and 134.4 MeV. An approach based on the use of Mo grid with 500 nm deposited bismuth layer as a beam monitor was developed to determine the amount of particles delivered on the sample. The efficiency of the X-ray detector was determined using the calibration radioactive sources. The experimental results were compared to the predictions of the ECPSSR and PWBA theories calculated with the ISICS code. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Inner-shell vacancy production and characteristic X-ray emission in heavy ion-atom collisions are of great interest at recent time. This interest is caused by the fact that inner-shell ionization cross sections are required in different applications such as determination of stopping power, ion implantation and plasma studies [1–11]. However, determination of the ionization cross sections in this case is a difficult task for theoretical calculations due to the many-body nature of the process. As a rule, a projectile is not fully stripped of its electrons, so it is necessary to take into account both electron-nucleus and electron-electron interactions. In addition, several mechanisms may contribute to the production of vacancies in targets, including the direct Coulomb excitation and ionization, the electron capture by an incident ion and, the electronic exchange through quasi-molecular levels for nuclei collisions with similar charges at relatively low velocities. The process is complicated by the possibility of simultaneous ejection of some electrons from the higher shells of the target atoms in the case of multiple ionized final state of the atom [12,13]. As a result of these complications, the appropriate theoretical models for the calculation of vacancies formation cross sections in the inner shells of the target atoms for projectiles with the atomic ⇑ Corresponding author. E-mail address: [email protected] (I. Gorlachev). http://dx.doi.org/10.1016/j.nimb.2017.06.001 0168-583X/Ó 2017 Elsevier B.V. All rights reserved.

numbers (Z1) of the order of 18 or more have not been developed yet. The ECPSSR theory, developed by Brandt and Lapicki [14] is currently the most successful model describing the ionization processes in the atom-ion interactions [15]. This theory is a modification of the Born approximation of plane waves (the Plane Wave Born Approximation) (PWBA). It takes into account the ion energy loss after collision (E), the Coulomb deflection in ion trajectory (C), the modification of the electron energy states of atoms through the model of perturbed stationary states (PSS) and the adjustment of the electron mass due to the relativistic effects (R). There are other improvements to the model. For example, the united atom correction (UA) to the ECPSSR model (or ECPSSR-UA) includes a modification in the binding energy of the target electrons due to incident particle [16]. Furthermore, Benka et al. have improved the ECPSSR model, in order to take into account the formation of molecular orbitals (MO) during the ion-atom collisions in accordance with the UA approach. The ECPSSR model was changed (effective charge of target atom, reducing of binding energy and binding-polarization variable). This new model is known as MECPSSR. It has two variables, used to move from the separated atom to the ECPSSR-UA model for heavy ions. At present, the developed theoretical models quite successfully describe the processes of light ions interaction with target atoms. As a rule, the discrepancy between the experimental and theoretical data in this case does not exceed 10%. At the same time, in

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order to assist the theorists in expanding of the theoretical models for heavy ions, new experimental data are required. Furthermore, there is an increased interest in the use of heavy ions for PIXE applications (HIPIXE technique) [17–23], since improvement of the conventional PIXE technique sensitivity is possible due to greater X-ray productions. These articles show that a good knowledge of the X-ray production cross sections in excitation of the target atoms by heavy ions is necessary to obtain reliable results in the quantitative analysis. This paper describes the obtained data of characteristic X-rays production cross sections under ionization of the K-, L- and Mshells of the target atoms by accelerated krypton ions. The K-shell X-ray productions of 12 thin films: Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, the L- shells for the targets Zn, Ag, Cd, In, Sn, Sb, Ta, W, Pb, Bi, and the M-shells of the Pb, Bi targets induced by the krypton ions were measured. For this purpose the 84Kr12+ beam with energy of 67.2 MeV, the 84Kr13+ beams with energies of 84.0, 100.8 and 117.6 MeV and the 84Kr15+ beam with energy of 134.4 MeV were used. The X-ray productions were not measured for the L- shells of Zr, Nb, Mo, Lb Pb and Bi, Lc Ta and W, and Mshells Ta and W because of large overlaps of the detected X-rays with the radiation from the projectiles. 84Kr ions were accelerated at the cyclotron DC-60 [24] of the Institute of Nuclear Physics. The obtained data were compared with the theoretical predictions of the PWBA and ECPSSR models calculated with the ISICS software [25].

2. Experiment The samples in the form of metal films deposited onto Mylar substrate using the magnetron plasma deposition were prepared. The thicknesses of the metal films were measured with the 14N2+ Rutherford backscattering technique and calculated with the RUMP code [26]. The results ranged from 40.6 (Titanium) to 515 (Bismuth) lg/cm2. The estimated accuracy of the thickness determination was ±8%. For such thicknesses the values of energy losses for 67.2 MeV krypton do not exceed 10% (for the other energies the losses were even less). The experiments were carried out at the heavy ion cyclotron DC-60 (the maximum energy of 1.75 MeV/nucleon) of the Institute of Nuclear Physics. The krypton beams with energies in the range from 67.2 MeV up to 134.4 MeV with a step of 16.8 MeV were used. The targets were placed perpendicular to the beam direction. The average krypton beam current in the experiments was ranged from 0.5 nA for the K-lines measurements down to 0.1 nA for the L- and M-lines measurements. The Si(Li) detector with an active area of 12 mm2, and an energy resolution of 135 eV at 5.9 keV was used for the X-rays detection. The detector was located at an angle of 135° to the beam direction. The 0.1 mm Mylar absorber was placed in front of the detector to absorb the low-energy X-rays for all Klines and L-lines of Ta, W, Pb, Bi. The X-ray detector efficiency was determined using the calibration radioactive sources 152Eu, 154Eu, 155Eu, 133Ba, 109Cd, 57Co, 241 Am and 55Fe manufactured by Canberra Industries Inc. (USA). The measured and calculated curves are shown in Fig. 1. The set of calibration sources covers the 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 the 200 nm protective window and the 100 nm dead layer of the detector. Thicknesses of the protective window and dead layer are specified by the manufacturer in the detector specification. The points in the range of 3–20 keV with filter were calculated from the X-rays mass attenuation coefficient in Mylar. Finally, the efficiency values were interpolated using a least squares fit with the estimated error of 7%.

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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.)

The approach based on the calculation of X-ray production cross sections through the Rutherford backscattering cross sections, applied in our previous studies [27,28], cannot always be used in this case. For some targets, the scattering of krypton ions at an angle of more than 90° is impossible (Ti, Cr, Cu, Zn), or the cross sections are too small to obtain data with the desired statistical confidence (Zr, Nb, Mo, Ag, Cd, In, Sn, Sb). Therefore, the following expression was used to calculate the Xray production cross sections for the individual lines:

rX ¼

N X DX M Kf Kt deX N P DP N0

1 elf qf x
 lt t Kt ¼  l t 1e t Kf ¼

ð1Þ ð2Þ ð3Þ

where NX and NP are the measured number of X-rays corrected for dead time DX and number of krypton ions incident on the sample corrected for dead time DP respectively; M(g/mol) – is the target molar mass; d(g/cm2) – is the target thickness; eX (EX) is the Si(Li) detector efficiency for X-ray energy EX; N0(1/mol) – is the Avogadro constant; 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 X-ray 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. As follows from the formula (1), one of the parameters that should be measured in the experiment is a number of particles Np reaching the sample. The direct measurement of the beam current integral is difficult for several reasons: 1. The conductive metal backing may be an additional source of characteristic X-ray background. Therefore, to avoid the appearance of additional X-ray peaks in spectra, the 100 nm Mylar film as a backing was used. However, in this case, non-conductive nature of the substrate results in incomplete discharging of the target and, consequently, in inaccuracies in measurement of the beam current and the number of particles reaching the sample.

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Table 1 The measured and calculated K-shell X-ray production cross sections (in barns). Target

EKr (MeV)

Ka

Kb

Ktot

Ktot ECPSSR

Ktot PWBA

Ti

67.2 84.0 100.8 117.6 134.4

700 ± 90 3500 ± 500 3700 ± 500 7800 ± 1000 11000 ± 1000

78 ± 12 360 ± 50 440 ± 60 970 ± 130 1400 ± 200

780 ± 90 3900 ± 500 5100 ± 600 8700 ± 1000 12000 ± 2000

20.2 131 621 2281 6718

53807 86964 124210 163720 204110

Cr

67.2 84.0 100.8 117.6 134.4

1300 ± 200 5300 ± 700 7100 ± 900 10000 ± 1000 13000 ± 2000

150 ± 20 640 ± 90 850 ± 110 1300 ± 200 1600 ± 200

1400 ± 200 6000 ± 700 7900 ± 900 11000 ± 1000 15000 ± 2000

7.08 40.0 173 608 1784

30356 51181 75717 102820 131520

Cu

67.2 84.0 100.8 117.6 134.4

1100 ± 200 4700 ± 600 6100 ± 800 8900 ± 1200 12000 ± 2000

150 ± 20 600 ± 80 760 ± 100 1200 ± 200 1600 ± 200

1300 ± 200 5300 ± 600 6800 ± 800 10000 ± 1000 13000 ± 2000

1.09 4.74 16.6 49.6 130

7255 13334 21230 30720 41545

Zn

67.2 84.0 100.8 117.6 134.4

650 ± 90 3400 ± 500 4600 ± 600 7100 ± 900 9500 ± 1600

85 ± 11 400 ± 50 570 ± 80 890 ± 120 860 ± 160

740 ± 90 3800 ± 500 5200 ± 600 8000 ± 900 10000 ± 2000

0.814 3.40 11.5 33.3 85.4

5452 10168 16397 23993 32771

Zr

67.2 84.0 100.8 117.6 134.4

30 ± 4 190 ± 30 390 ± 50 670 ± 90 900 ± 100

4.0 ± 0.6 21 ± 3 46 ± 6 76 ± 11 110 ± 20

34 ± 4 210 ± 30 440 ± 50 750 ± 90 1000 ± 100

0.0946 0.31 0.825 1.91 4.00

322 669 1187 1894 2799

Nb

67.2 84.0 100.8 117.6 134.4

18 ± 2 110 ± 20 230 ± 30 450 ± 60 640 ± 80

2.5 ± 0.4 13 ± 2 28 ± 4 52 ± 8 73 ± 11

20 ± 2 130 ± 20 260 ± 30 510 ± 60 710 ± 90

0.082 0.26 0.681 1.55 3.21

246 514 919 1476 2194

Mo

67.2 84.0 100.8 117.6 134.4

12 ± 2 63 ± 8 170 ± 20 240 ± 30 350 ± 50

1.8 ± 0.3 10 ± 2 24 ± 4 30 ± 4 46 ± 7

14 ± 2 73 ± 9 200 ± 20 270 ± 30 390 ± 50

0.069 0.221 0.572 1.29 2.62

189 398 716 1157 1729

Ag

67.2 84.0 100.8 117.6 134.4

0.85 ± 0.14 2.5 ± 0.4 8.7 ± 1.3 19 ± 3 34 ± 5

0.14 ± 0.07 0.42 ± 0.07 1.3 ± 0.4 1.9 ± 0.5 2.9 ± 1.5

0.98 ± 0.15 2.9 ± 0.4 10 ± 1 21 ± 3 37 ± 5

0.035 0.108 0.263 0.56 1.08

52.3 113 210 348 533

Cd

67.2 84.0 100.8 117.6 134.4

0.40 ± 0.10 0.96 ± 0.15 3.2 ± 0.5 7.8 ± 1.0 14 ± 2

0.062 ± 0.031 0.11 ± 0.04 0.49 ± 0.11 0.80 ± 0.21 1.4 ± 0.4

0.46 ± 0.10 1.1 ± 0.2 3.7 ± 0.5 8.6 ± 1.1 15 ± 2

0.031 0.0954 0.231 0.487 0.931

40.8 89.1 166 275 424

In

67.2 84.0 100.8 117.6 134.4

0.25 ± 0.09 0.48 ± 0.08 1.3 ± 0.2 4.3 ± 0.8 8.4 ± 1.4

0.038 ± 0.019 0.057 ± 0.028 0.20 ± 0.06 0.45 ± 0.13 0.89 ± 0.30

0.29 ± 0.09 0.53 ± 0.08 1.5 ± 0.2 4.7 ± 0.8 9.3 ± 1.4

0.028 0.0845 0.203 0.425 0.805

31.9 70.0 131 219 338

Sn

67.2 84.0 100.8 117.6 134.4

0.17 ± 0.06 0.35 ± 0.08 0.70 ± 0.19 2.1 ± 0.7 4.2 ± 1.0

0.03 ± 0.02 0.043 ± 0.019 0.11 ± 0.03 0.12 ± 0.05 0.44 ± 0.17

0.20 ± 0.06 0.39 ± 0.08 0.81 ± 0.19 2.2 ± 0.7 4.6 ± 1.0

0.025 0.0754 0.180 0.373 0.701

25.0 55.1 103 174 269

Sb

67.2 84.0 100.8 117.6 134.4

0.14 ± 0.04 0.22 ± 0.05 0.34 ± 0.06 0.91 ± 0.21 3.3 ± 0.5

0.028 ± 0.014 0.027 ± 0.014 0.054 ± 0.028 0.10 ± 0.03 0.37 ± 0.13

0.17 ± 0.04 0.25 ± 0.05 0.39 ± 0.07 1.0 ± 0.2 2.3 ± 0.4

0.023 0.0675 0.160 0.33 0.614

19.7 43.5 81.9 138 215

2. The minimum beam current available for measurement by ORTEC 439 integrator is 0.1 nA. However, in some experiments for the L- and M-lines measurements the real beam current on the sample was much less. 3. In addition to X-rays, the irradiated target emits ionization and Auger electrons. To suppress ionization electrons a metal shield at a few hundreds of volts is usually used in PIXE technique.

However, this approach is not appropriate for Auger electrons having the energies corresponding to the K- transition energies of the target atoms (in our case up to 30 keV). It also results in errors in beam charge measurement. Therefore, a new approach based on the use of beam monitor has been developed to measure the number of particles incident

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I. Gorlachev et al. / Nuclear Instruments and Methods in Physics Research B 407 (2017) 86–91 Table 2 The measured and calculated L-shell X-ray production cross sections (in barns). Target

EKr (MeV)

Zn

La + Ll

Lb

Ltot

Ltot ECPSSR

Ltot PWBA

67.2 84.0 100.8 117.6 134.4

17000 ± 4000 49000 ± 8000 120000 ± 20000 130000 ± 20000 210000 ± 30000

734580 1677000 2842900 4078400 5275000

2492200 2898000 3191600 3400900 3547300

Mo

67.2 84.0 100.8 117.6 134.4

35000 ± 6000 55000 ± 10000 77000 ± 13000 110000 ± 20000 150000 ± 30000

5182 19541 50391 103050 180430

474190 659250 835830 998540 1145400

Ag

67.2 84.0 100.8 117.6 134.4

18000 ± 3000 75000 ± 12000 110000 ± 20000 170000 ± 30000 190000 ± 30000

1133 4497 12585 27652 51589

233950 344710 459410 572780 681600

Cd

67.2 84.0 100.8 117.6 134.4

14000 ± 2000 53000 ± 9000 73000 ± 12000 120000 ± 20000 130000 ± 20000

875 3453 9755 21690 40895

205130 305510 411110 516890 619640

In

67.2 84.0 100.8 117.6 134.4

9100 ± 1500 45000 ± 7000 49000 ± 8000 120000 ± 20000 120000 ± 20000

681 2663 7569 17012 32400

179010 269360 365830 463760 559980

Sn

67.2 84.0 100.8 117.6 134.4

7900 ± 1300 40000 ± 6000 45000 ± 7000 110000 ± 20000 110000 ± 20000

534 2059 5872 13315 25596

154940 235380 322510 412110 501140

Sb

67.2 84.0 100.8 117.6 134.4

8200 ± 1500 26000 ± 5000 37000 ± 7000 69000 ± 11000 78000 ± 13000

428 1625 4636 10590 20530

135320 207340 286410 368710 451380

Ta

67.2 84.0 100.8 117.6 134.4

900 ± 120 3700 ± 500 5600 ± 800 7600 ± 1000 11000 ± 1000

960 ± 130 4000 ± 500 5600 ± 800 7100 ± 900 9600 ± 1300

31.0 80.8 179 359 662

10139 17509 26729 37705 50341

W

67.2 84.0 100.8 117.6 134.4

820 ± 110 3300 ± 500 5100 ± 700 6500 ± 900 8600 ± 1100

810 ± 110 3600 ± 500 5300 ± 700 6300 ± 800 7800 ± 1000

28.8 74.7 164 326 597

9092 15796 24208 34242 45816

Pb

67.2 84.0 100.8 117.6 134.4

600 ± 80 3100 ± 400 4800 ± 600 4800 ± 600 3900 ± 500

18 ± 6 130 ± 20 190 ± 30 270 ± 50 150 ± 20

16.4 41.3 86.7 163 285

3732 6853 10901 15820 21566

Bi

67.2 84.0 100.8 117.6 134.4

520 ± 70 2400 ± 300 4200 ± 600 5200 ± 700 7300 ± 1000

21 ± 4 110 ± 20 190 ± 30 270 ± 50 260 ± 40

15.2 38.2 80.0 150 261

3319 6142 9824 14315 19570

on a sample. A molybdenum grid with the transparency of about 50% with the deposited 500 nm Bi layer is used for this goal. The grid is placed in the beam path. Krypton ions are scattered at the bismuth layer at an angle of 120° and detected with the surface barrier detector located at a distance of 35 mm from the grid plane. In the first step the sample holder is removed, and the beam particles are brought into the Faraday cup. In this case the beam current is measured with the current integrator. The simultaneous measurement of a backscattered spectrum and current on the target allows to associate number of the scattered particles with the beam charge on the target. After that, the holder is returned to its original

Lc

position. The simultaneous measurement of the X-ray spectrum from the target and backscattered spectrum from the monitor is performed for the selected energy of the accelerated krypton beam. Number of the backscattered ions from the bismuth surface layer is used to determine the amount of the incident particles. The relative uncertainties of the X-ray production cross sections were calculated by the formula:

dr

r

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  2  2  2  2  2ffi dK f dN x dd deX dNP dK t ¼ þ þ þ þ þ d Nx eX NP Kf Kt

ð4Þ

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Table 3 The measured and calculated M-shell X-ray production cross sections (in barns). Target

EKr (MeV)

Mtot

Mtot ECPSSR

Mtot PWBA

Pb

67.2 84.0 100.8 117.6 134.4

65000 ± 11000 110000 ± 20000 140000 ± 20000 150000 ± 30000 160000 ± 30000

11023 21975 36305 53008 71269

699400 941700 1185900 1423800 1649600

Bi

67.2 84.0 100.8 117.6 134.4

69000 ± 16000 130000 ± 30000 170000 ± 40000 200000 ± 40000 210000 ± 40000

10034 20137 33482 49152 66362

637800 861010 1087600 1310100 1523100

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; dNP b NP – the error in determining and the number of scattered ions, respectively; is the relative error in film thickness determination; term ratio dd d

dK f Kf

is the relative error of X-ray attenuation in the Mylar absorber and t is the relative error of target X-rays self-absorption. term dK Kt The errors in correction of the self-absorption effect and determining of the X-rays number are predominant for the soft X-ray lines due to the high background level. For the K-lines of heavy elements the error in determination of the X-rays number is predominant due to the poor statistics.

3. Results and discussion Tables 1 (K-line), 2 (L-line) and 3 (M-line) contain both individual and total (sum of the individual lines) X-ray productions for 67.2 MeV 84Kr12+, 84.0 MeV, 100.8 MeV, 117.6 MeV 84Kr13+ and 134.4 M'B 84Kr15+. In some cases, only the group of lines can be identified since the energy difference of the individual lines is less than the detector energy resolution. Therefore Table 2 provides only the total Ltot cross sections for Zn, Mo, Ag, Cd, In, Sn, Sb elements and Table 3 provides the total Mtot cross sections for Pb

Fig. 2. Energy variations of the

84

Kr Ktot X-ray production cross sections.

and Bi elements. Tables 1–3 include the errors in the determination of the characteristic X-ray production cross sections obtained from equation (4). The theoretical data, presented in Tables 1–3, were calculated from the single vacancy fluorescence yields, the Coster-Kronig probabilities and the ionization cross sections within the ECPSSR and PWBA approaches using the ISICS code [25]. Fig. 2 shows graphically the dependence of the Ktot X-ray cross sections from the atomic number of the target nucleus at the energies of krypton ions in the range of 67.2–134.4 MeV. The measured Ktot cross sections for 134.4 MeV ions 84Kr15+, as well as those calculated under the ECPSSR and PWBA approaches, are presented in Fig. 3. The dependencies for the other energies of the 84Kr accelerated ions are similar and therefore not presented here. As follows from Fig. 3 the experimental data and data calculated using the ECPSSR model are differed. The two curves come close in the extreme points and lay apart in the region of the middle elements, where Z2 of the target is close to that of the projectile. The observed deviations of the experimental values from the theoretical cross sections at the excitation of target atoms by krypton ions can be explained by the existence of the regions of validity for the various theoretical models [29]. These regions can be determined through the ratios Z1/Z2 and v1/vK, where Z1 and Z2 – the atomic numbers of incident particle and target atom, respectively, and v1 and vK – the ion velocity and the electron velocity in the inner shell of target atom, respectively. The ECPSSR model is

Fig. 3. Comparison of the measured Ktot X-ray production cross sections (red squares) and calculated in the frame of the ECPSSR (blue rhombuses) and PWBA (green triangles) approaches for 134.4 MeV 84Kr15+. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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appropriate for asymmetric and fast collisions 0.3 > Z1/Z2 and v1/ vK > 0.3 [29]. For symmetric and slow collisions one needs to consider the molecular mechanisms of the ion-atom interaction i.e. the overlap of electron shells and the formation of a quasimolecule. These processes are described by the theory of molecular orbitals [30] taking into account the mutual distortion of the atomic orbitals of colliding partners and the quasimolecule formation. In our experiments, the ratios Z1/Z2 and v1/vK are in the ranges: 0.71 < Z1/Z2 < 1.64 and 0.0143 < v1/vK < 0.176 for the K-shells, 0.43 < Z1/Z2 < 1.2 and 0.0266 < v1/vK < 0.729 for the L-shells and 0.43 < Z1/Z2 < 0.44 and 0.218 < v1/vK < 0.266 for the M-shells. Thus, the projectile velocities are insufficient in relation to the K-shell electron velocities for the approaches based on consideration of the colliding particles as individual atoms (ECPSSR, PWBA). In our case it is necessary to take into account the effects caused by the overlap of atomic orbitals and the union of atoms in a quasimolecule (the theory of molecular orbitals). It should lead to increase in the values of ionization cross sections in comparison with the calculated using the ECPSSR model. Thus, it can be assumed that taking into account the quasimolecular effects in the ECPSSR model will allow reducing the differences between the experimental data and the data obtained within the ECPSSR model. The experimental data of krypton induced X-ray production cross sections are not available or scanty in the literature. Early experiments with ions Br, Kr, I, Xe, and Pb were described by Meyerhof et al. in the pioneering series of papers [12,31–33]. These authors tested the K-vacancy productions dependence versus the target atomic number (Z2) for the fixed Z1 and E1 (where E1 is the energy of incident particles) and discovered peculiarities relating to the transition from the atomic region for asymmetric colliding partners to the molecular region for the systems with symmetric collisions. Somewhat later Anholt et al. [34] investigated the dependence of the target atoms inner shells ionization in collisions with ions Ne, Kr, Xe, La, and U at relativistic energies. A general agreement within 30% between the measured cross sections and the predictions of the Born approximation of plane waves (PWBA) was discovered. Finally, in 2006 R. L. Watson et al. [35] measured the K-vacancy production cross sections for accelerated ions argon, krypton and xenon with energies in the range from 2.5 to 25 MeV / nucleon. However, the energies of the accelerated ions, presented in all these experiments, exceeded those used by us. In more recent articles the X-ray production cross sections for projectiles 12C [36], 28Si [37], 12C and 16O [38] are presented. 4. Conclusions This paper presents the experimentally measured krypton induced X-ray production cross sections from the targets with Z from 22 to 83. Krypton beams were produced with the energies ranging from 67.2 MeV to 134.4 MeV, with the 16.8 MeV step. The obtained data were compared with the theoretical predictions of PWBA and ECPSSR models calculated with the ISICS code. The observed deviations of the experimental values from the theoretical cross sections at the excitation of target atoms by krypton ions can be explained by the existence of the regions of validity for the various theoretical models. The experiments carried out are outside the region of the ECPSSR model validity. In our case, in addition to the direct Coulomb interaction it is necessary to take into account the effects caused by the overlap of atomic orbitals and unification of the colliding atoms in the quasimolecule (the theory of molecular orbitals). The process is complicated by the possibility of simultaneous ejection of some electrons from the higher shells of the target atoms in the case of multiple ionized final state of the atom. This should strongly affect the inner shell fluorescence yields. These effects should lead to the increase in

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