Kramers' opacity law
Kramers' opacity law describes the opacity of a medium in terms of the ambient density and temperature, assuming that the opacity is dominated by bound-free absorption or free-free absorption. It is often used to model radiative transfer, particularly in stellar atmospheres. The relation is named after the Dutch physicist Hendrik Kramers, who first derived the form in 1923.
The general functional form of the opacity law is where
Often the overall opacity is inferred from observations, and this form of the relation describes how changes in the density or temperature will affect the opacity.
Calculation
The specific forms for bound-free and free-free absorption are:- Bound-free
- Free-free
Here, and are the Gaunt factors of circa 1 associated with bound-free and free-free transitions respectively. The is an additional correction factor, typically having a value between 1 and 100. The opacity depends on the number density of electrons and ions in the medium, described by the fractional abundance :
With only helium present is proportional to mass density and valid also for in lithium etc. medium.