By D.R. Bates and Benjamin Bederson (Eds.)
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Extra resources for Advances in Atomic and Molecular Physics 11
The first two terms in the asymptotic expansion in l/El are the same as for (EO), and the remaining terms are comparatively small in the region where the binary encounter theory is valid. l Banks' thesis (1972) contains a comprehensive review of analytic forms and conditions of validity for binary encounter cross sections obtainable at that time. The above binary encounter cross sections are valid for target atoms or ions. For atoms they are strictly high energy approximations, as shown by comparisons with Monte Carlo and combined theory cross sections, but the somewhat unphysical though often used approximation of including acceler- COLLISIONS OF PARTICLES A N D HIGHLY EXCITED ATOMS 39 + ation (El) without focusing introduces a further factor El /(El 2U), which makes the electron ionization cross section reasonable for El > 4U.
This theory is an improvement on normal binary encounter for low energy charge transfer and ionization. D. CLASSICAL DIPOLE PERTURBATION THEORY Let 1 be the incident particle of charge Z1e and mass m, and (2, 3) the target atom, consisting of an electron 2 of charge - e and mass me orbiting around a nucleus 3 of positive charge 2, e and mass m3 much larger than m e . Typically Z , = - 1 for an incident electron and + 1 for an incident proton. The following approximations are made: Al. The atom is supposed to be originally at rest with its center of mass at the origin.
As a result methods based upon the SCCP are adequate, and cross sections can be obtained relatively easily. First we consider the approximation of Beigman et al. (1969); they have shown that the transition amplitude for one degree of freedom is given approximately by the expression j 2R S(y', y) = lim t+m dB exp i 0 where W(0, t ) is the change in the classical action of the bound system due to the perturbation. It can be shown (Richards, 1972) that W(0, t ) = jt dt'Vc((x(8+ w(t' - t ) ) , t') (89) -m which, on substitution into (88) and taking the limit as t + co, gives (83), apart from an arbitrary phase factor.
Advances in Atomic and Molecular Physics 11 by D.R. Bates and Benjamin Bederson (Eds.)