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Doughnut effect with relativistic electrons and a Si crystal

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Abstract

We present here the results of an experimental and theoretical study of the transmission of relativistic electrons through the  <\(100\)> axial channels of a Si crystal. The electron kinetic energy is 255 MeV and the crystal thickness 470 nm. The measurements were done for different tilt angles of the channel axis relative to the velocity vector of the incident electron beam. The calculations have been performed using the theory of crystal rainbows. The interaction of an incident electron and a crystal’s atom has been described by Molière’s approximation of the Thomas–Fermi interaction potential. We have used the continuum approximation, included the thermal vibrations of the crystal’s atoms, and disregarded the energy loss and the dispersion of the channeling angle of the electrons, caused by their collisions with the crystal’s atoms. The angular distributions of transmitted electrons have been generated by solving the electron equations of motion and using a computer simulation method. They have been analyzed via the corresponding rainbow patterns. The comparison of the obtained experimental and theoretical results for two values of the tilt angle has demonstrated that the doughnut effect in axial electron channeling is the rainbow effect with a tilted crystal.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request].

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Acknowledgements

The theoretical part of the research presented in this paper was funded by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through the Grant No. 451-03-47/2023-01/200017, with the calculations carried out partly using the Hybrilit heterogeneous cluster computer at the Joint Institute for Nuclear Research, Dubna, Russia. The experimental part of the work was supported in part by JSPS KAKENHI Grant Number JP17K05483.

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Authors and Affiliations

  1. World Academy of Art and Science, Napa, CA, USA

    N. Nešković

  2. Vinča Institute of Nuclear Sciences, University of Belgrade, P. O. Box 522, 11001, Belgrade, Serbia

    M. Ćosić

  3. SAGA Light Source, Tosu, Saga, Japan

    Y. Takabayashi

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  1. N. Nešković
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Correspondence to M. Ćosić.

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Nešković, N., Ćosić, M. & Takabayashi, Y. Doughnut effect with relativistic electrons and a Si crystal. Eur. Phys. J. Plus 139, 196 (2024). https://doi.org/10.1140/epjp/s13360-024-04963-0

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