where h is Planck's constant, c the speed of light, l and u refer to the lower and upper state, respectively, N is the molecular number density, n\ and nu are the populations of each state, g are statistical weights that take into consideration the electronic, vibrational, rotational and nuclear degrees of freedom of the molecule and Blu is the Einstein coefficient for induced absorption in units cm3/(erg s2). For LTE conditions the population of each state is defined by Boltzmann statistics, which means that the line strength is temperature dependent, eqn (4.65).
3. The line pressure-broadened half-width at half-maximum (HWHM), 7a;r in units cm"1 /atm, which depends on temperature and pressure, eqn (4.5).
The above data allow the calculation of the monochromatic absorption coefficient, ku (cm2 molecule"1), at a specific wave number, w, due to a single transition, wiu, given by
where 4>(w — wiu) is the absorption line profile or line shape function in units of cm. The total contribution to wave number w from all the lines j corresponding to each transition lu with Wj, will then be
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