Population dummy-level

Dummy level population. With no laser, the population of the dummy level is set at 11% of the total, the thermal equilibrium fraction in v=l at 2000°K. Because vibrational energy transfer rates are generally slow, the laser excitation causes a sizeable fraction of the total to be pumped into the dummy level. Fig. 3 shows the dummy level population for three laser intensities as a function of assumed a. (In the imensionless notation used in the computer, 1=1 corresponds to 10 erg sec- cm Hz-, or that of the unfocussed output of the fundamental from an efficient dye pumped by a powerful doubled Nd YAG laser). At the nominal 0.4 A, nearly 40% of the population is driven into the dummy level at high I. Clearly the value of C, a poorly known parameter, is important for a quantitative description of fluorescence saturation. 

Figure 3. Dummy (vibrationally excited)-level population, as a fraction of the total, as a function of assumed transfer Cross section av (insquare angstroms) to v = 0 of X2H for three values of laser intensity...

Thus, at high I, the pair population is a considerably smaller fraction of the total OH population than the initial fraction given by a Boltzmann distribution at the flame temperature. For example, for the nominal values of 14 and 0.4 A for Oq and Oy, the infinite-intensity fraction is < 1% of the total while the zero-intensity value is 4%. This result is generally valid for the entire range of parameters inserted into the model, which represent physically realistic energy transfer rates. However, the precise numerical values depend sensitively on the actual parameters inserted. These facts form the central conclusions of this study (4). A steady state model with no dummy level and a different set of rate constants and level structure (5) shows some similar features. 

Equation (10.27) shows that the polarizability is dependent on the level populations and pfP This dependence is more clearly demonstrated if we note that the summation over all values of m and n in Equation (10.27) allows us to rewrite it as [by interchanging the dummy indices m and n in the second term of Eq. (10.27)]... 

Alternatively, the dummy effect can be taken as the repeatability of the factor effects. Recall that a dummy experiment is one in which the factor is chosen to have no effect on the result (sing the first or second verse of the national anthem as the -1 and +1 levels), and so whatever estimate is made must be due to random effects in an experiment that is free of bias. Each factor effect is the mean of N/2 estimates (here 4), and so a Student s t test can be performed of each estimated factor effect against a null hypothesis of the population mean = 0, with standard deviation the dummy effect. Therefore the t value of the ith effect is ... 

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