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The isotropic scattering of radiation from an asymmetric spherical source in a finite atmosphere

Published online by Cambridge University Press:  24 October 2008

M. G. Smith
M. G. Smith
Affiliation:
Department of Mathematics, Sir John Cass College, Central House, Whitechapel High Street, London, E. 1
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Abstract

A singular integral equation is derived for the three-dimensional Fourier transform of the source function, when the scattering atmosphere is contained in a finite convex volume.

This equation is shown to reduce to the usual equation in the case of an isotropic point source in a finite spherical atmosphere of radius R0, and is used to solve the same problem when the source is anisotropic.

It is shown that in the latter case an expansion in Legendre polynomials results, in which the coefficients are obtained from the integral equations of a similar construction to those for an isotropic source. The error in taking the dominant part is now however of order 1/R0 and not e–R0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 213 - 224
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Smith, M. G.The isotropic scattering of radiation from a point source in a finite spherical atmosphere. Proc. Cambridge Philos. Soc. 61 (1965), 923–937.CrossRefGoogle Scholar
(2)Cassell, J. S.Note on the isotropic scattering of radiation from a point source in a finite spherical atmosphere. Proc. Cambridge Philos. Soc. 64 (1968), 711–719.CrossRefGoogle Scholar
(3)Smith, M. G. and Hunt, G. E.The isotropic scattering of radiation in a finite homogeneous two-dimensional atmosphere. Proc. Cambridge Philos. Soc. 63 (1967), 209–220.CrossRefGoogle Scholar
(4)Watson, G. N.Theory of Bessel functions (Cambridge, 1966).Google Scholar
(5)Muskhelishvili, N. I.Singular integral equations (Noordhoff; Gröningen, 1953).Google Scholar