Fly-through relaxation ground state

It is assumed here that the molecule in its ground (initial) state a either crosses the light beam without collisions, or passes, as the result of collisions with rate 7, into another state with different rovibronic numbers. Elastic collisions, including disorienting collisions, are neglected in this case if they do not remove molecules from state a. The corresponding fluorescence intensity has to be calculated from (3.39), where pa is replaced by p according to (3.40). 

Let us consider the limiting case, namely the absence of collisions, assuming that icoi = 0 in (3.40), in other words that the mean free path considerably exceeds the characteristic diameter of the beam. 

For the case of a rectangular beam profile, where the power density wp(y, z) = Wpr(y,z) = 0 at y2 + z2 (see Fig. 3.19) and possesses constant value wp inside the circle y2 + z2 r2, it can be found, within the limit Bwpro/vp — 00, that the analytical solution has the following form (with accuracy up to a constant)  

In other words, one may speak here of a certain fly-through lifetime Tq of the optically depopulated lower level. 

At small values of BWpVp/ro the dependence approaches an exponential one (see Fig. 3.20(6, c), curve 1). However, the exponent of the approximating exponential curve depends on Bwpvp/ro, which deprives the parameter A l in (3.42) of the conventional meaning of lifetime . 

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