2.3: Absorption, Scattering and Attenuation Coefficients

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Max Fairbairn & Jeremy Tatum
University of Victoria

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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.