By D.R. Bates and Benjamin Bederson (Eds.)
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Additional info for Advances in Atomic and Molecular Physics 11
AN EXTENSION OF BOHR’SCORRESPONDENCE PRINCIPLE In Section V we obtain classical cross sections for the excitation of atoms by charged particles. On applying the density-of-states correspondence principle of Section II,E for high incident energies El one obtains cross sections which are proportional to l/El; this is the wrong asymptotic form, which should be proportional to (In El)/El. In this section we describe how an extension of Bohr’s correspondence principle has been used to obtain the correct asymptotic form of these cross sections.
Quantum Mechanics Applied to Excitation A. THEBORNAPPROXIMATION The Born approximation and its derivative, the Bethe approximation, are the only time-independent theories that can be readily applied to transitions between highly excited states. The mean cross section for transitions between states of a given (n, I), (n', 1') in the Born approximation is and for transitions between levels, Here hk and hk' are the initial and final momentum of the incident particle and hK the momentum transferred to this particle, which has charge Z, e.
Classical binary encounter theory may be used when the collisions are sudden, that is when the interaction time is short when compared to the period of the orbit, and the resultant energy transfer sufficiently large. For high enough normalized incident particle energies b l ,those for which 8' g 1 (136) one approximation or the other may be used, and there is a range of impact parameters b a 6 b G bad = bo/vl (137) for which both theories are valid. For incident energies 2 , satisfying (136) a combined theory can be formulated, which is valid for all impact parameters b and energy transfers AE (Percival, 1973b).
Advances in Atomic and Molecular Physics 11 by D.R. Bates and Benjamin Bederson (Eds.)