Abstract
This study is devoted to the construction of the universal ion–crystal interaction potential in proton transmission through very thin crystals. We show how to obtain the interaction potential by using the crystal rainbow theory and rainbows’ morphological analysis in the proton transmission angular plane. By adjusting the shapes of rainbow lines, we modified the Molière’s interaction potential to make it accurate in all regions of the crystal channels. This procedure was based on our previous experimental and theoretical works. As a result, the two axial channeling directions can be treated in the same way leading to more consistent values of the fitting parameters in the ion–atom interaction potential. We obtained the universal rainbow ion–crystal interaction potential for very thin cubic crystals in the (001) and (111) orientations in the case of transmission channeling of 2 MeV proton beam.
Graphic abstract
Similar content being viewed by others
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors' comment: The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request]”.
References
M. Nastasi, J.W. Mayer, J.K. Hirvonen, Ion-Solid Interaction: Fundamentals and Applications (Cambridge University Press, Cambridge, 1996)
B. Schmidt, K. Wetzig, Ion Beams in Materials Processing and Analysis (Springer, Vienna, 2013)
J. Lindhard, Influence of crystal lattice on motion of energetic charged particles. K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 34(14), 1–64 (1965). https://doi.org/10.4236/epe.2020.121001
D.S. Gemmell, Channeling and related effects in the motion of charged particles through crystals. Rev. Mod. Phys. 46, 129 (1974). https://doi.org/10.1103/RevModPhys.46.129
Gert Moliere, Theorie der Streuung schneller geladener Teilchen I. Einzelstreuung am abgeschirmten Coulomb-Feld. Zeitschrift für Naturforschung A 2(3), 133–145 (1947). https://doi.org/10.1515/zna-1947-0302
J.F. Ziegler, J.P. Biersack, M.D. Ziegler, J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids (Pergamon Press, New York, 1985)
O.B. Firsov, Calculation of the interaction potential of atoms. Sov. Phys. JETP 6, 534 (1958)
S. Petrović, L. Miletić, N. Nešković, Theory of rainbows in thin crystals: The explanation of ion channeling applied to Ne10+ ions transmitted through a <100> Si thin crystal. Phys. Rev. B 61, 184 (2000). https://doi.org/10.1103/PhysRevB.61.184
M. Motapothula, Z.Y. Dang, T. Venkatesan, M.B.H. Breese, M.A. Rana, A. Osman, Axial ion channeling patterns from ultra-thin silicon membranes. Nucl. Instrum. Methods Phys. Res. B 283, 29 (2012). https://doi.org/10.1016/j.nimb.2012.04.006
S. Petrović, N. Nešković, M. Ćosić, M. Motapothula, M.B.H. Breese, Proton–silicon interaction potential extracted from high-resolution measurements of crystal rainbows. Nucl. Instrum. Methods Phys. Res. B 360, 23 (2015). https://doi.org/10.1016/j.nimb.2015.07.104
M. Motapothula, S. Petrović, N. Nešković, Z.Y. Dang, M.B.H. Breese, M.A. Rana, A. Osman, Origin of ringlike angular distributions observed in rainbow channeling in ultrathin crystals. Phy. Rev. B 86, 205426 (2012). https://doi.org/10.1103/PhysRevB.86.205426
M. Ćosić, M. Hadžijojić, R. Rymzhanov, S. Petrović, S. Bellucci, Investigation of the graphene thermal motion by rainbow scattering. Carbon 145, 161 (2019). https://doi.org/10.1016/j.carbon.2019.01.020
M. Hadžijojić, M. Ćosić, R. Rymzhanov, Morphological analysis of the rainbow patterns created by point defects of graphene. J. Phys. Chem. C 125, 21030 (2021). https://doi.org/10.1021/acs.jpcc.1c05971
H.F. Krause, J.H. Barrett, S. Datz, P.F. Dittner, N.L. Jones, J. Gomez del Campo, C.R. Vane, Angular distribution of ions axially channeled in a very thin crystal: experimental and theoretical results. Phys. Rev. A 49, 283 (1994). https://doi.org/10.1103/physreva.49.283
S. Petrović, N. Starčević, M. Ćosić, Universal axial (0 0 1) rainbow channeling interaction potential. Nucl. Instrum. Meth. Phys. Res. B 447, 79 (2019). https://doi.org/10.1016/j.nimb.2019.03.050
N. Starčević, S. Petrović, Crystal rainbow channeling potential for (001) and (111) cubic crystallographic crystals. Nucl. Inst. Methods Phys. Res. B. 499, 39 (2021). https://doi.org/10.1016/j.nimb.2021.03.004
X. Artru, S.P. Fomin, N.F. Shulga, K.A. Ispirian, N.K. Zhevago, Carbon nanotubes and fullerites in high-energy and X-ray physics. Phys. Rep. 412, 89 (2005). https://doi.org/10.1016/j.physrep.2005.02.002
Acknowledgements
The author acknowledges the support of the Ministry of Science, Technological Development and Innovation of Serbia under the contract No. 451-03-47/2023-01/ 200017.
Author information
Authors and Affiliations
Contributions
All authors contributed to the study’s conception and design. Material preparation, data collection, and analysis were performed by NS and SP. The first draft of the manuscript was written by NS, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
T.I.: Physics of Ionized Gases and Spectroscopy of Isolated Complex Systems: Fundamentals and Applications.
Guest editors: Bratislav Obradović, Jovan Cvetić, Dragana Ilić, Vladimir Srećković and Sylwia Ptasinska.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Starčević, N., Petrović, S. Universal axial rainbow channeling interaction potential. Eur. Phys. J. D 77, 61 (2023). https://doi.org/10.1140/epjd/s10053-023-00641-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjd/s10053-023-00641-5