- 1.37 -


where

        N (T,p) = number of particles/cc in state a
        a

        aab(V) = microscopic cross section for transition from state a to state b

             hv = photon energy

        After radiation has been absorbed and reemitted many times, the intensity of the radiation as a function of frequency becomes characteristic of the temperature rather than the emitting species. This thermal or blackbody radiation is applicable in the case of opaque materials in which the radiative energy absorption is so intense that the radiation is in local thermodynamic equilibrium with the radiating material. When the temperature, density, and composition of the material vary slightly per photon mean free path for many mean free paths in any direction, the medium is said to be optically thick and the absorption coefficient is given by the Rosseland mean value of K  (63), which is defined as

                     f: dB (T)
                       0dT     d
               KR =                                 (8.2)
                R      1 dB (T)
                       K   dT    d
                     0

where B (T) is the frequency dependent black-body radiation intensity given by the Planck formula