Title
A surprise in the first Born approximation for electron scattering
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Amsterdam ,
Subject
Chemistry
Source (journal)
Ultramicroscopy. - Amsterdam
Volume/pages
119(2012) , p. 57-62
ISSN
0304-3991
ISI
000308079200010
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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.
E-info
https://repository.uantwerpen.be/docman/iruaauth/8b5710/5e33447.pdf
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