Theory of the isotropic scattering of radiation in a plane layer: Feasibility of obtaining a complete analytical solution of the problem

Abstract

Analytical investigations of the method of linear nonsingular integral equations, originally proposed by É. Kh. Danielyan [Astrofizika 36,225 (1993)] for the solution of problems in the theory of radiative transport in a medium of finite optical thickness with isotropic scattering, are continued in the present article. It is shown that the solution of problems of the stated class reduce to the determination of only the functions u ^± (η, τ) in the general case with true absorption. Explicit expressions are obtained for these functions at τ=0. The feasibility of a complete analytical solution of the problem is newly formulated as the solution of a Fredholm integral equation on the semiaxis with a kernel that admits representation by a superposition of exponential functions [Eq. (25)]. The choice of an efficient procedure for determining the Ambartsumyan ϕ-function for a semiinfinite medium is discussed. In particular, a new equation is given for this function.