By D.R. Bates and Benjamin Bederson (Eds.)
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Additional resources for Advances in Atomic and Molecular Physics 11
CLASSICAL RADIATIONTHEORY In the last section we described the relative motion of two charged particles attracted toward one another by a Coulomb force; in describing this motion we ignored the field radiated by the accelerating charges. In this section we include this emitted radiation in order to introduce the simplest example of the correspondence principle. A vector notation is freely used for the angle variables, 8 = (el, O,, 03),angular frequencies o = (al,a,,03), integer coefficientss = (sl, sz, s3) of Section II,B, and even for quantum numbers n = ( n l , nz, n3).
As a consequence of scaling the classical ionization cross section $ON, for example, need be obtained as a function of E for only one value of U-the ionization energy of the target atom. Normalization may then be used to obtain the normalized cross section and thus ionization cross section for any other value of U . E. DENSITY-OF-STATES CORRESPONDENCE PRINCIPLE It is generally accepted that macroscopic systems obey the laws of classical mechanics; but the transition from the quantum mechanics of atoms to the classical mechanics of macroscopic systems is more subtle than is 16 I .
Now consider a collision of an incident proton or other ion with the hydrogen atom. The classical channels are Direct scattering 1 + (3, 2) (106a) Ionization 1+2+3 (106b) Charge transfer (1, 2) +3 (106c) These channels cannot be uniquely distinguished by a single parameter like AE as in the previous case. In the final state it is useful to consider a barred or transfer system in which the incident ion is considered to be at rest. The electron 2 has final energy E; in the transfer system, which is negative for charge transfer and positive for ionization.