Line width collision

Fig. 3.7. The CARS line width dependence on T = 1 /cqqte at different collision strengths [144] (1) y = 0 (strong collisions) (2) y = 0.4 (3) y =0.7 (4) y = 0.9 (5) y — 1 (weak collisions). The dots denote the perturbation theory result A < = 2coQ/r.

Fig. 3.8. The Q-branch Raman width alteration with condensation of nitrogen. The theoretical results for the strong (A) and weak (B) collision limits are shown together with experimental data for gaseous [89] ( ) and liquid nitrogen [145] ( ) (point a is taken from the CARS experiment of [136]). The broken curves in the inset are A and B limits whereas the intermediate solid curve presents the rotational contribution to line width at y = 0.3. The straight line estimates the contribution of vibrational dephasing [143], and the circles around it are the same liquid data but without rotational contribution.

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

Fig. 5.19. Experimental line width and calculated line widths predicted by the fitting laws in binary collision approximation [251] (o) experimental (+) PEG (A) ECS-EP ( ) MEG ( ) ECS-P.

Measurement of integrated absorption requires a knowledge of the absorption line profile. At 2000-3000 K, the overall line width is about 10-2 nm which is extremely narrow when compared to absorption bands observed for samples in solution. This is to be expected, since changes in molecular electronic energy are accompanied by rotational and vibrational changes, and in solution collisions with solvent molecules cause the individual bands to coalesce to form band-envelopes (p. 365). The overall width of an atomic absorption line is determined by ... 

This formula is valid as soon as (Aco)-1, where Aco is the interval over which f(a>) varies appreciably. This interval is here the line width and (Aco)-1 plays the role of a collision time. We now analyse successively the various terms of the collision operator. 

The second factor involves the theory that defines the natural width of the lines. Radiations emitted by atoms are not totally monochromatic. With plasmas in particular, where the collision frequency is high (this greatly reduces the lifetime of the excited states), Heisenberg s uncertainty principle is fully operational (see Fig. 15.4). Moreover, elevated temperatures increase the speed of the atoms, enlarging line widths by the Doppler effect. The natural width of spectral lines at 6000 K is in the order of several picometres. 

The sample must be in the gas phase. Microwave absorption lines are considerably broadened by molecular collisions at intermediate and high pressures at atmospheric pressure, microwave absorption lines are tens of thousands of megacycles wide. Hence the gas is kept at low pressure, typically 0.01 to 0.1 torr under these conditions, line widths run about MHz. The compound studied need not be a gas at room temperature, but it must have sufficient vapor pressure to give detectable absorption. To study involatile compounds such as the alkali halides, the waveguide must be heated to 500-1000°C high-temperature microwave spectroscopy presents great experimental difficulties, but it has been used to study most of the alkali halides. 

For a heavier system, such as N2O + Ar, a calculation of rotational transitions and microwave or infrared line widths would follow the same course through the flow chart, as that followed above in detail for HC1 + Ar. However, at the last stage (low j, small b collisions), the number of coupled states would probably be too large for the non-perturbative, fixed classical path calculation to be practical. Then one should calculate "classical S matrices" including interference between trajectories, to cover these remaining collisions. 

While collisional resonances 5 MHz wide are interesting for spectroscopic purposes, what makes them most interesting is that the 5 MHz line width implies that the collision lasts at least 200 ns, a time not much less than the 1 fxs period allowed for the collisions to occur. If the collision linewidths can be reduced to the inverse of the time allowed for the collisions to occur, the collisional resonances become transform limited, and we know when each collision begins and ends. 

Fig. 22 shows the results of photometry of plates similar to that illustrated in Fig. 21. The relative intensities of suitable transitions were determined from the asymptotic limit at long time delays when the system attains equilibrium. (These resemble, but are not identical to, the relative/ values because of the usual instrumental effects which depend on line width.) The time variation of the relative concentrations is shown in Fig. 23 the upper four levels attain Boltzmann equilibrium amongst themselves after 100 /isec, to form a coupled (by collision) system overpopulated with respect to the 5DA state. The equilibration of the upper four levels causes the initial rise (Fig. 22) in the population of Fe(a5D3). Thus relaxation amongst the sub-levels is formally similar to vibrational relaxation in most polyatomic molecules, in which excitation to the first vibrational level is the rate determining step. In both cases, this result is due to the translational overlap term, for example, in the simple form of equation (14) of Section 3.

In studies of bulk gas samples, as in conventional microwave absorption experiments, one must take account of the fact that one is studying an assembly of molecules moving in different directions at different velocities, and suffering frequent collisions which change both the velocity and direction. It may be shown that for a gas at thermal equilibrium, the Doppler full line width Av at half-height is given by... 

Radiation damping No collisions or or quantum mechanical interactions uncertainty (natural line width)... 

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