On the Bethe approximation
- 28 December 1978
- journal article
- Published by IOP Publishing in Journal of Physics B: Atomic and Molecular Physics
- Vol. 11 (24) , 4271-4282
- https://doi.org/10.1088/0022-3700/11/24/019
Abstract
It is shown that in the limit of infinite impact energies the Coulomb-Bethe total collision cross section tends to twice the value given by the Born approximation. The discrepancy can be removed by introducing a lower cut-off in the partial-wave expansion in order to exclude close encounters for which the Coulomb-Bethe approximation is invalid. The approximation introduced by Bethe for electron impact excitation of a neutral target has been reformulated. The results generalised Bethe approximation is valid at all energies and involves a more precise definition of the cut-off than that suggested by Bethe. It also gives cross sections of correct form for transitions with vanishing oscillator strength.Keywords
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