On the Overestimation of Efficiency in Relativistic Electron Scattering
Research Article|Updated:2026-03-12
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On the Overestimation of Efficiency in Relativistic Electron Scattering
Ultrafast ScienceVol. 6, Issue 1, (2026)
Affiliations:
The Ultrafast Electron Imaging Laboratory, Department of Chemistry and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo,ON,Canada,N2L 3G1
Grant Brassem, Christian Viernes, Germán Sciaini. On the Overestimation of Efficiency in Relativistic Electron Scattering[J]. Ultrafast Science, 2026, 6(1).
DOI:
Grant Brassem, Christian Viernes, Germán Sciaini. On the Overestimation of Efficiency in Relativistic Electron Scattering[J]. Ultrafast Science, 2026, 6(1). DOI: 10.34133/ultrafastscience.0129.
On the Overestimation of Efficiency in Relativistic Electron Scattering
摘要
Abstract
With the rapid global advancement of relativistic ultrafast electron diffraction systems
the impact of relativistic effects on electron scattering efficiency has attracted renewed attention. Recent reviews emphasize the scaling of the differential elastic-scattering cross-section with increasing electron energy. Although such observations are not formally incorrect
they can lead to a misperception of the relative scattering efficiency of relativistic electrons compared to that of their nonrelativistic counterparts. The scaling originates from analyses conducted in the angular domain
where the compression of the scattering angle (or solid angle ) with increasing energy creates an enhancement of the differential elastic-scattering cross-section
. In this work
we recast the problem in momentum-transfer space
where scattering is accurately accounted for. This transformation eliminates the angular compression artifact and reveals that high-energy scaling follows a simple dependence
with no intrinsic relativistic gain. We demonstrate this by directly integrating relativistic differential elastic-scattering cross-sections from ELSEPA and by applying a straightforward transformation of the well-known Mott–Massey formalism into -space. The results are general
with calculations performed for elements from carbon to gold and for energies between 50 and 5
000 keV. They reproduce the long-established trend in total elastic-scattering cross-sections
in which scattering strength decreases with increasing electron kinetic energy. Practically
at energies above roughly 50 keV
scattering is already dominated by the forward direction
and most of the scattered intensity falls within the acceptance range of typical ultrafast electron diffraction detectors.
关键词
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