The thermalization length by the green function method

We study the concept of the thermalization lenght by the Green function method, using Sobolev's escape and destruction probabilities. A unique analytical procedure yields the usual numerical estimates for the noncoherent scattering case (with complete redistribution in frequency) as well as for the case of coherent scattering. The on-the-spot approximation is used to remove the assumption of an infinite geometry. Rybicki and Hummer's longest flight approximation is shown to yield the on-the-spot approximation. A generalization to the multilevel case is sketched.