A method of cauchy integral equation for non-coherent transfer in half-space |
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Authors: | H Frisch U Frisch |
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Institution: | Centre National de la Recherche Scientifique, Observatoire de Nice, B.P. 252, 06007 Nice-Cedex, France |
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Abstract: | A technique is presented which allows easy construction of solutions for various half-space problems arising in non-coherent radiative transfer with complete redistribution. By use of an inverse Laplace transform method, Wiener-Hopf integral equations are reduced to Cauchy-type singular integral equations. The factorization technique used by Case and Zweifel for coherent scattering can then be carried over to non-coherent transfer. The method is applied to the inhomogeneous integral equation for the source function of a two-level atom, previously solved by Ivanov. It is also applied to the conservative, homogeneous case and to singular Wiener-Hopf equations arising from asymptotic expansions in the limit of vanishing probability of collisional destruction ?. Consequences for the scaling laws in a finite slab are examined in a companion paper. |
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