Green's Functions for One-Velocity Neutron Transport in a One-Dimensional Slab and Sphere

Published in: Proceedings of the National Academy of Sciences, v. 52, no. 3, Sept 1964, p. 683-688

Posted on RAND.org on January 01, 1964

by Anthony Leonard, T. W. Mullikin

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The memorandum presents an exact and efficient method of computing a well-defined resolvent, or Green's function, for one-velocity neutron transport or radiative transfer in a one-dimensional slab or sphere with isotropic scattering. It is shown that the resolvent for the slab may be simply expressed in terms of a 'complex-valued' solution to the transport equation, using the Laplace transform and contour deformation. (The procedure for computing this solution by means of simple quadratures and rapidly convergent Fredholm equations is given.) The result for the sphere resolvent, which is closely related to that for the slab, is also presented, with particular attention to the flux resulting from a point source in the center of a sphere. (Author)

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