2.3: Absorption, Scattering and Attenuation Coefficients

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.