https://doi.org/10.1140/epjp/s13360-024-04963-0
Regular Article
Doughnut effect with relativistic electrons and a Si crystal
1
World Academy of Art and Science, Napa, CA, USA
2
Vinča Institute of Nuclear Sciences, University of Belgrade, P. O. Box 522, 11001, Belgrade, Serbia
3
SAGA Light Source, Tosu, Saga, Japan
Received:
11
December
2023
Accepted:
31
January
2024
Published online:
26
February
2024
We present here the results of an experimental and theoretical study of the transmission of relativistic electrons through the <> 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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.