By D.R. Bates and Benjamin Bederson (Eds.)

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**Extra resources for Advances in Atomic and Molecular Physics 11**

**Sample text**

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 .

The validity of these approximations is discussed in Section VI. Applying Heisenberg’s form of the correspondence principle we obtain m 2nlo S(y‘, y) = J‘0 dr exp i dtV‘(x(r), t)/ (Sudden) (81) I . C . Percival and D. Richards 28 where S W ~ = E, - E,, - y’, w being the fundamental frequency of the classical motion. In the time-independent formulation of the scattering problem only the Born approximation and its derivative, the Bethe approximation (see Section VI), have the simple form of a matrix element.

The entries are to be multiplied by the powers of 10 given in brackets Because C(4) is close to the binary encounter form for large q, the theory of this section reduces to the binary encounter theory in that limit, which is also the limit of large energy transfers. However, as given by inequality (137), the range of validity of the classical dipole perturbation theory overlaps that of the binary encounter theory. Thus although the derivation of the theory in COLLISIONS OF PARTICLES A N D HIGHLY EXCITED ATOMS 45 this section is based on dipole perturbation theory alone, it cannot be justified on the basis of that theory for b 5 a and thus for the largest energy transfers.