Download Advances in Atomic and Molecular Physics 11 by D.R. Bates and Benjamin Bederson (Eds.) PDF

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

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Percival and D. Richards The correspondence principles for emission and absorption may be written as follows: CP2. The mean power spontaneously emitted as radiation in the transition n --+ n‘ tends to coincide with the mean emitted power derived b y classical theory from the Fourier components of order s and -s, where s = n - n’. CP3. The mean net power absorbed from incident radiation due to induced upward and downward transitions n ct n’ tends t o coincide with the absorbed power derived b y classical theory from the components of order s and -s.

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.

For incident electrons the derivation of da/dAE is complicated by three effects: (El) Acceleration of the incident electron by the nuclear charge. (E2) Focusing of the incident electron by the nuclear charge. g. p, . Neglect of (E 1) is unsatisfactory, because incident and bound electrons should be treated on the same basis. (El) has often been used without (E2), and leads to better agreement with more exact calculations, but is physically unjustified. , 1933), and even a theory including all three effects can have the same analytic form.

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