It is usually assumed that the first-Born approximation for electron-atom ionization becomes valid for the fully differential cross section at sufficiently high impact energies, at least for asymmetric collisions where the projectile suffers only a small energy loss and is scattered by a small angle. Here we investigate this assumption quantitatively for ionization of hydrogen atoms. We find that convergence of the Born approximation to the correct nonrelativistic result is generally achieved only at energies where relativistic effects start to become important. Consequently, the assumption that the Born approximation becomes valid for high energy is inaccurate, since by the time it converges, nonrelativistic scattering theory is not valid.
S. J. Jones and D. H. Madison, "Slow Convergence of the Born Approximation for Electron-Atom Ionization," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 66, no. 6, pp. 627111-627113, American Physical Society (APS), Dec 2002.
The definitive version is available at https://doi.org/10.1103/PhysRevA.66.062711
Keywords and Phrases
Approximation theory; Electron scattering; Electrons; Energy dissipation; Impact ionization; Asymmetric collisions; Atomic physics
International Standard Serial Number (ISSN)
Article - Journal
© 2002 American Physical Society (APS), All rights reserved.