Slowly varying continuum approximation

It is often the case that the Franck-Condon factors contained in dq(ij) vary sufficiently slowly over the range of E encompassed by the dump pulse to be regarded as constant [191], (This assumption, called the slowly varying continuum approximation is discussed in detail in Chapter 10). Under these circumstances we can use the following generalized Parseval s equality to show that P(q) is independent of the coherence properties of the dump pulse. Specifically we have... 

By invoking the slowly varying continuum approximation (SVCA) [Eq. (10.13)1 WB v. obtain the two-photon analog of Eq. (10.15) ... 

The derivation of Eqs. (102-104) invokes the slowly varying continuum approximation (SVGA) [253] ("flat" continuum approximation), according to which the Rabi frequencies are approximated as = i k,e E) ... 

Equations 8.13 can be further simplified using the flat continuum or slowly varying continuum approximation (SVGA). This approximation assumes that the variation of the continuum-bound dipole matrix elements with energy over the pump laser bandwidth is negligible. With this assumption, and after changing the lower limit of integration over each continuum channel to —oo, we can rewrite the second term in Equation 8.14 as... 

This approximation, called the flat continuum or slowly varying continuum approx- imation (SVCA) [191, 325, 326] localizes the autocorrelation function in time, since by Eqs. (10.9) and (10.12)... 

It follows from Eq. (10.15) that a slowly varying continuum acts as an irreversible perfect absorber since in this approximation bx(t) decreases monotoni-cally (though not necessarily as a simple exponential) with time. 

Because /lisa relatively slowly varying function of Reynolds number, the efficiency varies approximately as which means that fine fibers are more efficient aerosol collectors than coarse ones. Because Pe = // ), tj/f ond for the continuum and... 

The simplest (though approximate) solution of Eq. (10.11) is obtained by assuming that all the continua are flat, that is, that the bound-continuum matrix elements vary slowly with energy and can be replaced by their value at some average energy, say El = Ei + fi(oh... 

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