Population of excited levels

In the following subsections we will discuss some experimental methods of lifetime measurements [794,795]. Nowadays lasers are generally used for the selective population of excited levels. In this case, the induced emission, which contributes to the depletion of the excited level, has to be taken into account if the exciting laser is not switched off during the fluorescence detection. The rate equation for the time-dependent population density of the level k), which gives the effective lifetime is then... 

A typical experimental arrangement for such investigations is depicted in Fig. 8.23. In a flow system, where the reactive collisions take place, the levels (u, J) of the reactant molecules are selectively excited by a pulsed infrared laser. The time-dependent population of excited levels in the reactants or the product molecules are monitored through their fluorescence, detected by fast, cooled infrared detectors (Vol. l,Sect. 4.5). 

To compare the relative populations of vibrational levels, the intensities of vibrational transitions out of these levels are compared. Figure B2.3.10 displays typical potential energy curves of the ground and an excited electronic state of a diatomic molecule. The intensity of a (v, v ) vibrational transition can be written as... 

A progression with v = 2, illustrated in Figure 7.18, can be observed only in emission. Its observation could result from a random population of v levels or it could be observed on its own under rather special conditions involving monochromatic excitation from v" = 0 to if = 2 with no collisions occurring before emission. This kind of excitation could be achieved with a tunable laser. 

Figure 10.7 The population of excited energy states relative to that of the ground state for the CO molecule as predicted by the Boltzmann distribution equation. Graph (a) gives the ratio for the vibrational levels while graph (b) gives the ratio for the rotational levels. Harmonic oscillator and rigid rotator approximations have been used in the calculations. The dots represent ratios at integral values of v and 7. which are the only allowed values.

In order to probe the population of rotational levels of the desorbed NO, the time delay between the desorption laser and the LIF probe was flxed, and rotational excitation spectra were recorded. Fixed time delays of 9.0 or 3.0 is (corresponding to velocities of 415 and 1250m/s, respectively) were used to selectively interrogate desorbing molecules belonging primarily to either the thermal or non-Boltzmann component of the total desorbed flux. The desorption Hux in the thermal channel, probed at a time delay of 9.0 /is, was fitted well by a single Boltzmann distribution, with Tf = 200 20 K, somewhat lower than T .,. 

Considering first the case where the population of excited vibrational levels is negligible, we have for the rotational frequencies... 

Now consider the case with appreciable population of excited vibrational levels. The set of molecules with vibrational quantum number v will have its own value of Bv and will give rise to its own pure-rotation spectrum. Thus each line in Fig. 4.5 will have a series of vibrational satellites. Bv is given by (4.75), where ae is small compared to Be, so that the vibrational satellites lie near the main line. These satellites are shown for the transition in Fig. 4.6. Note the rapid decrease in intensity... 

As previously mentioned, for most diatomic molecules at room temperature, the population of excited vibrational levels is negligible. We therefore first consider transitions for which the initial vibrational level is u = 0. The selection rules (4.108) allow the transitions v = 0- l, 0— 2,... 

A more sophisticated version of the Tannor-Rice scheme exploits both amplitude and phase control by pump-dump pulse separation. In this case the second pulse of the sequence, whose phase is locked to that of the first one, creates amplitude in the excited electronic state that is in superposition with the initial, propagated amplitude. The intramolecular superposition of amplitudes is subject to interference whether the interference is constructive or destructive, giving rise to larger or smaller excited-state population for a given delay between pulses, depends on the optical phase difference between the two pulses and on the detailed nature of the evolution of the initial amplitude. Just as for the Brumer-Shapiro scheme, the situation described is analogous to a two-slit experiment. This more sophisticated Tannor-Rice method has been used by Scherer et al. [18] to control the population of a level of I2. The success of this experiment confirms that it is possible to control population flow with interference that is local in time. 

This technique is known as the passive Q-switch. The dye acts as an absorber for weak light, so that the population of excited atoms or molecules in the active material can increase until its maximum level is reached. The dye cell is in fact a high-speed shutter. 

Population Nk(t) of excited level k decreases with time, obeying an exponential law... 

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