18.104.22.168 Temperature-dependence of the bandwidth parameter The bandwidth parameter, Aa, scales as the separation, \J8BkTj he, between the P and R maxima in the band envelope, and so
22.214.171.124 Temperature dependence of the line half-width The Doppler line half-width, bD, and the collisionally induced line half-width, bc, scale with temperature according to where the parameter n for molecular bands takes a mean value close to 0.7, to a good approximation. From the elementary kinetic theory of gases n = 1/2 for a collisionally broadened rotational line. This arises from the fact that bc for a line scales as the frequency of collisions (see §7.3.2) which is proportional to n\/T, where n is the number density given by n = p/kT. Both theoretical work and experimental work indicate that for rotational lines of molecular bands, the parameter n is about 3/4 near the band centre decreasing to 1/2 for lines in the band wings, for atmospheric temperatures (see also the HITRAN database discussed in §4.7 for individual line values for each molecule).
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