Fly-through relaxation

It is important to produce a simultaneous description of collisional and fly-through relaxation. At first sight this appears to be a simple enough problem, namely, similarly to the excited state (2.42), one must introduce the total rate 7s additively ... 

The problem of passing from the dimensionless parameter x = p/lT, to values of 7s in s-1 has been approached in different ways. The simplest idea is to use extrapolation in the x 1(N) dependence to N = 0, leading to 7coi = 0 and 7s = 70 if one assumes that (3.2) holds. This allows us to obtain Tp = 7ox(0) by evaluating the fly-through relaxation rate 70 as a reciprocal transit time of molecules with the most probable velocity through the effective diameter of the laser beam [102]. 

Fig. 3.20. Signals of fluorescence kinetics representing fly-through relaxation of an optically depopulated initial level (a) rectangular profile of the beam (b) limited Gaussian profile (c) unlimited Gaussian profile (d) experimentally registered signal. Values of the non-linearity parameter Bwpvp/ro are shown in brackets.

The kinetics signal registered in [13] for K2(X1S+, 1,73) under condition of prevalence of fly-through relaxation is shown in Fig. 3.20(d) and demonstrates the expected delay . The solid line represents calculated data in accordance with (3.38), (3.39) and (3.40), applying experimentally measured distributions wPtPr(y,z) by scanning the diaphragm (0.1 mm diameter). The distributions obtained were close to the Gaussian with 2ro = 3 mm. 

Here Maxwellian distribution of particle velocities is assumed. It can be seen that widening of the entrance slit l diminishes the role of fly-through relaxation. Substituting the expressions obtained into (2.24), it becomes possible to calculate the intensity I(t — to)- If we assume that To — Ti = 1 2 = T the expression becomes independent of the light polarization and transition type of the observation and excitation, and is quite simple ... 

Fig. 3.21. Connection between the pumping parameter x-1 and the rate of collisional relaxation 7col in the fly-through region 7 < vp/ro (a), and the collisional region 7coi > vp/ro (b). a(jcoi) shows the calculated dependence of the exponent (3.33) on the collisional relaxation rate (c). The beam diameter is assumed to be 2ro = 3 mm.

The elapsed time for particles to pass through the shock front may be approximated by dv/U. Since U is of the same order of magnitude as the speed of sound in the gas, the ratio of the flying time to the Stokes relaxation time of a particle can be expressed by... 

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