Statistical description of radiation fields on the basis of the invariance principle. III. Average time a photon remains in the scattering medium

The approach proposed in the previous papers of this series, based on the invariance principle and the use of generating and characteristic functions, is used to determine the average time a photon remains in a threedimensional semi-infinite medium. Under fairly general assumptions about the elementary scattering event, equations and expressions are obtained that make it possible to calculate this average time as a function of the characteristics of the initial photon. It is shown that the average time spent in the medium by photons which leave it during diffusion can be found by formal differentiation with respect to β of the corresponding equation or expression for the escape probability (or the line profile). A relation is obtained that establishes a connection between the mean number of scatterings and the average time of remaining in the medium, these being calculated for all photons irrespective of whether they are absorbed subsequently in the medium or leave it. The calculations made in the paper can be used to determine any continuously distributed random variable that describes the process of multiple scattering