Publication
Title
A surprise in the first Born approximation for electron scattering
Author
Abstract
A standard textbook derivation for the scattering of electrons by a weak potential under the first Born approximation suggests that the far-field scattered wave should be in phase with the incident wave. However, it is well known that waves scattered from a weak phase object should be phase-shifted by pi/2 relative to the incident wave. A disturbing consequence of this missing phase is that, according to the Optical Theorem, the total scattering cross section would be zero in the first Born approximation. We resolve this mystery pedagogically by showing that the first Born approximation fails to conserve electrons even to first order. Modifying the derivation to conserve electrons introduces the correct phase without changing the scattering amplitude. We also show that the far-field expansion for the scattered waves used in many texts is inappropriate for computing an exit wave from a sample, and that the near-field expansion also give the appropriately phase-shifted result. (C) 2011 Elsevier B.V. All rights reserved.
Language
English
Source (journal)
Ultramicroscopy. - Amsterdam
Publication
Amsterdam : 2012
ISSN
0304-3991
Volume/pages
119(2012), p. 57-62
ISI
000308079200010
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
[E?say:metaLocaldata.cgzprojectinf]
Optimal experimental design for quantitative electron microscopy.
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 22.11.2012
Last edited 11.10.2017
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