Fractional thermal population

At OK, only the lowest energy level is populated. An increase in temperature will additionally populate levels at higher energy. The fractional thermal population XpXT) of the initial level A (= level from which the absorption or luminescence process starts) at temperature T can be calculated by using the formula for the Bolt2mann distribution ... 

The vibrational frequency of the CS molecule is 1285.08 cm-1, or (multiplying by the speed of light) v=3.8526 x 1013 s 1. At 300 K, the factor in the exponent of Eq. 8.71 is x = 6.1632. Thus the partition function room temperature the fraction of vibrationally excited CS molecules is very small. However, at T — 5000 K, x = 0.3698, and <7vib=3.235. Thus, at very high temperatures, the thermal population of vibrationally excited molecules becomes significant. 

While the intensity of anti-Stokes radiation is very small in spontaneous Raman scattering due to the low thermal population density in excited molecular levels (Sect. 3.1), this is not necessarily true in stimulated Raman scattering. Because of the strong incident pump wave, a large fraction of all interacting molecules is excited... 

The intrinsic case applies at small doping levels or at high temperatures where the thermal equilibrium site fraction of the intrinsic cation vacancy population exceeds that due to the aliovalent solute atoms. In this case, the effect of the added solute atoms is negligible. The activation energy for cation self-diffusion is therefore the same as in the pure material and is given by Eq. 8.44. 

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. 

Here pt and pj denote the fractional populations of states i and j (p( = exp —Ei/kT /q in thermal equilibrium, where q is the partition function) pm and pn denote the corresponding fractional populations of the energy levels, and dm and dn the degeneracies (pf = pm/dm, etc.). The absorption intensity Gji9 and the Einstein coefficients and Bji9 are fundamental measures of the line strength between the individual states i and j they are related to each other by the general equations... 

The selection of the best analytical line has not been discussed explicitly and deserves attention. Because LEI is at least a two-step process involving laser excitation and thermal ionization steps, many transitions may be preferred for LEI which are not usable by purely optical methods. In other words, excited states which have low fractional populations may produce good LEI sensitivity due to proximity of the laser-populated state to the ionization potential. This makes the choice of the most sensitive LEI lines more complicated but it introduces an important practical advantage for dye laser spectrometry. 

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