Oscillator strength definition

To further reduce of the cross section formula (4.11), we note that it is proportional to the area of the curve of Fn(K)/en plotted against In (Kag)2 between the maximum and minimum momentum transfers. Since T is large and the generalized oscillator strength falls rapidly with the momentum transfer, the upper limit may be extended to infinity. In addition, the minimum momentum transfer decreases with T in such a manner that the limit Fn(K) may be replaced by /, the dipole oscillator strength for the same energy loss. This implies that a mean momentum transfer can be defined independently of T such that the relevant area of the curve of Fn(K)/ n is equal to (// ) [ (In Kag)2 - (In Ka0)2]. Thus, by definition (Bethe, 1930 Inokuti, 1971),... 

Comparison with Eq. (A3.5) then leads to the definition of a dimensionless oscillator strength ... 

In eq. (13-1) the first equality gives the definition of the oscillator strength in the dipole-length representation, while the second equality gives the definition in the momentum (or velocity) representation. As usual, and T, are the total molecular wavefunctions for the final and initial states, and Ef and Et are the energies of the final and initial states, respectively. 

Recalling the definition of the generalized oscillator strength (II.4) and using equation (11.24), we find... 

It can be seen from Fig. 25 that there is no evidence for any significant increase in oscillator strength at the A -ionization edge in the CO+ + spectrum, and this, in part, may well be the result of PCI (see Refs. 152-155 and also section V.B). Similar results were obtained for nitrogen,173 but the interpretation is less certain because of the superimposition of N+ and N2++. More definitive quantitative work on the inner-shell... 

Finally, it is useful to extend the definition of oscillator strength above the ionization limit using... 

In the crude Born-Oppenheimer approximations, the oscillator strength of the 0-n vibronic transition is proportional to (FJ)2. Furthermore, the Franck-Condon factor is analytically calculated in the harmonic approximation. From the hamiltonian (2.15), it is clear that the exciton coupling to the field of vibrations finds its origin in the fact that we use the same vibration operators in the ground and the excited electronic states. By a new definition of the operators, it becomes possible to eliminate the terms B B(b + b ), BfB(b + hf)2. For that, we apply to the operators the following canonical transformation ... 

The first electronic transition in butadiene has been the subject of many experimental and theoretical studies.The absorption, which has a maximum at 2100 A., is strong and represents a tt tt transition from a ground singlet to an upper singlet state. Analysis of the spectrum, which shows very little structure, has not been carried out. Since no fluorescent radiation has ever been detected on excitation of any of the simple dienes even at low temperature, a definite assignment of the 0 — 0 band has not been made. The 0 — 0 band had been placed at 2300 A. (124 kcal./mole), at which point the absorption is only /so as intense as at its maximum. The oscillator strength is 0.53, which leads to a radiative lifetime of 10 sec. Since emission of radiation has not... 

Almost all of the semiconductor clusters prepared so far show red-shifted broad band luminescence (e.g., Figure 13). These luminescences cannot be attributed to states that are populated directly by optical absorption. Rather, they are usually associated with defects such as vacancies, interstitials, impurities, and so on (Figure 10). These defect states have low oscillator strength and therefore are not observable in the absorption spectrum. Very few definitive facts are known about the nature of these defects, except that they are located mostly on the surfaces of the cluster. 

To relate oscillator strengths to the above derived equations, we now return to our definition of absorption intensity, as follows ... 

Here, e is the electron charge, /is the oscillator strength, and me is the mass of the electron. It has been found that abetter definition of oscillator strength can be given in terms of the electric field which exists between states, as follows ... 

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