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What is the absorption cross section, how is it measured?

How to convert it to the absorption coefficient (measured in cm$^{-1}$)?

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The cross section $\sigma$ is related to the absorption coefficient $\alpha$ by:

$$ \sigma = \frac{\alpha}{N} $$

where $N$ is the number density of the scattering medium i.e. the number of particles per unit volume. This is described in more detail in the Wikipedia article on the absorption cross section.

If you want $\alpha$ in units of cm$^{-1}$ you need to express $\sigma$ in cm$^2$ and the density as the number of particles per cubic cm.

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Do you mean that the number of particles is the number of molecules or it is the number of atoms? For example, what is the cross section for CO$_2$? –  jokersobak Jul 15 at 4:32
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@jokersobak: if you use the number density of molecules of CO$_2$ you get the scattering cross section for a CO$_2$ molecule. If you use the number density of atoms you get the cross section for an atom. So it depends on what cross section you want to calculate. –  John Rennie Jul 15 at 5:01
    
What cross section values are specified in HITRAN and HITEMP databases? –  jokersobak Jul 15 at 6:13
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I don't have access to HITRAN, but if you look on HITEMP you'll see data on molecules like CO$_2$, CO, NO, OH, etc. You need to use the number density of these molecules e.g. the number of CO$_2$ molecules per unit volume. Note that while the answer I've given is generally true it wouldn't hurt to check the FAQs on the database just to make sure they don't use some other convention. –  John Rennie Jul 15 at 6:40

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