# 2.3: Absorption, Scattering and Attenuation Coefficients

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The decrease in radiance $$-dL$$ as a beam of radiance $$L$$ passes through a medium of thickness $$ds$$ as a result of absorption is

$- dL = \alpha L ds$

where $$α$$ is the linear absorption coefficient. With similar equations we can define the linear scattering coefficient $$σ$$ and the linear attenuation (extinction) coefficient $$ε$$. The SI units of $$α$$, $$σ$$ and $$ε$$ are m-1 and $$ε = σ + α$$.

The mass absorption coefficient, mass scattering coefficient and mass extinction coefficient each with units m2 kg-1 are defined respectively as α/ρ, σ/ρ and ε/ρ, where ρ is the density (kg m-3) of the medium. Chandrasekhar uses κ for the mass extinction coefficient, which, in the theory of stellar atmospheres, is also known as the opacity.

The atomic (or molecular) absorption, scattering and extinction coefficients are respectively α/N, σ/N and ε/N, where N is the number density (atoms or molecules per unit volume), with units of m2/atom (or molecule). Because of these units the coefficients are often referred to as cross-sections.

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