High-temperature thermal radiation, cavity

In the special case of a cavity filled in with a high-temperature thermal radiation, the initial distribution over modes reads v (0) = (-)/ , where the constant 0 is proportional to the temperature. Then ... 

The Einstein derivation assumes an idealized situation in which the excitation and de-excitation processes are controlled by the radiation in the cavity. This situation is achieved in reality only inside stars or very high temperature plasmas. In a low pressure discharge there is usually no thermal equilibrium between the atoms and the radiation because the light readily escapes from the source. Consequently we observe a line spectrum rather than a continuum, Collisions play the dominant role in maintaining the equilibrium populations in a low pressure discharge. However, this does not invalidate the arguments used here since the A- and B-coefficients depend only on the internal structure of the atoms and not on their external environment. 

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