Mathematics – Probability
Scientific paper
Feb 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978afz....14..169p&link_type=abstract
Astrofizika, vol. 14, Feb. 1978, p. 169-190. In Russian.
Mathematics
Probability
7
Anisotropic Media, Deep Scattering Layers, Green'S Functions, Incoherent Scattering, Radiative Transfer, Scattering Functions, Absorptivity, Distribution Functions, Frequency Distribution, Invariance, Monochromatic Radiation, Optical Thickness, Probability Theory, Slabs
Scientific paper
A probabilistic treatment is used to study the Green's function of a plane-parallel slab of finite optical depth in the general case of incoherent anisotropic scattering with an arbitrary frequency and angular redistribution law. It is shown that the Green's function can be determined without integrating the equation of radiative transfer. Invariance relations that interrelate the Green's functions of slabs with different optical depths are obtained by applying Ambartsumian's (1943) layer-addition method. Formulas are derived which allow the Green's function to be determined by a simple procedure of 'summing' optical depths or slab thicknesses without having to perform any iterations or solve any equations; only a simple integration over angular variables and frequency is required. As an example, the Green's function of a semiinfinite slab with monochromatic isotropic scattering is determined.
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