Skip to main content
Log in

Universal axial rainbow channeling interaction potential

  • Regular Article – Atomic and Molecular Collisions
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

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

Schematically presented process of transmission of 2 MeV proton beam through very thin silicon crystal

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

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

  1. M. Nastasi, J.W. Mayer, J.K. Hirvonen, Ion-Solid Interaction: Fundamentals and Applications (Cambridge University Press, Cambridge, 1996)

    Book  Google Scholar 

  2. B. Schmidt, K. Wetzig, Ion Beams in Materials Processing and Analysis (Springer, Vienna, 2013)

    Book  Google Scholar 

  3. 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

    Article  Google Scholar 

  4. 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

    Article  ADS  Google Scholar 

  5. 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

    Article  ADS  MATH  Google Scholar 

  6. 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)

    Google Scholar 

  7. O.B. Firsov, Calculation of the interaction potential of atoms. Sov. Phys. JETP 6, 534 (1958)

    ADS  MATH  Google Scholar 

  8. 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

    Article  ADS  Google Scholar 

  9. 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

    Article  ADS  Google Scholar 

  10. 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

    Article  ADS  Google Scholar 

  11. 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

    Article  ADS  Google Scholar 

  12. 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

    Article  Google Scholar 

  13. 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

    Article  Google Scholar 

  14. 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

    Article  ADS  Google Scholar 

  15. 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

    Article  ADS  Google Scholar 

  16. 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

    Article  ADS  Google Scholar 

  17. 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

    Article  ADS  Google Scholar 

Download references

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

Authors

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

Correspondence to N. Starčević.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-023-00641-5

Navigation