By David Bates, Benjamin Bederson
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The aim of this text is to study spontaneous emission from a number of assorted viewpoints, even supposing a wide a part of it will likely be dedicated to the quantum statistical theories of spontaneous emission that have been built lately, and to discussing the interrelations between diversified ways.
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121) are set equal to zero, then a system of uncoupled Riccati-type equations is obtained, which can be solved exactly. )I2 =Po,l(l - PO“) (1 25) where Po, is the exact probability for the two-state problem. Inserting Eq. ( 125) into Eqs. ( 123), one obtains the probability Wonfor population of the nth state in the charge transfer process: - Won= T-IPonFn, P, = n (1 - Po,) ( 126) m#n - Thus, apart from the normalization factor T-l, probability Wonis expressed as a product of the two-state probability Po,for the 0 n transition and the probability p,, that during the collision, transition to other states does not occur.
K. Janev the eikonal cross section can be evaluated analytically. It takes the form of a product of the first-order Brinkman - Kramers cross section oBK and a factor which varies slowly with the quantum numbers of the final state, and the ratios of partial cross sections in the eikonal approximation are given approximately by OR,, although the absolute magnitude is very different. , 1978). As can be seen from Eqs. (1 57) and (1 58), the second-order term in the expansion in powers of 2, of a,(b, co)is purely real, whereas the corresponding term in the Brinkman - Kramers series is complex.
This method has not, as yet, been extensively applied to the Z H( 1s) system for large Z , but for small Z it is very successful. For example, the experimental data for the Li3+ H reaction are very well represented by the computed cross sections + + ELECTRON CAPTURE 49 t h 10 102 Energy LkeV) FIG. 10. , 1978). (see Fig. , 1979; Crothers and Todd, 1980). As Crothers (1982) has shown, the CDW model is capable of further development, by using the functions yi and t,uf as the basis of a two-state coupled-channel calculation.