The pressure broadening of spectral lines based in the Unified Franc-Condon (UCF) treatment, leads to universal line shape function L(z) which is a highly complicated integral of the Airy function and exponentials L(z) = ∫_0^∞ xi^-2 [Ai (-zxi)]^2 exp (-xi^-3) dxi. An approximated analytical expression to this function has been found in terms of elementary functions, which is more precise than any previous one, giving also enough accuracy for most of the applications in molecular and plasma spectroscopy. This approximant has been obtained using the recently developed technique of two-point quasifractional approximation. A unique approximant has been found with better accuracy for both sides of the variable. The method used here is an improvement of previous procedures leaving enough free parameters in order to determine exactly the value of the maximum. On the other hand, since there are two different asymptotic forms for large negative and positive values of z, a new way to impose this additional condition has been found.
Astrophysics and Space Science
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