Energy Dependency of Proton-Induced Outer-Shell Multiple Ionization for <sub>48</sub>Cd and <sub>49</sub>In

Zhou, Xianming; Wei, Jing; Cheng, Rui; Chen, Yanhong; Zhao, Yongtao; Zhang, Xiaoan

doi:https://doi.org/10.1155/2021/6653739

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Research Article | Open Access

Volume 2021 | Article ID 6653739 | https://doi.org/10.1155/2021/6653739

Energy Dependency of Proton-Induced Outer-Shell Multiple Ionization for ₄₈Cd and ₄₉In

Xianming Zhou,^1,2Jing Wei,¹Rui Cheng,³Yanhong Chen,³Yongtao Zhao,^2,3and Xiaoan Zhang^1,3

Academic Editor: Dieter H.H. Hoffmann

Received05 Nov 2020

Revised13 Dec 2020

Accepted18 Dec 2020

Published20 Jan 2021

Abstract

L subshell X-rays of ₄₈Cd and ₄₉In have been measured for the impact of protons with energies from 75 to 250 keV. Obviously, it is found that Lγ₂ (abbreviation Lγ_2,3 for ₄₈Cd and Lγ_2,3,4 for ₄₉In) X-ray emission is enhanced in comparison with Lγ₁ X-ray emission. The relative intensity ratios of Lγ₂ to Lγ₁ X-ray are larger than the atomic data and increase with decreasing proton energy. This is caused by the multiple ionization of outer-shell electrons. To verify this explanation, the enhancements for relative intensity ratio of Lι and Lβ₂ to Lα X-ray in experiments are discussed, and the direct ionization cross sections of 4d, 5s, and 5p electrons are calculated using BEA theory.

1. Introduction

X-ray emission, an important consequential result from ion-atom collisions, involves several inner-shell processes, from primary inner-shell ionization by the incident ions up to the subsequent vacancy decay, including intrashell transitions. The detailed knowledge of X-ray emission provides important information to understand the charged ion-atom interaction mechanism and to test relevant ionization theories [1–4]. Furthermore, accurate parameters of X-ray are required for the application of trace element analysis known as particle-induced X-ray emission (PIXE), which has application in many fields, such as environmental studies, archaeology, biomedicine, and forensic science [5–8].

Multiple ionization, which means more than one orbital electron is knocked off during ion-atom collisions, can be caused by concurrent direct single ionization or subsequent Coster–Kronig (CK) or Auger transitions. Such action can reduce the screening of nuclear charge and alter the fluorescence yield because of the absence of some outer-shell electrons. Consequently, the blue shift of the X-ray energy may occur, and the relative intensity ratio of the subshell X-ray will be changed. As we all know that such multiple ionization can be induced by heavy ions [9–12], that has been also tested and verified in our previous work [13–15]. Besides, this can also be produced by relativistic electron impact and is dependent on the incident energy [16–18]. Generally, the ionization produced by high-energy protons is considered to be single ionization, and the corresponding X-ray data are chosen as the standard atomic data. However, recently, it has been found that the multiple ionization can also be produced by low-energy protons, which is not only discussed in our earlier work [19] but has also been mentioned by other researchers [20–22]. In spite of that, the dependence of multiple ionization on the proton energy is still not clear. Therefore, in this work, such a phenomenon is further investigated, and special attention is devoted to the incident energy dependency. In order to verify such a question clearly, the targets ₄₈Cd and ₄₉In are selected based on their atomic structure, in which the Lγ emission involves the outermost electrons.

1.1. Description of the Experiment

The measurements have been carried out at the 320 kV high-voltage experimental platform at the Institute of Modern Physics, Chinese Academy of Sciences (IMP, CAS) in Lanzhou, China. More details of the experimental system have been described in the previous work [23]. In brief, the protons are produced by the electron cyclotron resonance (ECR) ion source. In order to ensure single collision, the current intensity of the ion beam is regulated and controlled in the magnitude of only few nA. The emitted X-rays are detected by a silicon drift detector (SDD). The SDD is placed at 80 mm far away from the target surface in the chamber and at 135° to the beam direction. The number of incident projectiles, which could not be measured immediately by recording the target current due to the influence of the secondary electron emission, is detected indirectly by the combined use of a penetrable Faraday cup and a common one.

The maximum projected range of the proton in the present work is 1.45 μm and 1.65 μm for Cd and In, respectively. Those are all shorter than the target thickness. The experimental target can be taken as a thick target. The X-ray production cross section can be derived to measure the X-ray yield and the proton’s stopping power [24]. The principal uncertainties for the experimental data result from the X-ray count statistics 5%, incident ions recording 3%, detector efficiency 10%, solid angle 2%, slope calculation of the experimental yield curve 2%, and stopping power calculation 10%. The maximal uncertainty of the yield is about 12%, that of the ratio of the subshell X-rays is about 14%, and that of X-ray production cross section is about 16%.

2. Results and Discussion

In Figure 1, the typical X-ray emission spectra of ₄₈Cd and ₄₉In produced by proton are presented as a function of the proton energy and well fitted by a nonlinear curve Gaussian fitting program. The structure of the spectra is similar for the two targets under different incident energies as a whole. It mainly consists of six distinct lines which are the L subshell X-rays arising from the relative deexcitation of target atomic L vacancies. The first five transitions are the same for both elements and identified as L_ι (3s_1/2-2p_3/2), Lα_1,2 (3d_5/2,3/2-2p_3/2), Lβ_1,3,4 (3d_3/2-2p_1/2, 3p_3/2,1/2-2s_1/2), Lβ_2,15 (4d_5/2,3/2-2p_3/2), and Lγ₁ (4d_3/2-2p_1/2). Due to the difference in the electron configuration for the two elements, there is a small distinction for the sixth line. Electronic configuration of ₄₈Cd atom is 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰5s², but that of ₄₉In atom is 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰5s²5p¹. Therefore, the last peak is L_γ2,3 (4p_3/2,1/2-2s_1/2) and L_γ2,3,4 (4p_3/2,1/2/5p_1/2-2s_1/2) for ₄₈Cd and ₄₉In [25], respectively, and they are abbreviated as “Lγ₂” in order to present the following discussion clearly and briefly.

(a)

(b)

One can see in Figure 1 that although the spectrum of the two targets is similar for various proton energies, there is an obvious decrease in the Lγ₂ X-ray emission with increasing incident energy, compared to Lγ₁ X-ray emission. For further quantitative analysis, the relative intensity ratios of Lγ₂ to Lγ₁ X-ray are extracted from the original data after taking into account the detection efficiency of the detector and the self-absorption inside the target material. As shown in Figure 2, the ratios are larger than the theoretical data of single ionization which is calculated based on the ECPSSR theory [26], and it decreases rapidly and is closer and closer to the atomic data as the proton energy increases, in the present experimental energy region. For example, the enhancement factor, namely, the ratio of the experimental result to the atomic data for Lγ₂/Lγ₁, is about 6 for ₄₈Cd and 7 for ₄₉In at the energy of 100 keV, but those drop approximately to 2 when the energy is 250 keV.

(a)

(b)

It is proposed that the enhancement effect of Lγ₂ X-ray can be understood by the outer-shell multiple ionization. As mentioned in the Introduction, such multiple ionization can also occur for the impact of lower energy proton, except for the case of highly charged heavy ions. When it takes place, owing to the absence of outer-shell electrons, some of the nonradiative transitions, such as Auger transition, CK transition, and super CK transition, are restrained. Accordingly, the radiative transition probability of the X-ray emission is changed [9–12]. As a result, the measured relative intensity ratio of subshell X-ray is altered. Figure 3 gives the experimental results of the intensity ratios of Lι and Lβ₂ to Lα X-ray as a function of the proton energy, respectively, which are all larger than the atomic data [26], decrease with the increase of proton energy, and present a similar trend as that of I(Lγ₂)/I(Lγ₁). Based on that result, an estimation can be deduced that the M and N subshell electrons of ₄₈Cd and ₄₉In are multiply ionized by lower energy proton impacting, as similarly discussed in our previous work [19].

(a)

(b)

Lι and Lα X-rays originate from the main transitions for M₁ and M_4,5 electrons filling the same lower energy vacancy of L₃, respectively. The multiple ionization on M₁ subshell can be regarded as to be insignificant compared to that on M_4,5 shells because of three main reasons. The first is the large deviation of direct ionization due to the difference in binding energy and electron number between various subshells; for instance, the ionization energy of M₁ electrons is about 1.7 times larger than that of M₅ for ₄₈Cd element [27–29], and the single ionization cross section of M₅ electrons is higher than that of M₁ by almost one to two orders of magnitude in the present experimental energy region [26]. The second is the high decay probability of M₁ vacancies via CK effects being promoted to higher M subshells. The last one is that the vacancy production in M₁ shell by CK rearrangement among the L subshells is energetically forbidden. One assumes that, besides the fluorescence yield, the X-ray emission intensity is proportional to the electronic number in the upper energy shell for filling the identical vacancy. The enhancement of ratios of Lι to Lα to the atomic data in Figure 3 indicates directly the multiple ionization in M_4,5 shells, and the diminished trend denotes that the extent of that multiple ionization decreases with the increase of proton energy. For example, the average number of multiple vacancies in M _4,5 shells is estimated using the relationship between the experimental ratios of Lι to Lα and the theoretical values [20, 21, 30, 31]. That is about 5.6 ± 0.8, 5.1 ± 0.7, 4.8 ± 0.7, 4.4 ± 0.6, 3.8 ± 0.5, 4.1 ± 0.6, 4.0 ± 0.6, and 4.1 ± 0.6 for ₄₉Cd and 6.1 ± 0.9, 4.8 ± 0.7, 4.2 ± 0.6, 4.0 ± 0.6, 3.9 ± 0.5, 3.9 ± 0.5, 3.8 ± 0.5, and 3.8 ± 0.5 for ₄₉In, with the proton energy of 75, 100, 125, 150, 175, 200, 225, and 250 keV, respectively.

Lβ₂ and Lα X-rays mainly come from the transitions having the same lower energy level L₃ but different upper levels, i.e., N_4,5 and M_4,5 shells, respectively. When the outer-shell multiple ionization occurs, with the absence of some M and N shell electrons, the Auger transition ratio for filling L₃ vacancies will decrease, while the fluorescence yield ω₃ will be enlarged [9–12, 27–29]. The Auger transition probability a₃ of L₃ vacancies for Cd is almost a factor of 20 and 170 larger than the fluorescence yield of Lα (ω_Lα) and Lβ₂ (ω_Lβ2) X-ray, and that factor is about 18 and 149 for In, respectively [27–29]. Therefore, ω_Lβ2 will have a larger increase than ω_Lα; as a result, the actual emission of Lβ₂ X-ray will present an enlargement compared to that of Lα, namely, the measured relative intensity ratio of Lβ₂ to Lα X-rays is enhanced than the atomic data of the singly ionized atom. Conversely, the results of Lβ₂/Lα in Figure 3 illustrate the multiple ionization of M_4,5 and N_4,5 shells, and it decreases with the increase of incident energy.

Multiple ionization can be produced by concurrent direct Coulomb ionization, charge transfer, or subsequent excitation by CK and Auger transitions. The cross section for the loss of outer-shell electron due to charge transfer can be calculated on the basis of Oppenheimer–Brinkman–Kramer (OBK) approximation [32–35]. For ₄₈Cd impacted by proton with energy of 75–250 keV, this cross section is about 1.96 × 10⁻¹²∼3.92 × 10⁻¹⁰ barn for N shell and 2.57 × 10⁻¹²∼2.01 × 10⁻¹⁰ barn for O shell. For ₄₉In, that is about 8.49 × 10⁻¹²∼2.80 × 10⁻¹⁰ barn for N shell and 3.11 × 10⁻¹²∼1.43 × 10⁻¹⁰ barn for O shell. That is at least 19 orders of magnitude smaller than the direct ionization cross section. So, the multiple ionization results from charge transfer can be neglected for the present result. If leaving the subsequent excitation by nonradiative transitions and the effect of electron correlation out of account, the multiple ionization probability is positive to the single ionization cross section for the direct Coulomb collision. Single ionization is inversely proportional to the binding energy of the related orbital electrons. Besides, the bounding energy of outer-shell electrons is diminished with ascending energy level. So, in consideration of the above confirmed multiple ionization in M and N shells, it is easy to deduce that the O shell electrons of ₄₈Cd and ₄₉In are also multiply ionized by lower energy protons in the present work. That is just the reason for the enhanced emission of Lγ₂ X-ray as shown in Figures 1 and 2.

In order to further clarify the dwindling trend of the multiple ionization reflected in Figure 2, the direct ionization cross sections of some outermost-shell electrons for ₄₈Cd and ₄₉In are simulated theoretically by binary encounter approximation (BEA) model [36], in which the ionization cross section is proportional to the function of the scaled velocity G(V) (, where is the velocity of the projectile, is the velocity of the ionized orbital electron) for a certain collision. Here, the of proton is approximately 1.42–3.15 a.u. (a.u. is atomic units), and the is about 1.10 and 0.73 a.u. for the 4d and 5s electrons of ₄₈Cd, and that is about 1.28 and 0.82 a.u. for the 4d and 5s electrons of ₄₉In and 0.59 a.u. for the 5p electron of ₄₉In, respectively. is in the region of about 1.1∼5.3. The is diminished as a function of . So, those cross sections decrease with the increase of proton energy as given in Figure 4. Taking into account the positive proportion between the single and multiple ionization, one can deduce easily the decrease of the extent for the multiple ionization from the above calculated result of single ionization, which leads to the change of ratios of Lγ₂ to Lγ₁ X-ray as in Figure 2.

(a)

(b)

3. Conclusions

The Cd and In L subshell X-ray emission has been investigated for 75–250 keV proton impact. The relative intensity ratios of some L subshell X-rays are analyzed. The ionization cross sections of some outermost shells are simulated theoretically. The results indicate that, besides the L shell single ionization, the M, N, and O shell electrons of the target atoms are also multiply ionized. The multiple ionization is strongly dependent on the collision energy, and the extent of that is decreased with the increase of proton energy, which results in an obvious enhanced emission of Lγ₂ X-ray compared to Lγ₁ and the enlargement of the relative intensity ratios of Lι/Lα and Lβ₂/Lα; however, such enhancement is gradually diminished as a function of incident energy.

Data Availability

The basic data used to support the findings of this study can be found in the figures of the study.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the National Key R&D Program of China under Grant no. 2017YFA0402300, the National Natural Science Foundation of China (Grant nos. 11505248, 11775042, 11875096, U1532263, 11605147, and 11775278), Scientific Research Program funded by Shaanxi Provincial Education Department (Grant no. 20JK0975), Scientific Research Plan of Science and Technology Department of Shaanxi Province (Grant no. 2020JM-624), and Xianyang Normal University Science Foundation (Grant nos. XSYK20009 and XSYK20024). The authors sincerely acknowledge the technical support from the group of 320 kV HCI platform.

References

J. Miranda, G. Murillo, B. Méndez et al., “Measurement of L X-ray production cross sections by impact of proton beams on Hf, Ir, and Tl,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 316, pp. 113–122, 2013.
View at: Publisher Site | Google Scholar
T. Schenkel, A. V. Hamza, A. V. Barnes, and D. H. Schneider, “Interaction of slow, very highly charged ions with surfaces,” Progress in Surface Science, vol. 61, no. 2–4, pp. 23–84, 1999.
View at: Publisher Site | Google Scholar
D. E. Johnson, G. Basbas, and F. D. McDaniel, “Nonrelativistic plane-wave born-approximation calculations of direct Coulomb M-subshell ionization by charged particles,” Atomic Data and Nuclear Data Tables, vol. 24, no. 1, pp. 1–11, 1979.
View at: Publisher Site | Google Scholar
G. Lapicki, “The status of theoretical L-subshell ionization cross sections for protons,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 189, no. 1–4, pp. 8–20, 2002.
View at: Publisher Site | Google Scholar
N. Siddique, S. Waheed, M. Daud, A. Markwitz, and P. K. Hopke, “Air quality study of Islamabad: preliminary results,” Journal of Radioanalytical and Nuclear Chemistry, vol. 293, no. 1, pp. 351–358, 2012.
View at: Publisher Site | Google Scholar
N. K. Mohammed and N. M. Spyrou, “Trace elemental analysis of rice grown in two regions of Tanzania,” Journal of Radioanalytical and Nuclear Chemistry, vol. 281, no. 1, pp. 79–82, 2009.
View at: Publisher Site | Google Scholar
D. Beasley, I. Gomez-Morilla, and N. Spyrou, “Elemental analysis of hair using PIXE-tomography and INAA,” Journal of Radioanalytical and Nuclear Chemistry, vol. 276, no. 1, pp. 101–105, 2008.
View at: Publisher Site | Google Scholar
A. İ. Garip, “PIXE, particle induced X-ray emission A concise review,” Turkish Journal of Chemistry, vol. 22, pp. 183–199, 1998.
View at: Google Scholar
M. Czarnota, D. Banaś, M. Berset et al., “High-resolution X-ray study of the multiple ionization of Pd atoms by fast oxygen ions,” The European Physical Journal D, vol. 57, no. 3, pp. 321–324, 2010.
View at: Publisher Site | Google Scholar
M. Czarnota, M. Pajek, D. Banas et al., “Multiple ionization effects in X-ray emission induced by heavy ions,” Brazilian Journal of Physics, vol. 36, no. 2b, pp. 546–549, 2006.
View at: Publisher Site | Google Scholar
G. Lapicki, G. A. V. RamanaMurty, G. J. Naga Raju et al., “Effects of multiple ionization and intrashell coupling in L-subshell ionization by heavy ions,” Physical Review A, vol. 70, Article ID 062718, 2004.
View at: Publisher Site | Google Scholar
K. Słabkowska and M. Polasik, “Effect of L- and M-shell ionization on the shapes and parameters of the K X-ray spectra of sulphur,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 205, pp. 123–127, 2003.
View at: Publisher Site | Google Scholar
X. Zhou, R. Cheng, Y. Lei et al., “Ionization of highly charged iodine ions near the Bohr velocity,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 342, pp. 133–136, 2015.
View at: Publisher Site | Google Scholar
X. Zhou, R. Cheng, Y. Lei et al., “Ionization of Ar¹¹⁺ ions during the collisions near the Bohr velocity,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 340, pp. 11–14, 2014.
View at: Publisher Site | Google Scholar
X. Zhou, Y. Zhao, R. Cheng et al., “L-subshell X-ray intensity ratio of Xenon for 6 MeV Xe²⁰⁺ impact on selected targets,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 304, pp. 32–35, 2013.
View at: Publisher Site | Google Scholar
D. H. H. Hoffmann, H. Genz, W. Löw, and A. Richter, “Z and E dependence and scaling behaviour of the K-shell ionization cross section for relativistic electron impact,” Physics Letters A, vol. 65, no. 4, pp. 304–306, 1978.
View at: Publisher Site | Google Scholar
H. Genz, D. H. H. Hoffmann, W. Löw, and A. Richter, “L-shell ionization by relativistic electrons and energy dependence of the Lβ/Lα branching ratio,” Physics Letters A, vol. 73, no. 4, pp. 313–315, 1979.
View at: Publisher Site | Google Scholar
D. H. H. Hoffmann, C. Brendel, H. Genz et al., “Inner-shell ionization by relativistic electron impact,” Zeitschrift für Physik A, vol. 293, pp. I87–I201, 1979.
View at: Publisher Site | Google Scholar
X. Zhou, R. Cheng, Y. Wang et al., “L X-ray production in ionization of ₆₀Nd by 100-250 keV protons,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 408, pp. 140–145, 2017.
View at: Publisher Site | Google Scholar
S. J. Cipolla, “L X-ray intensity ratios for proton impact on selected rare-earth elements,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 261, no. 1-2, pp. 153–156, 2007.
View at: Publisher Site | Google Scholar
S. j. Cipolla and B. P. Hill, “Relative intensities of L X-rays excited by 75–300 keV proton impact on elements with Z = 39–50,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 241, no. 1–4, pp. 129–133, 2005.
View at: Publisher Site | Google Scholar
J. Miranda, O. G. de Lucio, E. B. Téllez, and J. N. Martı́nez, “Multiple ionization effects on total L-shell X-ray production cross sections by proton impact,” Radiation Physics and Chemistry, vol. 69, no. 4, pp. 257–263, 2004.
View at: Publisher Site | Google Scholar
X. Zhou, Y. Zhao, R. Cheng et al., “K and L-shell X-ray production cross section for 50–250 keV proton impact on elements with Z = 26–30,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 299, pp. 61–67, 2013.
View at: Publisher Site | Google Scholar
G. Basbas, W. brandt, and R. Laubert, “Universal cross section for K-shell ionization by heavy charged particles. I. Low particle velocities,” Physical Review A, vol. 7, no. 3, pp. 983–1001, 1973.
View at: Publisher Site | Google Scholar
A. C. Thompson, D. T. Attwood, E. M. Gullikson et al., X-ray Data Book’, Lawrence Berkeley National Laboratory, Livermore, CA, USA, 2nd edition, 2001, http://xdb.lbl.gov/.
W. Brandt and G. Lapicki, “Energy-loss effect in inner-shell Coulomb ionization by heavy charged particles,” Physical Review A, vol. 23, no. 4, pp. 1717–1729, 1981.
View at: Publisher Site | Google Scholar
J. Crawford, D. Cohen, G. Doherty, and A. Atanacio, Calculated K, L and M-shell X-ray Line Intensities for Light Ion Impact on Selected Targets from Z = 6 to 100, Institute for Environmental Research, Australian Nuclear Science and Technology Organization, Sydney, Australia, 2011.
M. O. Krause, “Atomic radiative and radiationless yields for K and L shells,” Journal of Physical and Chemical Reference Data, vol. 8, no. 2, pp. 307–327, 1979.
View at: Publisher Site | Google Scholar
S. I. Salem, S. L. Panossian, and R. A. Krause, “Experimental K and L relative X-ray emission rates,” Atomic Data and Nuclear Data Tables, vol. 14, no. 2, pp. 91–109, 1974.
View at: Publisher Site | Google Scholar
F. P. Larkins, “Dependence of fluorescence yield on atomic configuration,” Journal of Physics B: Atomic and Molecular Physics, vol. 4, no. 5, pp. L29–L32, 1971.
View at: Publisher Site | Google Scholar
Y. Ramakrishna, K. R.. Rao, G. J. N. Raju et al., “L X-ray energy shifts and intensity rations in tantalum with C and N ions—multiple vacancies in M, N and O shells,” Pramana—Journal of Physics, vol. 59, no. 4, pp. 685–691, 2002.
View at: Publisher Site | Google Scholar
V. S. Nikolaev, “Calculation of the effective cross section for proton charge exchange in collisions with multi-electron atoms,” Soviet Physics JETP, vol. 24, pp. 847–857, 1967.
View at: Google Scholar
V. S. Nikolaev, “Calculation of the effective cross section for proton charge exchange in collisions with multi-electron atoms,” Journal of Experimental and Theoretical Physics, vol. 51, pp. 1263–1280, 1966.
View at: Google Scholar
G. Lapicki and F. D. McDaniel, “Electron capture from K shells by fully stripped ions,” Physical Review A, vol. 22, no. 5, pp. 1896–1905, 1980.
View at: Publisher Site | Google Scholar
D. P. Dewangan and J. Eichler, “Charge exchange in energetic ion-atom collisions,” Physics Reports, vol. 247, no. 2-4, pp. 59–219, 1994.
View at: Publisher Site | Google Scholar
J. H. McGuire and P. Richard, “Procedure for computing cross section for single and multiple ionization of atoms in the binary-encounter approximation by the impact of heavy charged particles,” Physical Review A, vol. 8, no. 3, pp. 1374–1384, 1973.
View at: Publisher Site | Google Scholar

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Laser and Particle Beams

Energy Dependency of Proton-Induced Outer-Shell Multiple Ionization for 48Cd and 49In

Abstract

1. Introduction

1.1. Description of the Experiment

2. Results and Discussion

3. Conclusions

Data Availability

Conflicts of Interest

Acknowledgments

References

Copyright

Energy Dependency of Proton-Induced Outer-Shell Multiple Ionization for ₄₈Cd and ₄₉In