Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...409..841j&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 409, no. 2, p. 841-845.
Astronomy and Astrophysics
Astrophysics
34
Atomic Excitations, Electron Impact, Electron Trajectories, Ionization Cross Sections, Approximation, Hyperbolic Trajectories
Scientific paper
The threshold behavior of the electron impact excitation cross sections for hydrogenic ions is investigated using the semiclassical approximation with the hyperbolic orbit for the projectile path, rather than the straight line path. The symmetric approximation is applied to modify the ordinary hyperbolic orbit. The modification factor due to the hyperbolic orbit approximation produces the correct energy dependence of the cross section near the excitation threshold. This result is very similar to that of the quantum mechanical case. The semiclassical enhancement factor due to this simple modification corresponds to the Coulomb focusing factor in the Born-Bethe approximation. In the high-energy limit, the semiclassical cross sections approach the Born-Bethe cross sections, with a finite cutoff in the momentum transfer for dipole transitions.
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