Relation Between Absorption Cross Section and Einstein Coefficients

4 Relation Between Absorption Cross Section and Einstein Coefficients 

At a density A, of molecules in level i) and a negligible population Nk in the upper level of a transition the power absorbed from the incident light wave within the volume element AV is 

The comparison with (2.56a, 2.56b) gives with 7( w) = c p a)) for a plane incident light wave 

The integration limits can be extended from 0 to oo, because the absorption coefficient outside the absorption profile is zero. 

The Einstein coefficient for absorption Bik is proportional to the absorption coefficient a, integrated over the absorption profile. 

---