Difference between absorption and scattering cross sections

[Madap]

Hi. I'm trying to model the attenuation (extinction) of a weak laser through a gas sample using the Beer-Lambert law. I've found that the attenuation cross section can be written as the sum of both a scattering and absorption cross section, however I'm having difficulty finding a source that lists equations for both of those.

One book I keep seeing referenced, and have been using myself is Loudon's "The Quantum Theory of Light" . He gives a lot of information, but it's confusing me a little bit. In chapter 2 he lists an equation for an attenuation coefficient, and then in chapter 8 he lists the same equation and calls it the Elastic Raleigh scattering cross section. I haven't seen any mention of an absorption cross section anywhere, so I was wondering where that would fit into this model.

 

[muscaria]

Can I ask first if you are comfortable with the idea of a cross section? Do you have a mental schema of any kind for this?
How about the difference between a scattering and absorption process? If not at all that's fine of course, just trying to gauge what you might find obvious and not so obvious. Do you want to understand what you are doing or just use a model to get a satisfactory answer?